Keywords: Predictive control for nonlinear systems, Robust adaptive control, Autonomous systems
Abstract: In an era where Artificial Intelligence (AI) is often seen as a universal solution for any complex problem, this presentation offers a critical examination of its role in the field of automatic control. To be concrete, I will focus on Optimal Control techniques, navigating through its history and addressing the evolution from its traditional model-based roots to the emerging data-driven methodologies empowered by AI.

The presentation will delve into how the theoretical underpinnings of Optimal Control have been historically aligned with computational capabilities, and how this alignment has shifted over the years. This juxtaposition of theory and computation motivates a deeper investigation into the diminishing relevance of certain traditional control methods amidst the AI revolution. We will critically examine scenarios where AI-driven approaches could outperform classical methods, as well as cases where the hype surrounding AI overshadows its actual utility.

The talk will conclude with a nuanced view of state-of-the-art optimal control methods in practical applications including self-driving cars, advanced robotics and energy efficient systems. From this perspective, we will identify and explore future potential directions for the field, including the design of learning control architectures which seamlessly integrate predictive capabilities at every level, focusing on systems that can autonomously refine their performance over time through continuous learning and interaction with their environment.

Keywords: Control applications, Building and facility automation, Optimization
Abstract: The ubiquity and energy needs of industrial refrigeration has prompted several research studies investigating various control opportunities for reducing energy demand. This study focuses on one such opportunity termed compressor sequencing, which involves selecting the optimal operational state of compressors to fulfill the required refrigeration load efficiently. We first investigate the static compressor sequencing problem and highlight its computational complexity and load-dependent variability. To address these issues, we propose integrating load shifting with compressor sequencing, in which the facility is strategically pre-cooled to enhance compressor efficiency. Our results, based on real-world sensor data from an industrial refrigeration site of Butterball LLC located in Huntsville, AR, demonstrate that without load shifting, even optimal compressor operation often results in inefficiencies due to compressors running at intermediate capacity levels. By implementing load shifting, we observe potential energy savings of up to 20% compared to optimal sequencing without load shifting.

Keywords: Distributed control, Optimization algorithms, Agents-based systems
Abstract: In this paper, we investigate distributed convex strongly concave minimax problem without the requirement of strong convexity. The distributed minimax problem is transformed into a distributed optimization with inner maximum operation and solved by a class of primal-dual gradient algorithms. By using the metric regularity, a criterion for exponential convergence is given. Moreover, we explain why the criterion corresponds to a weaker assumption than strict or strong convexity. Two numerical simulation examples demonstrate the effectiveness of the algorithm.

Keywords: Formal verification/synthesis, Distributed control, Agents-based systems
Abstract: We propose a method to decompose signal temporal logic tasks for multi-agent systems under communication constraints. Specifically, given a task graph representing task dependencies among couples of agents in the system, we propose to decompose tasks assigned to couples of agents not connected in the communication graph by a set of sub-tasks assigned to couples of communicating agents over the communication graph. To this end, we parameterize the predicates' level set of tasks to be decomposed as hyper-rectangles with parametric centres and dimensions. Convex optimization is then leveraged to find optimal parameters maximising the volume of the predicate's level sets. Moreover, a formal treatment of conflicting conjunctions of formulas in the considered STL fragment is introduced, including sufficient conditions to avoid the insurgence of such conflicts in the final decomposition.

Keywords: Learning, Automotive control, Optimization
Abstract: Drift-driving technique offers valuable insights to support safe autonomous driving in extreme conditions. Model predictive control (MPC) has become the dominant choice for drift vehicle control with a superior ability to handle the changing system dynamics and constraints. Existing control strategies necessitate a precise system model to calculate the reference drift equilibriums, which can be more intractable due to the highly nonlinear dynamics and sensitive vehicle parameters. Furthermore, MPC performance strictly contingents on appropriate controller parameters, presenting an additional hurdle for drift vehicles. To solve these problems, Bayesian optimization (BO) is first applied to compensate for modeling errors and optimize controller design for drift vehicles. A learning-based hierarchical model predictive control (LHMPC) strategy is proposed in this paper, where an upper-level BO supervisor provides learned drift equilibriums and controller parameters for a lower-level MPC. This hierarchical system architecture also effectively resolves the inherent conflict between path tracking and drifting. The LHMPC strategy is verified on the Matlab-Carsim platform, and simulation results demonstrate its effectiveness in guiding the vehicle following the reference trajectory while maintaining the drift states.

Keywords: Lyapunov methods, Optimization, Adaptive control
Abstract: Safety Index Synthesis (SIS) is critical for deriving safe control laws. Recent works propose to synthesize a safety index (SI) via nonlinear programming and derive a safe control law such that the system 1) achieves forward invariant (FI) with some safe set and 2) guarantees finite time convergence (FTC) to that safe set. However, real-world system dynamics can vary during run-time, making the control law infeasible and invalidating the initial SI. Since the full SIS nonlinear programming is computationally expensive, it is infeasible to re-synthesize the SI each time the dynamics are perturbed. To address that, this paper proposes an efficient approach to adapting the SI to varying system dynamics and maintaining the feasibility of the safe control law. The proposed method leverages determinant gradient ascend and derives a closed-form update to safety index parameters, enabling real-time adaptation performance. A numerical study validates the effectiveness of our approach.

Keywords: Optimization algorithms
Abstract: We study the scenario approach for solving chance-constrained programs in dynamic environments. Scenario generation methods approximate the true feasible region from scenarios generated independently and identically from the actual distribution. In this paper, we consider this problem in a dynamic environment, where the scenarios are assumed to be drawn in a sequential fashion from an unknown and time-varying distribution. Such dynamic environments are driven by changing environmental conditions present in many real-world applications. We couple the time-varying distributions using the Wasserstein metric between the sequence of scenario-generating distributions and the actual chance-constrained distribution. Our main results are bounds on the number of samples essential for ensuring the ex-post risk in chance-constrained optimization problems when the underlying feasible set is convex or non-convex. Finally, our results are illustrated on multiple numerical experiments for both types of feasible sets.

Keywords: Optimization algorithms, Optimization
Abstract: The Resource Constrained Shortest Path Problem (RCSPP) requires a minimum-cost simple path between two nodes that is subject to a resource consumption constraint. In this paper, we consider the Backtracking A* algorithm presented in previous works applied to the general RCSPP. Backtracking A* attempts to solve the RCSPP by iterative modification of paths generated by a shortest path algorithm such as A*. We consider the completeness of Backtracking A* and demonstrate that it cannot be a complete algorithm. Then we propose a complete, modified version of Backtracking A*. Finally, we give a result for the time complexity of Backtracking A*, and demonstrate it under worst-case conditions applied to randomly generated graphs.

Keywords: Stochastic systems, Power systems, Optimization
Abstract: The integration of renewable energy sources (RES) into power distribution grids poses challenges to system reliability due to the inherent uncertainty in their power production. To address this issue, battery energy sources (BESs) are being increasingly used as a promising solution to counter the uncertainty associated with RES power production. During the overall system planning stage, the optimal capacity of the BES has to be decided. In the operational phase, policies on when to charge the BESs and when to use them to support loads must be determined so that the BES remains within its operating range, avoiding depletion of charge on one hand and remaining within acceptable margins of maximum charge on the other. In this paper, a stochastic control framework is used to determine battery capacity, for microgrids, which ensures that during the operational phase, BESs' operating range is respected with pre-specified high probability. We provide an explicit analytical expression of the required BESs energy capacity for a single microgrid with RES as the main power source. Leveraging insights from the single microgrid case, the article focuses on the design and planning of BESs for the two-microgrid scenario. In this setting, microgrids are allowed to share power while respecting the capacity constraints imposed by the power lines. We characterize the optimal power transfer policy between the microgrids and the optimal BES capacity for multiple microgrids. This provides the BES savings arising from connecting the microgrids.

Keywords: Learning, Game theory, Markov processes
Abstract: We present a learning algorithm for players to converge to their stationary policies in a general sum stochastic sequential Stackelberg game. The algorithm is a two time scale implicit policy gradient algorithm that provably converges to stationary points of the optimization problems of the two players. Our analysis allows us to move beyond the assumptions of zero-sum or static Stackelberg games made in the existing literature for learning algorithms to converge.

Keywords: Learning, Uncertain systems, Randomized algorithms
Abstract: We study the incentivized exploration for the multi-armed bandit (MAB) problem with non-stationary reward distributions, where the players receive compensation for exploring arms other than the greedy choice and may provide a biased feedback on reward. We consider two different non-stationary environments: abruptly-changing and continuously-changing, and propose respective incentivized exploration algorithms. We show that the proposed algorithms achieve sublinear regret and compensation in time, and are therefore effective in incentivizing exploration, despite the nonstationarity and the biased/drifted feedback.

Keywords: Learning, Optimization, Optimization algorithms
Abstract: Deterministic bias and stochastic unbiased noise in gradients can affect the performance of online learning algorithms. While existing studies provide bounds for dynamic regret under these uncertainties, they offer limited insight into the specific functionality of the algorithms. This paper investigates the efficacy of online gradient-based algorithms (OGD) with inexact gradients, quantifying the degree of tolerance to these uncertainties and identifying conditions for ensuring robustness. Our analysis reveals that bias and variance function independently, and the tolerance of online gradient-based algorithms to inexactness depends on factors such as decision dimension, gradient norm, function variations, alignment of gradients, and function curvature. We verify our results numerically and experimentally, bridging a significant knowledge gap. As a case study, we introduce a general online optimization algorithm to explore the interplay between bias and variance with dynamic regret.

Keywords: Learning, Stochastic optimal control, Markov processes
Abstract: Accurate risk quantification and reachability analysis are crucial for safe control and learning, but sampling from rare events, risky states, or long-term trajectories can be prohibitively costly. Motivated by this, we study how to estimate the long-term safety probability of maximally safe actions without sufficient coverage of samples from risky states and long-term trajectories. The use of maximal safety probability in control and learning is expected to avoid conservative behaviors due to over-approximation of risk. Here, we first show that long-term safety probability, which is multiplicative in time, can be converted into additive costs and be solved using standard reinforcement learning methods. We then derive this probability as solutions of partial differential equations (PDEs) and propose Physics-Informed Reinforcement Learning (PIRL) algorithm. The proposed method can learn using sparse rewards because the physics constraints help propagate risk information through neighbors. This suggests that, for the purpose of extracting more information for efficient learning, physics constraints can serve as an alternative to reward shaping. The proposed method can also estimate long-term risk using short-term samples and deduce the risk of unsampled states. This feature is in stark contrast with the unconstrained deep RL that demands sufficient data coverage. These merits of the proposed method are demonstrated in numerical simulation.

Keywords: Linear systems, Learning, Robust control
Abstract: The problem of learning-to-control relaxation systems from data is considered. It is shown that the equilibrium of the relaxation system’s step response defines the solution of a class of robust control problems and provides a good suboptimal solution to a class of linear quadratic regulator problems. These results demonstrate the potential to efficiently learn policies for these control problems from a single, easy-to-implement trajectory data point, being the step response. More broadly, these results highlight how the system structure and problem definition of the control problem can be exploited to generate data efficient learning-to-control methods.

Keywords: Formal verification/synthesis, Computational methods, Autonomous systems
Abstract: This paper focuses on addressing the problem of computing controlled reach-avoid sets for continuous-time systems modeled by polynomial ordinary differential equations with control inputs in order to ensure the safety and reachability of safety-critical systems. In a controlled reach-avoid set (CRAS), there exists a feedback controller capable of driving the closed-loop system into a target set of desired states while avoiding hazardous regions. The computation of a controlled reach-avoid set can be transformed into a search for a guidance-barrier function in existing literature. However, existing guidance-barrier functions tend to produce conservative CRASs due to certain flaws. To overcome this issue, a new guidance-barrier function is introduced, which generates less conservative CRASs compared to existing ones. Given the inherent nonlinearity associated with searching for guidance-barrier functions in the control setting, an iterative computational approach is proposed. This approach modifies controllers from previous iterations to find these functions and expand CRASs by solving convex optimizations. Finally, numerical results demonstrate the efficiency of our method in generating less conservative CRASs.

Keywords: Human-in-the-loop control, Emerging control applications, Learning
Abstract: We address the personalization of control systems, which is an attempt to adjust inherent safety and other essential control performance based on each user's personal preferences. A typical approach to personalization requires a substantial amount of user feedback and data collection, which may result in a burden on users. Moreover, it might be challenging to collect data in real-time. To overcome this drawback, we propose a natural language-based personalization, which places a comparatively lighter burden on users and enables the personalization system to collect data in real-time. In particular, we consider model predictive control (MPC) and introduce an approach that updates the control specification using chat within the MPC framework, namely ChatMPC. In the numerical experiment, we simulated an autonomous robot equipped with ChatMPC. The result shows that the specification in robot control is updated by providing natural language-based chats, which generate different behaviors.

Keywords: Neural networks, Formal verification/synthesis, Model/Controller reduction
Abstract: In this paper, we propose a method of repairing compressed Feedforward Neural Networks (FNNs) based on equivalence evaluation of two neural networks. In the repairing framework, a novel neural network equivalence evaluation method is developed to compute the output discrepancy between two neural networks. The output discrepancy can quantitatively characterize the output difference produced by compression procedures. Based on the computed output discrepancy, the repairing method first initializes a new training set for the compressed networks to narrow down the discrepancy between the two neural networks and improve the performance of the compressed network. Then, we repair the compressed FNN by re-training based on the training set. We apply our developed method to the MNIST dataset to demonstrate the effectiveness and advantages of our proposed repair method.

Keywords: Neural networks, Learning, Formal verification/synthesis
Abstract: Barrier functions are a general framework for establishing a safety guarantee for a system. However, there is no general method for finding these functions. To address this shortcoming, recent approaches use self-supervised learning techniques to learn these functions using training data that are periodically generated by a verification procedure, leading to a verification-aided learning framework. Despite its immense potential in automating barrier function synthesis, the verification-aided learning framework does not have termination guarantees and may suffer from a low success rate of finding a valid barrier function in practice. In this paper, we propose a holistic approach to address these drawbacks. With a convex formulation of the barrier function synthesis, we propose to first learn an empirically well-behaved neural network basis function and then apply a fine-tuning algorithm that exploits the convexity and counterexamples from the verification failure to find a valid barrier function with finite-step termination guarantees: if there exist valid barrier functions, the fine-tuning algorithm is guaranteed to find one in a finite number of iterations. We demonstrate that our fine-tuning method can significantly boost the performance of the verification-aided learning framework on examples of different scales and using various neural network verifiers.

Keywords: Learning, Autonomous robots, Mechanical systems/robotics
Abstract: In a typical space debris mitigation mission, a space manipulator must plan maneuvers free of self-collision and collision with the noncooperative target satellite to perform a safe capture. We develop an effective model-free planner based on deep reinforcement learning for free-floating manipulators that only relies on an uncertain target position feedback. At its core, the learning agent employs the Deep Deterministic Policy Gradient (DDPG) algorithm capable of working with continuous states and actions. To improve the learning performance, we propose a five-step sequential learning that uses priority episode sampling to effectively transfer knowledge from a fixed-based manipulator trained to follow a moving target to an uncertain space manipulator capturing a target point on a satellite. Further, to avoid moving obstacles, we introduce the notion of multi-critic in the DDPG setting, such that one critic optimizes the task of chasing in an uncertain environment and another one focuses on obstacle avoidance. To show the efficacy of the developed trajectory planner, we compare its running average success rate and reward value with a baseline DDPG.

Keywords: Optimal control, Neural networks, Power systems
Abstract: In the context of charging electric vehicles (EVs), the price-based demand response (PBDR) is becoming increasingly significant for charging load management. Such response usually encourages cost-sensitive customers to adjust their energy demand in response to changes in price for financial incentives. Thus, to model and optimize EV charging, it is important for charging station operator to model the PBDR patterns of EV customers by precisely predicting charging demands given price signals. Then the operator refers to these demands to optimize charging station power allocation policy. The standard pipeline involves offline fitting of a PBDR function based on historical EV charging records, followed by applying estimated EV demands in formulation of downstream charging station operation optimization. However, the criterion used for evaluating demand prediction often differs from the ultimate criteria on which we evaluate the performance of EV charging optimization. And considering the relatively small scale of historical price-demand dataset, the model trained offline may not reliably predict outcomes for the incoming charging scheduling tasks. To tackle these problems as a whole, we propose a new decision-focused end-to-end framework for PBDR modeling that combines prediction errors and downstream optimization cost errors in the model learning stage. We evaluate the effectiveness of our method on a simulation of charging station operation with synthetic PBDR patterns of EV customers, and experimental results demonstrate that this framework can provide a more reliable prediction model for the ultimate optimization process, leading to more effective optimization solutions in terms of cost savings and charging station operation objectives with only a few training samples.

Keywords: Optimal control, Adaptive control, Machine learning
Abstract: This research proposes an innovative optimal trajectory tracking scheme for uncertain linear discrete-time (DT) systems, leveraging trajectory-dependent Q-learning. Unlike conventional optimal tracking control approaches, the proposed method eliminates the need for a desired trajectory generator function, typically modeled as the dynamics of an autonomous system. Instead, we tackle the tracking problem by learning a Q-function that depends on a horizon of reference trajectory points in the future, which enables the computation of optimal feedback gains and time-varying feedforward control inputs without prior knowledge of system parameters or access to the complete reference trajectory. To enhance the effectiveness of the controller in multitask scenarios, we use the Efficient Lifelong Learning Algorithm (ELLA) to generate a shared knowledge base and use online adaptive control methods to directly learn parameters for each task, enabling information transfer between tasks. Simulation results using a power system demonstrate the efficacy of our approach.

Keywords: Optimal control, Optimization algorithms, Intelligent systems
Abstract: This article considers a multiplayer target defense differential game (TDDG) between attacker team and defender team. The attackers aim at reaching the targets while the defenders aim at intercepting their opponents. In the 1 defender vs 1 attacker scenario, a geometric approach is proposed to explicitly obtain the optimal feedback controls of the players and the Value function of the differential game. For a multiplayer game, we propose a bipartite graph matching algorithm, utilizing the Value function, to obtain the optimal assignment. The proposed algorithm performs well in reducing the computational costs. Furthermore, we conduct several simulations to validate the optimality of the proposed method.

Keywords: Optimal control, Hybrid systems, Energy systems
Abstract: Proton exchange membrane (PEM) fuel cell electric vehicles (FCEVs) have gained attention owing to their significant advantages, including rapid refueling times, exceptional energy efficiency, and zero emissions. Nonetheless, FCEVs have a durability issue, a substantial obstacle to the widespread adoption of applications. This study proposes a novel predictive energy management strategy (P-EMS) with segmented roads that strikes a delicate balance between optimizing fuel consumption and safeguarding the durability of the stacks. Dynamic load and high-power operations are deemed avoidable operating conditions, and a control strategy is designed to avoid these factors. Subsequently, the optimal control problem is reformulated within road segments, transforming it into a quadratic programming (QP) framework. This allows for the utilization of model predictive control (MPC) to efficiently solve the optimal control problems. The reformulated problem needs the predictable driving parameters of each road segment, including travel time and average power demand. The simulation results show that the proposed method successfully avoids excessive stack degradation, even at the expense of some reduction in fuel consumption. Compared to dynamic programming (DP), which only considers fuel consumption, the proposed method shows superior performance in safeguarding stack degradation, showing 29% performance improvement, with only an 11% mileage decrease.

Keywords: Optimal control, Estimation, Iterative learning control
Abstract: This paper considers the problem of localizing a set of nodes in a wireless sensor network when both their positions and the parameters of the communication model are unknown. We assume that a single agent moves through the environment, taking measurements of the Received Signal Strength (RSS), and seek a controller that optimizes a performance metric based on the Fisher Information Matrix (FIM). We develop a receding horizon (RH) approach that alternates between estimating the parameter values (using a maximum likelihood estimator) and determining where to move so as to maximally inform the estimation problem. The receding horizon controller solves a multi-stage look ahead problem to determine the next control to be applied, executes the move, collects the next measurement, and then re-estimates the parameters before repeating the sequence. We consider both a Dynamic Programming (DP) approach to solving the optimal control problem at each step, and a simplified heuristic based on a pruning algorithm that significantly reduces the computational complexity. We also consider a modified cost function that seeks to balance the information acquired about each of the parameters to ensure the controller does not focus on a single value in its optimization. These approaches are compared against two baselines, one based on a purely random trajectory and one on a greedy control solution. The simulations indicate our RH schemes outperform the baselines, while the pruning algorithm produces significant reductions in computation time with little effect on overall performance.

Keywords: Distributed control, Adaptive control, Optimal control
Abstract: This paper proposes a novel reinforcement learning approach to solve the optimal output synchronization problem for discrete-time heterogeneous multi-agent systems. Different from existing learning methods, the optimal control protocol is obtained to guarantee zero synchronization error by solving the augmented algebraic Riccati equations (AREs). The proposed adaptive dynamic programming (ADP) method can stabilize the output synchronization error and solve the output regulator equations implicitly. To eliminate the dependency on information of system dynamics, an online Q-function-based policy iteration (PI) algorithm is developed. Finally, a numerical example is provided to demonstrate the advantages of the proposed ADP over traditional ADP in terms of synchronization performance.

Keywords: Optimal control, Mechanical systems/robotics, Numerical algorithms
Abstract: In this article, the optimal control problem for a harmonic oscillator with an inequality constraint is considered. The applied energy of the oscillator during a fixed final time period is used as the performance criterion. The analytical solution with both small and large terminal time is found for a special case when the undriven oscillator system is initially at rest. For other initial states of the Harmonic oscillator, the optimal solution is found to have three modes: wait-move, move-wait, and move-wait-move given a longer terminal time.

Keywords: Optimal control, Constrained control, Predictive control for nonlinear systems
Abstract: This paper introduces a new framework for analyzing the stability of discrete-time model predictive controllers acting on continuous-time systems. The proposed framework introduces the distinction between discretization time (used to generate the optimal control problem) and sampling time (used to implement the controller). The paper not only shows that these two time constants are independent, but also motivates the benefits of selecting a sampling time that is smaller than the discretization time. The resulting approach, hereafter referred to as Hypersampled Model Predictive Control, overcomes the traditional trade-off between performance and computational complexity that arises when selecting the sampling time of traditional discrete-time model predictive controllers.

Keywords: Optimal control, Linear systems, Large-scale systems
Abstract: We propose a sparse static output-feedback controller for a class of large-scale systems. Our approach starts with an initial stabilizing controller with a decentralized/distributed structure and then searches for nearby structured controllers limited by a budget of a predefined number of controller parameters. Our methodology relies on a predictor-corrector approach where a greedy gradient with respect to controller parameters is a predictor oracle and an existing non-smooth optimization algorithm specialized for sparse structures is applied to correct the predicted values in the previous step. We show the effectiveness of our algorithm in terms of performance and speed on a benchmark example.

Keywords: Stability of nonlinear systems, Optimal control, Lyapunov methods
Abstract: In this paper, we introduce the notion of safe predefined-time stability and address an optimal safe predefined-time stabilization problem. In particular, safe predefined-time stability characterizes parameter-dependent nonlinear dynamical systems whose trajectories starting in a given set of admissible states remain in the set of admissible states for all time and converge to an equilibrium point in a predefined time. Furthermore, we provide a Lyapunov theorem establishing sufficient conditions for safe predefined-time stability. We address the optimal safe predefined-time stabilization problem by synthesizing feedback controllers that guarantee closed-loop system safe predefined-time stability while optimizing a given performance measure. Specifically, safe predefined-time stability of the closed-loop system is guaranteed via a Lyapunov function satisfying a differential inequality while simultaneously serving as a solution to the steady-state Hamilton-Jacobi-Bellman equation ensuring optimality. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.

Keywords: H-infinity control, Robust control, Large-scale systems
Abstract: In this paper, we unify two already published results on state feedback H-infinity optimality. Previously, optimality has been shown for a particular controller structure in the case that the open-loop state matrix is symmetric, as well as in the case that the closed-loop system is internally positive. By contrast, the main result of the present paper gives optimality based on neither of these two properties. As a result, when applied to a class of buffer networks, it succeeds not only in showing optimality when the system parameters are chosen so as to give open-loop symmetry and closed-loop positivity, respectively, but also when both of these properties are absent.

Keywords: Optimal control, Constrained control, Autonomous systems
Abstract: This paper presents a new approach for guaranteed safety subject to input constraints (e.g., actuator limits) using a composition of multiple control barrier functions (CBFs). First, we present a method for constructing a single CBF from multiple CBFs, which can have different relative degrees. This construction relies on a soft minimum function and yields a CBF whose 0-superlevel set is a subset of the union of the 0-superlevel sets of all the CBFs used in the construction. Next, we extend the approach to systems with input constraints. Specifically, we introduce control dynamics that allow us to express the input constraints as CBFs in the closed-loop state (i.e., the state of the system and the controller). The CBFs constructed from input constraints do not have the same relative degree as the safety constraints. Thus, the composite soft-minimum CBF construction is used to combine the input-constraint CBFs with the safety-constraint CBFs. Finally, we present a feasible real-time-optimization control that guarantees that the state remains in the 0-superlevel set of the composite soft-minimum CBF. We demonstrate these approaches on a nonholonomic ground robot example.

Keywords: Optimal control, Constrained control, Autonomous robots
Abstract: This paper presents a time-varying soft-maximum composite control barrier function (CBF) that can be used to ensure safety in an a priori unknown environment, where local perception information regarding the safe set is periodically obtained. We consider the scenario where the periodically obtained perception feedback can be used to construct a local CBF that models a local subset of the unknown safe set. Then, we use a novel smooth time-varying soft-maximum function to compose the N most recently obtained local CBFs into a single CBF. This composite CBF models an approximate union of the N most recently obtained local subsets of the safe set. Notably, this composite CBF can have arbitrary relative degree r. Next, this composite CBF is used as a rth-order CBF constraint in a real-time optimization to determine a control that minimizes a quadratic cost while guaranteeing that the state stays in a time-varying subset of the unknown safe set. We also present an application of the time-varying soft-maximum composite CBF method to a nonholonomic ground robot with nonnegligible inertia. In this application, we present a simple approach to generate the local CBFs from the periodically obtained perception data.

Keywords: Optimal control, Game theory, Optimization
Abstract: We employ a game-theoretic approach to mitigate stealthy spoofing attacks on an aerial cyber-physical system. The attacker's objective is to drive the vehicle away from its nominal trajectory while misleading the system operator of the adversarial deviation. We characterize this as a dual actuation-deception attack; the former involves corrupting the vehicle's actuating input, and the latter is done by spoofing the measurable output; that is, the acceleration effort and the Global Navigation Satellite System (GNSS) sensor reading, respectively. The attack is designed to be stealthy, implying that its effect on the system's trajectory is indiscernible from that of a naturally occurring disturbance. The defender aims to counter such an attack and steer the aerial vehicle back towards its nominal path. We couple receding horizon control and game-theoretic methods to derive optimal attack and defense policies.

Keywords: Optimal control, Lyapunov methods, Linear systems
Abstract: Policy optimization has gained renewed attention from the control community, serving as a pivotal link between control theory and reinforcement learning. In the past few years, the global convergence theory of direct policy search on state-feedback linear control benchmarks has been developed. However, it remains difficult to establish the global convergence of policy optimization on the linear quadratic Gaussian (LQG) problem, marked by the presence of suboptimal stationary points and the lack of cost coerciveness. In this paper, we revisit the policy optimization intricacies of LQG via a case study on first-order single-input single-output (SISO) systems. For this case study, while the issue related to suboptimal stationary points can be easily fixed via parameterizing the policy class more carefully, the non-coerciveness of the LQG cost function still poses a substantial obstacle to a straightforward global convergence proof for the policy gradient method. Our contribution, within the scope of this case study, introduces an approach to construct a positive invariant set for the policy gradient flow, addressing the non-coerciveness issue in the global convergence proof. Based on our analysis, the policy gradient flow can be guaranteed to converge to the globally optimal full-order dynamic controller in this particular scenario. In summary, although centered on a specific case study, our work broadens the comprehension of how the absence of coerciveness impacts LQG policy optimization, highlighting inherent complexities.

Keywords: Linear systems, Optimal control, Optimization algorithms
Abstract: Though policy optimization (PO) has been acknowledged as an essential approach in reinforcement learning, its theoretical understandings still lag behind as we usually have to address non-convex problems. In this work, we study the convergence of the PO method for the linear quadratic regulator problem under asynchronous block parallel policy updates. Particularly, there are a group of agents to jointly compute the policy and each agent is only responsible for the updates of a block of the policy via asynchronously communicating with a central coordinator. Then, we rigorously prove its linear convergence to the optimal policy. Numerical results validate the performance of our method.

Keywords: Control applications, Optimal control, Robotics
Abstract: Unmanned aerial vehicles (UAVs), specifically quadrotors, have revolutionized various industries with their maneuverability and versatility, but their safe operation in dynamic environments heavily relies on effective collision avoidance techniques. This paper introduces a novel technique for safely navigating a quadrotor along a desired route while avoiding kinematic obstacles. We propose a new constraint formulation that employs control barrier functions (CBFs) and collision cones to ensure that the relative velocity between the quadrotor and the obstacle always avoids a cone of vectors that may lead to a collision. By showing that the proposed constraint is a valid CBF for quadrotors, we are able to leverage its real-time implementation via Quadratic Programs (QPs), called the CBF-QPs. Validation includes PyBullet simulations and hardware experiments on Crazyflie 2.1, demonstrating effectiveness in static and moving obstacle scenarios. Comparative analysis with literature, especially higher order CBF-QPs, highlights the proposed approach's less conservative nature.

Keywords: Power systems, Optimal control
Abstract: We study how high charging rate demands from electric vehicles (EVs) in a power distribution grid may collectively cause its dynamic instability, and, accordingly, how a price incentivization strategy can be used to steer customers to settle for lesser charging rate demands so that these instabilities can be avoided. We pose the problem as a joint optimization and optimal control formulation. The optimization determines the optimal charging setpoints for EVs to minimize the H₂-norm of the transfer function of the grid model, while the optimal control simultaneously develops a linear quadratic regulator (LQR) based state-feedback control signal for the battery currents of those EVs to jointly minimize the risk of grid instability. A subsequent algorithm is developed to determine how much customers may be willing to sacrifice their intended charging rate demands in return for financial incentives. Results are validated using numerical simulations of three EV charging stations in the IEEE 33-bus power distribution model.

Keywords: Automotive control, Predictive control for nonlinear systems, Optimal control
Abstract: This paper investigates the use of control barrier functions in conjunction with a recently developed output-tracking technique, with the aim of guaranteeing safe and smooth driving conditions for autonomous vehicles. The tracking technique in question has been developed by the authors of this paper for effectiveness as well as efficiency of computation, but its implementation may be fraught with large early input transients and state oscillations. The main objective of this paper is to investigate the use of control barrier functions for the dual purpose of safety guarantees and drastic reductions in the input oscillations and state overshoots. Furthermore, if the plant subsystem is differentially flat then we exploit this fact to further reduce the complexity of the control algorithm. As this is an initial study we focus the discussion on the particular example of a kinematic bicycle model, but argue for its potential generality to more complicated models of self-driving cars such as the dynamic bicycle. We test the aforementioned ideas by simulation and on a hardware platform, and the results suggest that the developed controller may have merits in autonomous vehicle applications.

Keywords: Control applications, Mechatronics, Constrained control
Abstract: The high-accuracy tracking and time-optimal response of mechanical systems are very important for modern manufacturing. However, the inevitable parametric uncertainties, disturbances, and constraints make achieving these high performances difficult. In this paper, a two-loop control algorithm combining online planning and adaptive robust control (ARC) is proposed for the 1-DOF mechanical systems to improve tracking accuracy and efficiency. In the outer loop, a time-optimal reference trajectory starting from the initial state of the plant is planned without violating the constraints. In the inner loop, the ARC law is synthesized to track the planned trajectory with high accuracy in the presence of parametric uncertainties and disturbances. The proposed method has a simpler inner-loop design compared with the existing work, and achieves the prescribed convergence of the tracking error. The widely used barrier Lyapunov function (BLF) based methods are compared with the proposed method in this paper. The experimental results verify the superiority of the proposed method in achieving fast response and high tracking accuracy. The limitations of the feasibility conditions of BLF on the tracking performance are analyzed.

Keywords: Control of networks, Distributed control, Optimization
Abstract: In this paper, we address the finite time synchronization of a network of dynamical systems with time-varying interactions modeled using temporal networks. We synchronize a few nodes initially using external control inputs. These nodes are termed as pinning nodes. The other nodes are synchronized by interacting with the pinning nodes and with each other. We first provide sufficient conditions for the network to be synchronized. Then we formulate an optimization problem to minimize the number of pinning nodes for synchronizing the entire network. Finally, we address the problem of maximizing the number of synchronized nodes when there are constraints on the number of nodes that could be pinned. We show that this problem belongs to the class of NP-hard problems and propose a greedy heuristic. We illustrate the results using numerical simulations.

Keywords: Robotics, Learning
Abstract: We present a novel framework that enables robots to learn motor skills from human demonstrations with guaranteed safety. Our framework comprises two components: a high-level planner and a low-level controller. The planner generates a safe trajectory region through an embodied state-action mapping (i.e., policy) computed using Dynamic Movement Primitives. The policy enables the robot to adapt to new environments, avoid obstacles, and stay within the predefined safe region. To execute the planned trajectories, we combine a control Lyapunov function controller, which tracks the mean trajectory of the distribution, and a control barrier function controller to strictly enforce constraints on the position of the robot's end effector, ensuring it remains within the safe zone. Our proposed framework is tested and validated through simulations and experiments with a Baxter robot to perform a pick and place task. These experiments demonstrate that the ProDMP is capable of generating distributions from demonstrated trajectories. Moreover, utilizing our proposed controller, the robot can navigate within these distributions from starting to goal locations while avoiding obstacles and reduces overall control effort.

Keywords: Robotics, Multivehicle systems
Abstract: In this article, we present a centralized approach for the control of multiple unmanned aerial vehicles (UAVs) for landing on moving unmanned ground vehicles (UGVs) using control barrier functions (CBFs). The proposed control framework employs two kinds of CBFs to impose safety constraints on the UAVs' motion. The first class of CBFs (LCBF) is a three-dimensional exponentially decaying function centered above the landing platform, designed to safely and precisely land UAVs on the UGVs. The second set is a spherical CBF (SCBF), defined between every pair of UAVs, which avoids collisions between them. The LCBF is time-varying and adapts to the motions of the UGVs. In the proposed CBF approach, the control input from the UAV's nominal tracking controller designed to reach the landing platform is filtered to choose a minimally-deviating control input that ensures safety (as defined by the CBFs). As the control inputs of every UAV are shared in establishing multiple CBF constraints, we prove that the control inputs are shared without conflict in rendering the safe sets forward invariant. The performance of the control framework is validated through a simulated scenario involving three UAVs landing on three moving targets.

Keywords: Robotics, Adaptive control, Learning
Abstract: This paper proposes a novel learning-based optimal control approach for the tracking control problem of a robot manipulator, which is allowed to have uncertainty in the model parameters. We first employ neural network (NN) technique to design an identifier for the system parameters estimation. Then, an optimal tracking controller is proposed with a critic NN. A novel online NN weight adaptation law is designed with the dynamic regression extension and mixing technique, for updating both the unknown parameters and the critic network's weight during the control process. With such setup, our approach can develop an important capability of relaxing the persistent excitation (PE) condition, leading to improved parameter-convergence accuracy and control applicability, which can be distinguished from the existing methods that use gradient-descent based weight adaptation laws. Rigorous theoretical analysis is conducted based on the Lyapunov stability theory and demonstrates the ultimately uniformly boundedness of the closed-loop systems. Effectiveness of the proposed method is validated through simulation study by using a 2 degree-of-freedom robot system.

Keywords: Robotics, Predictive control for nonlinear systems, Learning
Abstract: This paper presents an off-policy Gaussian Predictive Control (GPC) framework aimed at solving optimal control problems with a smaller computational footprint, thereby facilitating real-time applicability while ensuring critical safety considerations. The proposed controller imitates classical control methodologies by modeling the optimization process through a Gaussian process and employs Gaussian Process Regression to learn from the Model Predictive Control (MPC) algorithm. Notably, the Gaussian Process setup does not incorporate a built-in model, enhancing its applicability to a broad range of control problems. We applied this framework experimentally to a differential drive mobile robot, tasking it with trajectory tracking and obstacle avoidance. Leveraging the off-policy aspect, the controller demonstrated adaptability to diverse trajectories and obstacle behaviors. Simulation experiments confirmed the effectiveness of the proposed GPC method, emphasizing its ability to learn the dynamics of optimal control strategies. Consequently, our findings highlight the significant potential of off-policy Gaussian Predictive Control in achieving real-time optimal control for handling of robotic systems in safety-critical scenarios.

Keywords: Distributed control, Large-scale systems, Statistical learning
Abstract: This paper addresses the path-planning challenge for very large-scale robotic systems (VLSR) operating in complex and cluttered environments. VLSR systems consist of numerous cooperative agents or robots working together autonomously. Traditionally, many approaches for VLSR systems are developed based on Gaussian mixture models (GMMs), where the GMMs represent agents’ evolving spatial distribution, serving as a macroscopic view of the system’s state. However, our recent research into VLSR systems has unveiled limitations in using GMMs to represent agent distributions, especially in cluttered environments. To overcome these limitations, we propose a novel model called the skew-normal mixture model (SNMM) for representing agent distributions. Additionally, we present a parameter learning algorithm designed to estimate the SNMM’s parameters using sample data. Furthermore, we develop two SNMM-based path-planning algorithms to guide VLSR systems through complex and cluttered environments. Our simulation results demonstrate the effectiveness and superiority of these algorithms compared to GMM-based path-planning methods.

Keywords: Human-in-the-loop control, Mechanical systems/robotics, Adaptive control
Abstract: In this paper, we introduce control frameworks for physical human-robot interaction that rely on adaptive impedance learning and without force measurement. The adaptation laws are specifically designed to estimate human interaction forces, eliminating the need for a force sensor. These estimated forces are then utilized in the two controller designs. In the first one, estimated forces are used to compensate for the human’s force, ensuring the robot tracks a predefined trajectory. Conversely, the second control law uses the estimated forces to adjust the robot’s reference velocity in compliance with human intention. We employ Lyapunov’s technique to demonstrate stability and the uniform ultimate boundedness of the responses. Simulation results are presented to validate the proposed control algorithms. These results indicate that the approaches offer promising solutions for human-robot interaction with reduced cost and complexity.

Keywords: Mechatronics
Abstract: The reluctance actuator (RA) can provide more acceleration than the Lorentz actuators that are currently in use in next-generation wafer scanners used in semiconductor lithography systems. These wafer scanners are utilized in semiconductor lithography systems. Due to the significant amount of nonlinearity that exists between the RA's input current and output force, it might be challenging to build an effective control system. In the ten years prior, a great number of studies contributed to the modelling, design, and control of RAs; however, the geometrical topology of the actuator was not evaluated from the standpoint of control. This study presents topology selection criteria with the intention of improving the control design process. Additionally, it assesses the various accessible RA topologies, including C and E cores, with reference to the modelling of stiffness. The C-core RA was shown to have a lower magnitude of stiffness at low air gap values (less than 0.5 mm) when compared to the E-core RA. This was discovered through simulation as well as through experimentation.

Keywords: Mechanical systems/robotics, Mechatronics
Abstract: This paper presents development of a 2-degrees-of-freedom cable-suspended motion mechanism for a light-emitting diode (LED) horticultural light fixture with Internet-of-Things (IoT) connectivity. The proposed light motion mechanism is intended to provide uniform light distribution on the plant canopy to optimize growth through proper position and orientation control with set-points determined, for instance, by natural light conditions and based on the plant’s growth stage. The setup was built to have two main features: (i) Motion control of fixture’s height and roll angle; and (ii) IoT connectivity. The motion control unit consists of a trajectory planner, which receives the control set-points via an IoT module, and embedded firmware. The reference values are obtained, for instance, through a light recipe database that provide the required data from a remote digital twin computer. The desired motion trajectory is obtained based on the dynamics of the system such that the tension of cables remain positive during the motion. To this end, conditions are obtained for the desired motion trajectory to guarantee positive tension in the cables which is utilized in the trajectory tracking controller. A hardware prototype was built to evaluate performance of the system which is presented along with experimental results

Keywords: Mechanical systems/robotics, Uncertain systems, Variable-structure/sliding-mode control
Abstract: In this study, we propose a novel control framework to deal with position control for quadrotors subject to time-varying disturbances and uncertainty. High-order sliding mode observers (HSMOs) are utilized to estimate the uncertainty and disturbances. Then, a dynamic sliding mode controller (DSMC) is presented for tracking control of the inner-loop subsystem and a fast non-singular terminal sliding mode controller (FNTSMC) is developed for outer-loop subsystem tracking control. As a result, our proposed control law enables the quadrotor to precisely track a large class of reference signals under the presence of model uncertainty and a large class of time-varying external disturbances while reducing the chattering phenomenon. Both simulation and experiment are given to validate the effectiveness and superiority of the designed controllers.

Keywords: Mechanical systems/robotics
Abstract: Microsurgical operations such as embryo biopsy require extracting a material sample from inside the embryo for genetic testing. A precise perforation for embryo zona pellucida (ZP) is required to permit access for the biopsy micropipette to extract the sample. Many approaches developed for the ZP perforation, such as mechanical, chemical, and the Photothermolysis (the laser). In this paper, an automatic method for the blastocyst embryo ZP perforation is presented. This method utilizes a conventional laser system currently in use in manual approaches in research labs and In-Vitro Fertilization clinics and controls the whole perforation process using a vision feedback system. An experimental setup is developed to verify the behavior of the proposed method, in which a holding micropipette is used to hold and move the embryo, which is then moved in two coordinate directions toward the laser spot location. A computer vision algorithm is used to estimate the embryo ZP thickness to tune the laser parameters and estimate the ZP circle median quadrant coordinates. Then use this information as a feedback signal to a simple proportional controller to control the embryo motion. Experimental results demonstrate that the system is capable of embryo relocation and ZP perforation.

Keywords: Mechatronics
Abstract: Measuring magnetic flux plays a crucial role in developing a linearized controller for a variable reluctance actua- tor. However, the method used for measuring magnetic flux may have limitations that render it invalid under different operating conditions. This paper presents a flux estimation and control method based on the Extended High-Gain Observer (EHGO) approach for reluctance actuators, utilizing only the measured current. Initially, the dynamic model of the reluctance actuator is formulated in terms of the current in the coil, considering the magnetic field as unknown. Subsequently, EHGO is designed to use the measured current to estimate the magnetic field and magnetic flux. Finally, a feedforward controller is introduced to utilize the estimated magnetic field for achieving tracking performance of the desired magnetic flux. The analysis of the error bound in tracking errors demonstrates that minimizing the estimation error of the magnetic field reduces the tracking error. The effectiveness of the proposed flux estimator and the control approach is evaluated through numerical simulations. The results illustrate the EHGO’s capability to achieve accurate magnetic flux estimation, improving the tracking performance of the feedforward controller and minimizing tracking errors

Keywords: Multivehicle systems, Robotics, Automotive systems
Abstract: In this study, we introduce an innovative risk-aware behavior planning framework designed for autonomous driving, with the aim of fostering socially compliant vehicle behavior in diverse mixed-traffic highway scenarios. Our objective is to empower autonomous vehicles to exhibit behavior that aligns with societal norms, thus enhancing their acceptability among human drivers. We expand the scope of Control Barrier Function-inspired risk assessment to encompass a heterogeneous spectrum of road participants, allowing us to explicitly model varying degrees of social influences between different classes of vehicles. We also present a mathematical condition for accountability tracing, enabling the identification of responsible entities in situations where risks surge. Drawing inspiration from Isaac Asimov's "Three Laws of Robotics," we establish social compliance conditions grounded in our unique risk concept, which seamlessly integrates with a wide range of existing safety-critical controllers, regardless of their type or design. By incorporating these conditions, which encode societal expectations, into existing safe controllers, we demonstrate that autonomous vehicles can exhibit context-aware behavior without compromising the safety guarantees provided by existing controllers. This approach effectively excludes behaviors that may be safe but do not align with human intuition while guaranteeing the least interference with the existing controller.

Keywords: Optimization algorithms, Robotics, Manufacturing systems
Abstract: In this work, we present an approach to minimizing the time necessary for the end-effector of a redundant robot manipulator to traverse a given trajectory by optimizing the trajectory of its joints, under a number of restrictions. Each joint has limits in the ranges of position, velocity and acceleration, the latter making jerks in joint space undesirable. Furthermore, for the applications involved, the end-effector must traverse the path with high accuracy and at a constant path velocity, i.e. the tip of the manipulator must cover equal distances in equal amounts of time. The proposed approach takes this nonlinear optimization problem that has two variables (path speed and joint trajectory) and solves it in two steps - First, we solve an inner subproblem that considers a fixed joint trajectory and maximizes path speed, for which we obtain a closed-form solution that considers all joint velocity and acceleration restrictions. Moreover, we establish that the value of the inner subproblem is convex. Then, we solve an outer subproblem that takes a subgradient of the inner subproblem’s value to update the trajectory with a Primal-Dual optimization method that considers all path accuracy and joint position restrictions. We show the efficacy of our proposed approach with simulations.

Keywords: Adaptive control, Flight control, Lyapunov methods
Abstract: This paper presents a model-based, adaptive, nonlinear controller for the bicopter stabilization and trajectory-tracking problem. The nonlinear controller is designed using the backstepping technique. Due to the non- invertibility of the input map, the bicopter system is first dynamically extended. However, the resulting dynamically extended system is in the pure feedback form with the uncertainty appearing in the input map. The adaptive backstepping technique is then extended and applied to design the controller. The proposed controller is validated in simulation for a smooth and nonsmooth trajectory- tracking problem.

Keywords: Optimization algorithms, Robotics, Optimization
Abstract: Incremental motion planning has emerged as a powerful approach for generating safe trajectories in confined environments. However, its effectiveness can be hampered by susceptibility to local optima. This vulnerability arises from the algorithm's heavy dependence on the previously achieved configuration (pose) as a reference for the next step. This paper presents a novel incremental motion planning approach for redundant robot arms. It leverages an optimization-based planner combined with null-space exploration to escape local optima and generate high-quality trajectories satisfying task and collision constraints. Our approach is evaluated in an onsite polishing scenario with various robot and workpiece configurations, demonstrating significant improvements in trajectory quality compared to existing methods. The proposed approach has the potential for broad applications in industrial tasks involving redundant robot arms.

Keywords: Robust control, H-infinity control, Mechanical systems/robotics
Abstract: Next-generation motion control systems require fast and precise control, but advanced control strategies often rely on complex and expensive models. This paper proposes a data-driven approach to tune controllers for a joint used in a robotic arm. This is achieved by using the frequency response at different operating points and designing a low-bandwidth controller robust to multimodel uncertainties, not exciting the nonlinear modes of the system. Tracking performance is improved by tuning an appropriate feedforward controller, and additional constraints are derived to guarantee the stability of this filter. The proposed approach is applied to a joint in an industrial robotic arm.

Keywords: Robust control, Robotics, Biologically-inspired methods
Abstract: Rapid locomotion on complicated terrains with height and stiffness changes can be challenging. This paper presents a novel Sliding Cone Control (SCC), that offers a legged robot the capability to interact with rough terrains with explainable control commands and minimal computation resources. The proposed SCC is a sliding mode control-based robust controller that enforces the spring-like leg to undulate on the ground following the desired limit cycle in a finite-time converging manner. Its stability and robustness have been proved mathematically, which ensures a safe extension to the overall planar running control. The proposed controller is verified experimentally on a planer hopper. The results show desirable and stable running on the terrains with height and stiffness variations.

Keywords: Adaptive control, Feedback linearization, Control applications
Abstract: This paper presents an adaptive, model- based, nonlinear controller for the bicopter trajectory- tracking problem. The nonlinear controller is constructed by dynamically extending the bicopter model, stabilizing the extended dynamics using input-output linearization, augmenting the controller with a finite-time convergent parameter estimator, and designing a linear tracking con- troller. Unlike control systems based on the time separa- tion principle to separate the translational and rotational dynamics, the proposed technique is applied to design a controller for the full nonlinear dynamics of the system to obtain the desired transient performance. The proposed controller is validated in simulation for a smooth and nonsmooth trajectory-tracking problem.

Keywords: Flight control, Control applications, Predictive control for linear systems
Abstract: In this paper, a robust explicit model predictive control (EMPC) flight scheme is investigated for a quadrotor. MPC is widely recognized for its effectiveness in control, but its computational complexity for solving the online optimization problem, particularly for fast systems, poses a challenge. To address this, we introduce an innovative inner-outer loop control structure that incorporates EMPC which can transfer the overall optimization process offline. In the outer loop, we calculate reference roll and pitch angles, while the inner loop employs EMPC for rapid and optimized angle tracking within practical constraints. Additionally, integral sliding mode control (ISMC) is integrated to mitigate the effects of unbalanced payloads. The recursive feasibility is guaranteed for the proposed flight control method if the initial states are in the feasibility set, and the Lyapunov stability analysis is conducted. Finally, experiments show the efficacy of the proposed control strategies.

Keywords: Nonlinear output feedback, Predictive control for nonlinear systems, Numerical algorithms
Abstract: We apply the Newton-Raphson flow tracking controller to aggressive quadrotor flight and demonstrate that it achieves good tracking performance over a suite of benchmark trajectories, beating the native trajectory tracking controller in the popular PX4 Autopilot. The Newton-Raphson flow tracking controller is a recently proposed integrator-type controller that aims to drive to zero the error between a future predicted system output and the reference trajectory. This controller is computationally lightweight, requiring only an imprecise predictor, and achieves guaranteed asymptotic error bounds under certain conditions. We show that these theoretical advantages are realizable on a quadrotor hardware platform. Our experiments are conducted on a Holybrox x500v2 quadrotor using a Pixhawk 6x flight controller and a Rasbperry Pi 4 companion computer which receives location information from an OptiTrack motion capture system and sends input commands through the ROS2 API for the PX4 software stack.

Keywords: Adaptive control, Lyapunov methods, Constrained control
Abstract: In this paper, we present a framework for online parameter estimation and uncertainty quantification in the context of adaptive safety-critical control. The key insight enabling our approach is that the parameter estimate generated by the continuous-time recursive least squares (RLS) algorithm at any point in time is an affine transformation of the initial parameter estimate. This property allows for parameterizing such estimates using objects that are closed under affine transformation, such as zonotopes, and enables the efficient propagation of such set-based estimates as time progresses. We illustrate how such an approach facilitates the synthesis of safety-critical controllers for systems with parametric uncertainty and additive disturbances using control barrier functions, and demonstrate the utility of our approach through illustrative examples.

Keywords: Biomedical, Uncertain systems, Predictive control for linear systems
Abstract: Computer aided control in biomedical applications is gaining more and more popularity due to numerous research studies that have proven the efficiency of automatic control over manual dosing, which is highly susceptible to human errors. Optimal drug dosing is best achieved using automatic control, which triggers important benefits in terms of both costs and patient side-effects. However, mathematical models for patients are highly susceptible to large modeling uncertainty. A predictive control algorithm is designed in this paper for optimal multidrug control of hemodynamic variables. Improved closed loop performance is obtained compared to similar control strategies, for ±30% modeling uncertainty. The simulation results demonstrate that predictive control is a feasible solution for optimal drug dosing. An analysis of the closed loop performance for significant patient variability shows that controllers tuned using a nominal patient model often fail to achieve desired robustness. To limit the effect of modeling uncertainty, the prediction model should be updated using an online identification tool to extract patient features.

Keywords: Fault detection, Fault diagnosis, Uncertain systems
Abstract: The probabilistic boundary is necessary for safety-critical validation and control in uncertain dynamical systems. This paper addresses the problem of computing minimum-volume polynomial sublevel sets with chance constraints. Due to chance constraints, the original problem is intractable. To resolve this issue, we propose a sample-based continuous approximation method to approximate the original chance constraints, which leads to an approximate problem. The approximate problem is a tractable nonlinear optimization problem. We show that the optimal solution and cost of the approximate problem converge to those of the original one. The probabilistic feasibility of the approximate solution with finite samples is also discussed. Finally, a numerical example has been conducted to validate the proposed method.

Keywords: Filtering, Kalman filtering, Computational methods
Abstract: This paper gives a complete characterization of the complexity of computing the minimum mean square prediction error for wide-sense stationary stochastic processes. It shows that if the spectral density of the stationary process is a strictly positive, computable continuous function then the minimum mean square error (MMSE) is always a computable number. It is also shown that the computation of the MMSE is a #P₁ complete problem on the set of strictly positive, polynomial-time computable, continuous spectral densities. This means that if, as widely assumed, FP₁ and # P₁ do not coinside, then there exist strictly positive, polynomial-time computable continuous spectral densities for which the computation of the MMSE is not polynomial-time computable. So under the widely accepted assumptions of complexity theory, the computation of the MMSE is generally much harder than NP₁ complete problems.

Keywords: Filtering, Stochastic optimal control, Stability of nonlinear systems
Abstract: The average cost optimality is known to be a challenging problem for partially observable stochastic control, with few results available beyond the finite state, action, and measurement setup, for which somewhat restrictive conditions are available. In this paper, we present explicit and easily testable conditions for the existence of solutions to the average cost optimality equation where the state space is compact. In particular, we present a new contraction based analysis, which is new to the literature to our knowledge, building on recent regularity results for non-linear filters. Beyond establishing existence, we also present several implications of our analysis that are new to the literature: (i) robustness to incorrect priors (ii) near optimality of policies based on quantized approximations, (iii) near optimality of policies with finite memory, and (iv) convergence in Q-learning. In addition to our main theorem, each of these represents a novel contribution for average cost criteria.

Keywords: Game theory, Agents-based systems, Distributed control
Abstract: Self-interested behavior from individuals can collectively lead to poor societal outcomes. These outcomes can seemingly be improved through the actions of altruistic agents, which benefit other agents in the system. However, it is known in specific contexts that altruistic agents can actually induce worse outcomes compared to a fully selfish population --- a phenomenon we term altruistic perversity. This paper provides a holistic investigation into the necessary conditions that give rise to altruistic perversity. In particular, we study the class of two-strategy population games where one sub-population is altruistic and the other is selfish. We find that a population game can admit altruistic perversity only if the associated social welfare function is convex and the altruistic population is sufficiently large. Our results are a first step in establishing a connection between properties of nominal agent interactions and the potential impacts from altruistic behaviors.

Keywords: Game theory, Agents-based systems, Energy systems
Abstract: In uniform-price markets, suppliers compete to supply a resource to consumers, resulting in a single market price determined by their competition. For sufficient flexibility, producers and consumers prefer to commit to a function as their strategies, indicating their preferred quantity at any given market price. Producers and consumers may wish to act as both, i.e., prosumers. In this paper, we examine the behavior of profit-maximizing prosumers in a uniform-price market for resource allocation with the objective of maximizing the social welfare. We propose a scalar-parameterized function bidding mechanism for the prosumers, in which we establish the existence and uniqueness of Nash equilibrium. Furthermore, we provide an efficient way to compute the Nash equilibrium through the computation of the market allocation at the Nash equilibrium. Finally, we present a case study to illustrate the welfare loss under different variations of market parameters, such as the market's supply capacity and inelastic demand.

Keywords: Markov processes, Stochastic systems
Abstract: Bayesian attack graphs (BAGs) are powerful models to capture the time-varying progression of attacks in complex interconnected networks. Network elements are modeled by graph nodes, and connections among components are represented through edges. The nodes take binary values, representing the compromised and uncompromised state of the network components. BAGs also offer a probabilistic representation of the likelihood of external and internal attacks progressing through exploit probabilities. The accuracy and timely detection of attacks are major objectives in the security analysis of networks modeled by BAGs. This can ensure network safety by identifying network vulnerabilities and designing better defense strategies (e.g., reimaging devices, installing firewalls, changing connections, etc.). Two main challenges in achieving accurate detection in complex networks are 1) the partial monitoring of the network components due to the limited available resources and 2) the uncertainty in identifying and removing some compromises in the network due to the ever-evolving complexity of attacks. For a general class of BAGs, this paper presents an optimal minimum mean square error (MMSE) attack detection technique with arbitrary uncertainty in the monitoring and reimaging process. As with the Kalman filtering approach used for linear Gaussian state-space models, the derived solution exhibits the same optimality. A recursive matrix-form implementation of the proposed detection method is introduced, and its performance is examined through numerical experiments using a synthetic BAG.

Keywords: Stochastic optimal control, Stochastic systems, Uncertain systems
Abstract: In this paper, we study the finite-horizon optimal density steering problem for discrete-time stochastic linear dynamical systems for the case when the state distribution can be represented by Gaussian mixture models. First, we revisit the covariance steering problem for Gaussian distributions and derive its optimal control policy in closed-form. Subsequently, we leverage the latter (deterministic) control policy to define a randomized control policy which ensures that the state distribution will remain a Gaussian mixture over the whole time horizon. By leveraging these results, we reduce the Gaussian mixture steering problem to a linear program. We also discuss the problem of steering general distributions using Gaussian mixture approximations. Finally, we present the results of non-trivial numerical experiments which demonstrate that our approach can be applied to general distribution steering problems.

Keywords: Stochastic systems, Biomolecular systems, Systems biology
Abstract: In a chemical synapse, information flow occurs via the release of neurotransmitters from a presynaptic neuron that triggers an action potential (AP) in the postsynaptic neuron. At its core, this occurs via the postsynaptic membrane potential integrating neurotransmitter-induced synaptic currents, and AP generation occurs when potential reaches a critical threshold. This manuscript investigates feedback implementation via an autapse, where the axon from the postsynaptic neuron forms an inhibitory synapse onto itself. Using a stochastic model of neuronal synaptic transmission, we formulate AP generation as a first-passage time problem and derive expressions for both the mean and noise of AP-firing times. Our analytical results supported by stochastic simulations identify parameter regimes where autaptic feedback transmission enhances the precision of AP firing times consistent with experimental data. These noise attenuating regimes are intuitively based on two orthogonal mechanisms - either expanding the time window to integrate noisy upstream signals; or by linearizing the mean voltage increase over time. In summary, this work explores feedback modulation of the stochastic dynamics of autaptic neurotransmission and reveals its function of creating more regular AP firing patterns.

Keywords: Automotive control, Predictive control for nonlinear systems, Control applications
Abstract: Trajectory planning is an essential component in automated driving applications. Especially planning in urban environments imposes a multitude of constraints, which need to be handled within a short computational time frame. Towards this challenge, we propose a novel trajectory planning approach based on a spatial problem formulation, which can update at high rates over long horizons. Complementing our prior work on longitudinal optimization, this approach focuses on planning under lateral constraints. Using a constraint shaping step followed by an optimal control solution in a Frenet frame, a comfortable and anticipatory trajectory is generated. For solving the resulting dynamic optimization objectives, a tailored solution strategy based on the iterative linear quadratic regulator (ILQR) in the Augmented-Lagrangian framework is employed. Simulated results on various urban scenarios show the effectiveness and versatility of the approach.

Keywords: Behavioural systems, Linear systems, Subspace methods
Abstract: In this work, we propose a novel data-driven representation for general linear time-invariant (LTI) systems based on behavioral system theory. This representation relies solely on input-output data, eliminating the need for exact knowledge of the system structure. We also develop stabilizing controllers and finite/infinite horizon optimal linear quadratic (LQ) controllers using this data-driven representation. In the presence of noise-corrupted data, we present a certainty-equivalence LQ controller and demonstrate its effectiveness through performance analysis and a numerical example.

Keywords: Biologically-inspired methods, Biological systems, Stability of nonlinear systems
Abstract: Fish often swim in schools. Flow interactions are thought to be beneficial for schooling. Recent work shows that flow interactions cause a pair of free inline swimmers, flapping at the same frequency, to passively stabilize at discrete locations relative to each other and that these passively stable formations are energetically beneficial. However, the stability of these formations is sensitive to finite mismatch in flapping frequencies. Here, we propose a local flow sensing model and feedback controller that stabilize a pair of frequency-uncoordinated swimmers into a cohesive formation. Our findings bear relevance to understanding fish collective behavior and for designing bio-inspired underwater robotics.

Keywords: Distributed parameter systems, Sampled-data control, Nonlinear output feedback
Abstract: This paper provides sampled-data output feedback control of the Stefan problem with an explicit condition of sampling scheduling. The Stefan problem is a well-known physical model of the liquid-solid phase change, governed by a parabolic partial differential equation (PDE) of the temperature profile over a moving domain governed by an Ordinary Differential Equation (ODE). Utilizing two measurements of the liquid-solid interface position and the temperature gradient at the interface position for all time, we design a continuous-time PDE backstepping observer to estimate true temperature profile. Then, the output feedback control law is given based on the temperature estimate, and the sampled-data input is executed as Zero-Order-Hold (ZOH). Under the explicit condition of sampling scheduling, we rigorously prove that the closed-loop system is well-posed and satisfies the required condition of the physical model, and is exponentially stable. Numerical results are provided to illustrate the effectiveness of the proposed method.

Keywords: Flexible structures, Observers for nonlinear systems, Aerospace
Abstract: Observability of a cantilever beam attached to a rigid body rotating and translating in the plane is considered first using a differential-geometric approach and then using the empirical Gramian. Based on a modal approximation of the beam, the rank condition of the observability codistribution indicates that the body rotation rate and rigid body motion parallel to the length of the beam can be observed with strain sensors and accelerometers located on the flexible beam through the passive motion coupling so long as the body rotation rate is nonzero, however the rigid body motion lateral to the beam cannot. The empirical observability Gramian, generated through MATLAB and finite element analysis simulations, is used to provide further understanding of the observability characteristics and serves as a basis for the sensor selection problem for the cantilevered beam. Multiple objective functions are considered and a comparison of the sensor selection results is performed; differences in performance are demonstrated through the error estimates of an unscented Kalman filter run with simulated measurement data.

Keywords: Predictive control for nonlinear systems, Constrained control, Optimal control
Abstract: To reduce the computational footprint of model predictive control during online computation, a horizon-one scheme based on pre-computed inner-approximations of reachable sets is proposed. The inner-approximated reachable set allows to virtually predict the future system behavior over the full-horizon instead of repeatedly solving potentially large-scale optimal control problems. We provide theoretical proofs for recursive feasibility and asymptotic stability under mild assumptions. Furthermore, we illustrate how methods for sum-of-squares reachability analysis can be extended to meet these assumptions. The presented approach is demonstrated in simulation for functional verification and compared to other real-time methods from the literature.

Keywords: Constrained control, Lyapunov methods, Hybrid systems
Abstract: We propose a novel characterization of piecewise defined barrier functions for certifying forward invariant sets of piecewise continuous dynamical systems. Forward invariance is established by checking two conditions: the first condition is a usual barrier-type inequality on the interior of each piece, and the second condition imposes an appropriate interaction of the tangent cone and vector field at the boundary between pieces. We then show that this separation is especially well suited for constructing discontinuous barrier functions that are an appropriate generalization of high-order control barrier functions to the piecewise setting and can be used to construct controllers for forward invariance. In particular, the tangent cone condition at the boundary of pieces does not depend on the particular control strategy and can be checked, e.g., offline, while standard online methods can be used to enforce the barrier-type inequality on the interior of pieces.

Keywords: Observers for nonlinear systems, Power electronics, Adaptive systems
Abstract: It is a well-established fact that achieving precise control of an LLC resonant converter operating in sub-resonant mode hinges on the accurate measurement of the phase difference induced by the resonant tank’s parameters. Traditionally, this necessitates complex and costly software and hardware setups, presenting a formidable challenge. In this paper, we present a novel and innovative approach through which the phase difference is estimated. This method distinguishes itself by requiring the fewest sensors, resulting in significant cost savings during fabrication. With this method in hand, we propose an adaptive controller designed to maintain a constant output voltage, impervious to disturbances on the input side. To illustrate the performance of the designed observer and controller, the converter equipped with the suggested controller is simulated in MATLAB/Simulink. The results show that stability and disturbance rejection are achieved for the closed- loop system.

Keywords: Stability of nonlinear systems, Variable-structure/sliding-mode control, Aerospace
Abstract: This article presents a robust and finite-time stable control scheme for attitude stabilization of a rigid body using a Hölder-continuous differentiator. This scheme is designed directly on the state-space of rigid body rotational motion, which is the tangent bundle of the Lie group of three-dimensional rotations. This article presents the differentiator, its stability and robustness properties in detail. This is followed by its use in the attitude stabilization control scheme. The stability and robustness properties of the proposed Hölder-continuous design are obtained through a Lyapunov stability analysis, and juxtaposed with a sliding-mode design. This is followed by numerical simulation results that compare the performance of the two designs. These comparison results clearly demonstrate the advantages of the proposed Hölder-continuous stabilization scheme for rigid body attitude control.

Keywords: Robust control, Formal verification/synthesis
Abstract: Digital control has become increasingly prevalent in modern systems, making continuous-time plants controlled by discrete-time (digital) controllers ubiquitous and crucial across industries, including aerospace, automotive, and manufacturing. This paper focuses on investigating the reach-avoid problem in such systems, where the objective is to reach a goal set while avoiding unsafe states, especially in the presence of state measurement uncertainties. We propose an approach that builds upon the concept of exponential control guidance-barrier functions, originally used for synthesizing continuous-time feedback controllers. We introduce a sufficient condition that, if met by a given continuous-time feedback controller, ensures the safe guidance of the system into the goal set in its sampled-data implementation, despite state measurement uncertainties. The event of reaching the goal set is determined based on state measurements obtained at the sampling time instants. Numerical examples are provided to demonstrate the validity of our theoretical developments, showcasing successful implementation in solving the reach-avoid problem in sampled-data systems with state measurement uncertainties.

Keywords: Learning, Agents-based systems
Abstract: Autonomous cyber and cyber-physical systems need to perform decision-making, learning, and control in unknown environments. Such decision-making can be sensitive to multiple factors, including modeling errors, changes in costs, and impacts of events in the tails of probability distributions. Although multi-agent reinforcement learning (MARL) provides a framework for learning behaviors through repeated interactions with the environment by minimizing an average cost, it is not adequate to overcome the above challenges. In this paper, we develop a distributed MARL approach to solve decision-making problems in unknown environments by learning risk-aware actions. We use the conditional value-at risk (CVaR) to define the cost function that is being minimized, and introduce a Bellman operator to characterize the value function associated to a given state-action pair. We prove that this operator satisfies a contraction property, and that it converges to the optimal value function. We then propose a distributed MARL algorithm called the CVaR QD-Learning algorithm, and establish that value functions of individual agents reach consensus. We identify several challenges that arise in the implementation of the CVaR QD-Learning algorithm, and present solutions to overcome these. We evaluate the CVaR QD-Learning algorithm through simulations, and demonstrate the effect of a risk parameter on value functions at consensus.

Keywords: Learning, Lyapunov methods, Stability of nonlinear systems
Abstract: While there has been increasing interest in solving Zubov’s equation to find the maximal Lyapunov function, it remains a challenge for dynamical systems with limited knowledge of system dynamics. In this paper, we present a Zubov-Koopman approach to learning a Lyapunov function that is nearly maximal for an unknown nonlinear system but has a known equilibrium point. The proposed approach is a lifting approach to map observable data into an infinite dimensional function space, which generates a flow governed by our proposed ‘Zubov-Koopman’ operator. By learning a Zubov-Koopman operator over a fixed time interval, we can indirectly approximate the solution to Zubov’s Equation through iterative application of the learned operator on the identity function. We also demonstrate that a transformation of such an approximator can be readily utilized as a near-maximal Lyapunov function. We present an algorithm for learning Zubov-Koopman operators, asserting that this method not only decreases the necessary data volume but also achieves favorable outcomes in estimating regions of attraction, as illustrated by numerical examples.

Keywords: Learning, Uncertain systems, Lyapunov methods
Abstract: Control barrier functions (CBFs) have recently introduced a systematic tool to ensure system safety by establishing set invariance. When combined with a nominal control strategy, they form a safety-critical control mechanism. However, the effectiveness of CBFs is closely tied to the system model. In practice, model uncertainty can compromise safety guarantees and may lead to conservative safety constraints, or conversely, allow the system to operate in unsafe regions. In this paper, we use Gaussian processes to mitigate the adverse effects of uncertainty on high-order CBFs (HOCBFs). A particular structure of the covariance function enables us to convert the chance constraints of HOCBFs into a second-order cone constraint, which results in a convex constrained optimization as a safety filter. We analyze the feasibility of the resulting optimization and provide the necessary and sufficient conditions for feasibility. The effectiveness of the proposed strategy is validated through two numerical results.

Keywords: Learning, Optimal control, Optimization
Abstract: We investigate the problem of learning an epsilon-approximate solution for the discrete-time Linear Quadratic Regulator (LQR) problem via a Stochastic Variance-Reduced Policy Gradient (SVRPG) approach. Whilst policy gradient methods have proven to converge linearly to the optimal solution of the model-free LQR problem, the substantial requirement for two-point cost queries in gradient estimations may be intractable, particularly in applications where obtaining cost function evaluations at two distinct control input configurations is exceptionally costly. To this end, we propose an oracle-efficient approach. Our method combines both one-point and two-point estimations in a dual-loop variance-reduced algorithm. It achieves an approximate optimal solution with only mathcal{O}left(logleft(1/epsilonright)^{beta}right ) two-point cost information for beta in (0,1).

Keywords: Learning, Networked control systems, Agents-based systems
Abstract: We consider the problem of a learning-based, man-in-the-middle (MITM) attack in a cyber-physical system. We use a simple abstraction where an agent performs linear quadratic regulation (LQR) of a discrete-time, linear, time-invariant (LTI) system with stochastic disturbances, using model-free reinforcement learning. The system may be subject to an adversarial attack that overrides the feedback signal and the controller actions. We propose a ``Bellman Deviation'' algorithm that can be used by the agent to detect the attack. This algorithm only requires an estimate of the Q-function, and optimal average stage cost, and no explicit information of the system parameters. We show that the proposed algorithm asymptotically guarantees attack detection (AD) with high probability while avoiding false alarms, when an ``informational advantage'' condition is met. This condition compares the amount of information the agent has aquired about the system with the one aquired by the adversary.

Keywords: Agents-based systems, Learning
Abstract: In this paper, we formulate the multi-agent graph bandit problem as a multi-agent extension of the graph bandit problem introduced in (Zhang et al., 2023). In our formulation, N cooperative agents travel on a connected graph G with K nodes. Upon arrival at each node, agents observe a random reward drawn from a node-dependent probability distribution. The reward of the system is modeled as a weighted sum of the rewards the agents observe, where the weights capture some transformation of the reward associated with multiple agents sampling the same node at the same time. We propose an Upper Confidence Bound (UCB)-based learning algorithm, Multi-G-UCB, and prove that its expected regret over T steps is bounded by O(gamma N log(T)[sqrt(KT)+DK]), where D is the diameter of graph G and gamma a boundedness parameter associated with the weight functions. Lastly, we numerically test our algorithm by comparing it to alternative methods.

Keywords: Optimal control, Autonomous systems, Maritime control
Abstract: Navigating the highly unstructured maritime environment poses significant challenges for autonomous ships, particularly in the vicinity of static obstacles and inland waterways. Real-time algorithms capable of comprehending the complexity of nearby grounding hazards are crucial for safe and efficient operations. Electronic Navigational Charts (ENCs) serve as the standard for representing the static environment, providing detailed polygon-based information about obstacles and grounding hazards. However, the non-convex nature of these polygons presents difficulties for optimal control and Model Predictive Control (MPC) schemes. This article introduces an accurate and computationally feasible method for extracting and representing non-convex static obstacle polygons, specifically tailored for use in numerical optimization-based planning, path-following, and trajectory tracking close to static hazards. By employing geometric surface interpolation techniques, Thin Plate Spline (TPS) type of Radial Basis Function (RBF) interpolants are derived from each grounding hazard polygon's point set. These surface approximation functions are then utilized as inequality constraints within a Nonlinear MPC (NMPC) planning scheme to facilitate trajectory tracking with anti-grounding functionality. The integration of surface functions enables the NMPC to consider higher-detail maps, enabling the proposed control system to closely follow trajectories within the unstructured environment's hazardous areas, demonstrated through proof-of-concept simulations.

Keywords: Optimal control, Constrained control
Abstract: We explore a novel instance of an optimal control problem characterized by dynamics represented as a sweeping process subject to a drift, and incorporating an additional element: a non-regular mixed constraint. We investigate two distinct approaches for establishing the Pontryagin maximum principle. In the first approach, we employ an approximation technique, representing the sweeping term using a sequence of Lipschitz functions. In the second approach, we treat the sweeping as a coupling between an equality mixed constraint and a pure inequality state constraint. Through a rigorous analysis of both approaches, we observe notable similarities. Specifically, we identify the emergence of charges associated with the mixed constraints and the notable absence of the maximization condition within the maximum principle. These outcomes are a direct consequence of the non-regularity inher- ent in the mixed constraint.

Keywords: Optimal control, Differential-algebraic systems, Agents-based systems
Abstract: This paper studies a target-defense game played between a slow defender and a fast attacker. The attacker wins the game if it reaches the target while avoiding the defender's capture disk. The defender wins the game by preventing the attacker from reaching the target, which includes reaching the target and containing it in the capture disk. Depending on the initial condition, the attacker must circumnavigate the defender's capture disk, resulting in a constrained trajectory. This condition produces three phases of the game, which we analyze to solve for the game of kind. We provide the barrier surface that divides the state space into attacker-win and defender-win regions, and present the corresponding strategies that guarantee win for each region. Numerical experiments demonstrate the theoretical results as well as the efficacy of the proposed strategies.

Keywords: Optimal control, H-infinity control, Stochastic optimal control
Abstract: This paper studies online solutions for regret-optimal control in partially observable systems over an infinite-horizon. Regret-optimal control aims to minimize the difference in LQR cost between causal and non-causal controllers while considering the worst-case regret across all l2-norm-bounded disturbance and measurement sequences. Building on ideas from Sabag et. al (2021) on the the full-information setting, our work extends the framework to the scenario of partial observability (measurement-feedback). We derive an explicit state-space solution when the non-causal solution is the one that minimizes the H2 criterion, and demonstrate its practical utility on several practical examples. These results underscore the framework’s significant relevance and applicability in real-world systems.

Keywords: Optimal control, Learning, Chemical process control
Abstract: This work presents a constrained optimization framework for addressing the infinite-time optimal control problem for a class of nonlinear systems with constraints on control inputs and states. Specifically, the Koopman operator theory is employed first to transform the nonlinear system into a linear system. The optimal control problem for a nonlinear system with constraints is then reformulated as the optimal control problem for a linear system with constraints. Subsequently, by using an iterative algorithm and the concept of λ-contractivity, the constrained optimal control for the linear system is solved. Finally, two examples are used to demonstrate the effectiveness and advantages of the proposed strategy.

Keywords: Optimal control, Linear systems, Constrained control
Abstract: This paper develops an algorithm for upper-bounding the value function for a class of continuous-time optimal control problems. The upper bound can be used as a conservative estimate for the minimum cost that can be attained by any constraint admissible control from some initial state. Linear time-varying systems subject to convex input constraints and a state-independent running cost are considered. A collection of solutions of an augmented dynamical system is used to characterise viscosity supersolutions of a Hamilton-Jacobi-Bellman equation, which in turn yields an upper bound for the value function. The proposed algorithm has a computational complexity that scales in the number of these solutions as opposed to the dimension of the system, making the algorithm tractable for high dimensional systems.

Keywords: Closed-loop identification, PID control, Stability of linear systems
Abstract: We report an enhanced feedback control method to enable the simultaneous estimation of differential surface parameters di/dV and d(ln(Ri))/dδ during atomic-scale imaging of a surface with a Scanning Tunneling Microscope (STM). The proposed system enables exceptional signal-to-noise ratio (SNR) measurements of surface parameters by adding notch filters in the feedback loop. We then analyze the performance of a conventional PI controller for the ultra-fast feedback loop and demonstrate that changes in the work function (φ), a quantum mechanical property of the tip-sample junction, can destabilize the closed-loop system, leading to a possible tip crash. These tip crashes can compromise the STM’s efficiency and reliability, thus necessitating measures to address this loss of robustness. The effectiveness of this new STM feedback control system is validated by applying it to a set of STM images obtained from a Si(100) − 2 × 1:H passivated surface. We provide guidelines for PI tuning to optimize the system’s performance.

Keywords: Mechatronics, Fluid flow systems, Aerospace
Abstract: To improve the performance and reliability of electro-hydraulic servo control system (EHSCS), a position servo control strategy for a hydraulic valve-controlled cylinder with a digital piezo-actuator is proposed in this paper. Analytic model of the system is built firstly for control strategy design. To meet the accurate positioning requirement of the hydraulic cylinder under low and high-speed conditions, a compound control strategy is proposed with a dual control loop, i.e., the layer allocation control (LAC) and layer PWM control (LPC). The core idea of this strategy is a two-step control, where the actuation layers of the digital bits are first determined using the LAC and the LPC further compensates the residual error according to the reference speed. Experimental results show that the position servo control strategy with a digital piezo-actuator can improve the reliability of EHSCS as well as guarantee the position servo performance under different tracking conditions: (a) Under low-speed tracking conditions, the root-mean-square (RMS) errors for sinusoidal tracking at 0.08 Hz and 0.1 Hz using the proposed compound control are reduced by 42.3% and 64.7% compared with the cases using LAC. (b) Under high-speed tracking conditions, the LAC is enough for position servo control with fewer high-frequency on/off switching of the piezoelectric.

Keywords: Mechatronics
Abstract: This paper proposed an output feedback control design of a Galfenol-based actuator for active vibration control systems, considering unknown actuator dynamics under unknown load and external disturbance. The dynamic behavior of the Galfenol-based actuator was described by the constitutive relationship of the magnetostrictive materials. The objective is to devise a control signal, which is the input current of the coil, capable of generating an output force that counteracts any undesired motion of the platform caused by unknown loads or external disturbances. This implies maintaining a displacement at the output equal to zero. The simulation results show the proposed control approach's ability to regulate the platform's output displacement to about zero under different conditions of unknown loads and external disturbances.

Keywords: Mechatronics, Robotics, Nonlinear output feedback
Abstract: This paper proposes the modeling and control of a piezoelectric robotic manipulator used to characterize the behavior of a deformable object that exhibits nonlinear and viscoelastic deformation. To this aim, the manipulator's behavior, which exhibits nonlinearity, is approximated by a classical Bouc-Wen hysteresis model. Then, an output feedback control that ensures position reference tracking is designed for the manipulator. The output feedback is based on observers that estimate the manipulator's states and the interaction force with the characterized object. Finally, using the estimated force and the controlled position information, the force-deformation characteristics of the object are plotted, accessing its behavior and potentially its model parameters.

Keywords: Robotics, Predictive control for nonlinear systems, Constrained control
Abstract: Drifters are energy-efficient sampling platforms for oceanographic and other aquatic measurements. Steerable drifters may exert a small amount of control over their trajectory by modulating the drag on one or more rudders. Due to their limited mobility, it is of particular interest to characterize the reachability of steerable drifters over a range of initial velocity conditions. Established models of steerable drifters are highly nonlinear, and cannot be readily analyzed using existing methods for controllability analysis. In this paper a novel approach is proposed for characterizing the spatial reachability of a steerable drifter by using a modified empirical controllability gramian, which is relatively convenient to compute. In particular, the eigenvalues of the said gramian show strong coupling with the spatial coverage of the drifter as extracted from Monte Carlo simulations. A model is developed to capture the relationship between the eigenvalues and the span of achievable trajectories in the spatial domain. The predictive power of the model is demonstrated by comparing its estimates of the trajectory span with the Monte Carlo simulation results generated from random initial velocity conditions. Using this model to predict the span of the reachable subspace incurs a far lower computational cost than brute force strategies such as the Monte Carlo method.

Keywords: Mechatronics
Abstract: In this study, we propose a control technique that can be used to significantly reduce the tracking error of a short-stroke motion system whose dynamics are considered totally unknown with possibly input and output nonlinearities. As an example, the tracking performance of a uni-axial piezoceramic actuated positioning stage is examined under mainly sinusoidal test input signals with various frequencies and amplitudes, where we show that the proposed controller does invert the plant dynamics. Interestingly, neither modeling nor identification of the stage dynamics is needed. Mainly, the indented operation bandwidth is the only needed information when the proposed controller is synthesized. Experimental results demonstrate the effectiveness of the proposed approach when the piezoceramic actuated stage is attached to an existing long-stroke positioning motion system as an add-on to motivate the former usefulness in specifically enhancing the performance of wafer scanner machines used in semiconductor manufacturing.

Keywords: Linear systems, Robust control, Optimization
Abstract: We propose an approach to synthesize linear feedback controllers for linear systems in polygonal environments. Our method focuses on designing a robust controller that can account for uncertainty in measurements. Its inputs are provided by a perception module that generates probability mass functions (PMFs) for predefined landmarks in the environment, such as distinguishable geometric features. We formulate an optimization problem with Control Lyapunov Function (CLF) and Control Barrier Function (CBF) constraints to derive a stable and safe controller. Using the strong duality of linear programs (LPs) and robust optimization, we convert the optimization problem to a linear program that can be efficiently solved offline. At a high level, our approach partially combines perception, planning, and real-time control into a single design problem. An additional advantage of our method is the ability to produce controllers capable of exhibiting nonlinear behavior while relying solely on an offline LP for control synthesis.

Keywords: Formal verification/synthesis
Abstract: Real-world scenarios are characterized by timing uncertainties, e.g., delays, and disturbances. Algorithms with temporal robustness are crucial in guaranteeing the successful execution of tasks and missions in such scenarios. We study time-robust path planning for synthesizing robots' trajectories that adhere to spatial-temporal specifications expressed in Signal Temporal Logic (STL). In contrast to prior approaches that rely on discretized trajectories with fixed time steps, we leverage Piece-Wise Linear (PWL) signals for the synthesis. PWL signals represent a trajectory through a sequence of time-stamped waypoints. This allows us to encode the STL formula into a Mixed-Integer Linear Program (MILP) with fewer variables. This reduction is more pronounced for specifications with a long planning horizon. To that end, we define time-robustness for PWL signals. Subsequently, we propose quantitative semantics for PWL signals according to the recursive syntax of STL and prove their soundness. We then propose an encoding strategy to transform our semantics into a MILP. Our simulations showcase the soundness and the performance of our algorithm.

Keywords: Autonomous robots, Agents-based systems
Abstract: We introduce the concept of emph{community consensus} in the presence of malicious agents using a well-known median-based consensus algorithm. We consider networks that have multiple well-connected regions that we term emph{communities}, characterized by specific robustness and minimum degree properties. Prior work derives conditions on properties that are necessary and sufficient for achieving emph{global} consensus in a network. This, however, requires the minimum degree of the network graph to be proportional to the number of malicious agents in the network, which is not very practical in large networks. In this work, we present a natural generalization of this previous result. We characterize cases where, although global consensus is not reached, some subsets of agents V_i will still converge to the same values mathcal{M}_i among themselves. To reach this new type of consensus, we define more relaxed requirements in terms of the number of malicious agents in each community, and the number k of edges connecting an agent in a community to agents external to the community.

Keywords: Machine learning, Delay systems
Abstract: Data-driven controllers have gained prominence in diverse control applications, attributed to their inherent flexibility and adaptability to complex system dynamics. However, managing time delays in closed-loop systems remains a significant challenge in their deployment. These delays can arise from various sources, such as computational latency, actuator reaction time, and communication delays. Unaddressed, these time lags can induce system instability and degrade performance. This paper rigorously analyzes the impact of time delays on data-driven controllers and introduces methodologies to mitigate their adverse effects. Specifically, we explore the integration of the Smith predictor with Deep Reinforcement Learning (SP-DRL) to formulate a control law capable of effectively managing both time delays and system uncertainties, while ensuring robust performance. We demonstrate that this DRL-based framework, initially trained in stable environments, generalizes well to unstable systems. Our investigation delineates the scenarios conducive to the successful application of this approach and identifies factors influencing its effectiveness. To substantiate our findings, we present a case study involving a first-order delayed linear system with nonlinear actuation modules. Numerical simulations are employed to compare the robustness of SP-DRL scheme against the DRL standalone and the classical controls, such as PID and Linear Quadratic Regulator (LQR), in the presence of delays.

Keywords: Neural networks, Emerging control applications, Numerical algorithms
Abstract: The increasing prevalence of neural networks in safety-critical control systems underscores the imperative need for rigorous methods to ensure the reliability and safety of these systems. This work introduces a novel approach employing hybrid zonotopes to compute the over-approximation of backward reachable sets for neural feedback systems with nonlinear plant models and general activation functions. Closed-form expressions as hybrid zonotopes are provided for the over-approximated backward reachable sets, and a refinement procedure is proposed to alleviate the potential conservatism of the approximation. Two numerical examples are provided to illustrate the effectiveness of the proposed approach.

Keywords: Predictive control for nonlinear systems, Computational methods, Robust control
Abstract: Deploying nonlinear sampled-data systems in safety-critical applications requires us to ensure robust constraint satisfaction for an infinite time horizon. To maximize the region of safe operation, we aim to compute a robust control invariant set with maximum volume. In this work, we propose an iterative optimization-based algorithm that computes a sequence of candidate invariant sets, which is volume-wise monotonically increasing. By leveraging polynomialization-based techniques from reachability analysis and controller synthesis, our approach outperforms linearization-based approaches, especially for higher-dimensional systems. We show that the computational complexity of each iteration of our algorithm is polynomial in the state dimension and demonstrate its broad applicability using several examples from the literature with up to 10 dimensions.

Keywords: Information theory and control, Control over communications, Stochastic optimal control
Abstract: We study the problem of zero-delay coding of a Markov source over a noisy channel with feedback. Building and generalizing prior work, we first formulate the problem as a Markov decision process (MDP) where the state is a probability measure valued predictor along with a finite memory of channel outputs and quantizers. We then approximate this state by marginalizing over all possible predictors, so that our policies only use the finite-memory term to encode the source. Under an appropriate notion of predictor stability, we show that such policies are near-optimal for the zero-delay coding problem as the memory length increases. We also give sufficient conditions for predictor stability to hold, and present a reinforcement learning algorithm and establish its convergence to compute near-optimal finite-memory policies. These theoretical results are supported by simulations.

Keywords: Information theory and control, Markov processes, Stochastic optimal control
Abstract: We establish the Lipschitz continuity of the value functions of an active fixed-sample-size hypothesis testing problem when it is reformulated as a partially observed Markov decision process. These Lipschitz results enable us to develop novel upper and lower bounds on the value of information, which is the expected difference between the value functions before and after performing an experiment. Our novel Lipschitz and value-of-information results provide new practical insight into optimal policies for active fixed-sample-size hypothesis testing without resorting to approximate dynamic programming schemes or asymptotic analysis with infinite numbers of samples. We illustrate the utility of our results by showing that a simple scheme based on selecting experiments that maximize a value-of-information bound achieves near-optimal performance in simulations.

Keywords: Information theory and control, Stochastic optimal control, Predictive control for nonlinear systems
Abstract: We propose an adaptive model-predictive controller that balances driving the system to a goal state and seeking system observations that are informative with respect to the parameters of a nonlinear autoregressive exogenous model. The controller's objective function is derived from an expected free energy functional and contains information-theoretic terms expressing uncertainty over model parameters and output predictions. Experiments illustrate how parameter uncertainty affects the control objective and evaluate the proposed controller for a pendulum swing-up task.

Keywords: Markov processes, Autonomous systems, Information theory and control
Abstract: We consider a team of autonomous agents that navigate in an adversarial environment and aim to achieve a task by allocating their resources over a set of target locations. An adversary in the environment observes the autonomous team's behavior to infer their objective and responds against the team. In this setting, we propose strategies for controlling the density of the autonomous team so that they can deceive the adversary regarding their objective while achieving the desired final resource allocation. We first develop a prediction algorithm based on the principle of maximum entropy to express the team's behavior expected by the adversary. Then, by measuring the deceptiveness via Kullback-Leibler divergence, we devise convex optimization-based planning algorithms that deceive the adversary by either exaggerating the behavior towards a decoy allocation strategy or creating ambiguity regarding the final allocation strategy. A user study with 320 participants demonstrates that the proposed algorithms are effective for deception and reveal the inherent biases of participants towards proximate goals.

Keywords: Quantum information and control, Computational methods, Optimal control
Abstract: We present a framework for designing optimal optical pulses for the matter-wave splitting of a Bose-Einstein Condensate (BEC) under the influence of experimental inhomogeneities, so that the sample is transferred from an initial rest position into a singular higher diffraction order. To represent the evolution of the population of atoms, the Schrödinger's equation is reinterpreted as a parameterized ensemble of dynamical units that are disparately impacted by the beam light-shift potential in a continuous manner. The derived infinite-dimensional coupled Raman-Nath equations are truncated to a finite system of diffraction levels, and we suppose that the parameter that defines the inhomogeneity in the control applied to the ensemble system is restricted to a compact interval. We first design baseline square pulse sequences for the excitation of BEC beam-splitter states following a previous study, subject to dynamic constraints for either a nominal system assuming no inhomogeneity or for several samples of the uncertain parameter. We then approximate the continuum state-space of the ensemble of dynamics using a spectral approach based on Legendre moments, which is truncated at a finite order. Control functions that steer the BEC system from an equivalent rest position to a desired final excitation are designed using a constrained optimal control approach developed for handling nonlinear dynamics. This representation results in a minimal dimension of the computational problem and is shown to be highly robust to inhomogeneity in comparison to the baseline approach. Our method accomplishes the BEC-splitting state transfer for each subsystem in the ensemble, and is promising for precise excitation in experimental settings where robustness to environmental and intrinsic noise is paramount.

Keywords: Sensor networks, LMIs, Estimation
Abstract: In this paper, we address the problem of optimal sensor selection to ensure estimability in linear, steady-state processes in case of sensor failures. To this end, we follow the data reconciliation framework to formulate the sensor selection problem using information theoretic measures such as entropy, forward Kullback-Leibler (KL), reverse KL, and symmetric KL divergences. With the help of convex optimization theory, it was shown that all the proposed formulations can be solved to global optimality using a branch and bound method. The process flow network is used to illustrate the efficacy of the proposed formulations.

Keywords: Decentralized control, Large-scale systems, Network analysis and control
Abstract: This paper investigates the use of decentralised control architectures with heterogeneous dynamics for improving performance in large-scale systems. Our focus is on two well-known decentralised approaches; the ‘predecessor following’ and ‘bidirectional’ architectures for vehicle platooning. The former, utilising homogeneous control dynamics, is known to face exponential growth in disturbance amplification throughout the platoon, resulting in poor scalability properties. We demonstrate that by incorporating heterogeneous control system dynamics, this limitation disappears entirely, even under bandwidth constraints. Furthermore, we reveal that introducing heterogeneity in the bidirectional architecture allows the platoon’s behaviour to be rendered independent of its length, allowing for highly scalable performance.

Keywords: Decentralized control, Networked control systems, Delay systems
Abstract: This work focuses on enhancing the operational safety, cybersecurity, computational efficiency, and closed-loop performance of large-scale nonlinear processes with input delays. This is achieved by employing a decentralized model predictive controller (MPC) with encrypted networked communication. Within this decentralized setup, the nonlinear process is partitioned into multiple subsystems, each controlled by a distinct Lyapunov-based MPC. These controllers take into account the interactions between subsystems by utilizing full state feedback. To address the performance degradation associated with input delays, we integrate a predictor with each LMPC to compute the states after the input delay period. The LMPC process model is initialized with these predicted states. Furthermore, to enhance cybersecurity, all signals transmitted to and received from each subsystem are encrypted. Guidelines are established to implement this proposed control structure in any nonlinear system with input delays. The simulation results, conducted on a nonlinear chemical process network, illustrate the effective closed-loop performance of the decentralized MPCs alongside the predictor with encrypted communication when dealing with input delays in a large process.

Keywords: Power systems, Stability of nonlinear systems, Neural networks
Abstract: This paper designs decentralized controllers for energy storage systems (ESSs) to provide active power control for frequency regulation. We propose a novel safety filter design to gracefully enforce the satisfaction of the limits on the state of charge during transients. Our technical analysis identifies conditions on the proposed design that guarantee the asymptotic stability of the closed-loop system with respect to the desired equilibria. We leverage these results to provide a controller parameterization in terms of a single-hidden-layer neural network that automat- ically satisfies the conditions. We then employ a reinforcement learning approach to train the controller to optimize transient performance in terms of the maximum frequency deviation and the control cost. Simulations in an IEEE 39- bus network validate the significant transient performance improvements of the proposed controller design.

Keywords: Mean field games, Stochastic systems, Decentralized control
Abstract: For sequences of networks embedded in the unit cube [0, 1]^m in {mathbb R}^m (more generally compact sets in Riemannian manifolds), a notion related to that of graphons was introduced in [Caines, CDC 2022] in terms of (weak) measure limits of (sub-) sequences of empirical measures of vertex densities (vertexons) on [0, 1]^m and the associated (weak) measure limits of (sub-) sequences of empirical measures of edge densities (graphexons) on [0, 1]^{2m}, both of which exist regardless of sparsity or density of the limit graphs. This paper presents an extension of the Graphon Mean Field Game (GMFG) theory of [Caines-Huang, SICON, 2021] to the vertexon-graphexon MFG set-up (here denoted GXMFG). In particular, for sparse limit graphexons, an LQG GXMFG example is presented where the influence between agent populations on neighbouring nodes is modeled via a first order PDE.

Keywords: Optimization, Decentralized control, Networked control systems
Abstract: This paper focuses on distributed constrained optimization over time-varying directed networks, where all agents cooperate to optimize the sum of their locally accessible objective functions subject to a coupled inequality constraint consisting of all their local constraint functions. To address this problem, we develop a buffering drift-plus-penalty algorithm, referred to as B-DPP. The proposed B-DPP algorithm utilizes the idea of drift-plus-penalty minimization in centralized optimization to control constraint violation and objective error, and adapts it to the distributed setting. It also innovatively incorporates a buffer variable into local virtual queue updates to acquire flexible and desirable tracking of constraint violation. We show that B-DPP achieves O(1/sqrt{t}) rates of convergence to both optimality and feasibility, which outperform the alternative methods in the literature. Moreover, with a proper buffer parameter, B-DPP is capable of reaching feasibility within a finite number of iterations, which is a pioneering result in the area. Simulations on a resource allocation problem over 5G virtualized networks demonstrate the competitive convergence performance and efficiency of B-DPP.

Keywords: Automotive control, Control applications, Optimal control
Abstract: Torque response delay is a major disadvantage for turbocharged engines, especially for large diesel engines, due to turbo-lag. A coordinated control strategy is proposed in this paper for a diesel engine equipped with an electric compressor (eBoost) system to significantly reduce turbo-lag. A multi-input, multi-output Linear Quadratic Tracking with Integral (LQTI) control strategy and scheduling logic is developed for the Ford 6.7L V8 diesel engine equipped with a variable geometry turbocharger (VGT), exhaust gas recirculation (EGR), and added eBoost and bypass valve. Note that the production engine does not have an eBoost and bypass valve. Multiple model-based LQTI controllers were designed at different engine load conditions based on associated linearized models and the control outputs were scheduled using engine load and bypass valve position. The developed control strategy is validated in simulation and experimental studies, and the test results show a reduction of intake manifold pressure response by over 73% compared with the production configuration without a significant impact on NOx emissions.

Keywords: Automotive control, Modeling, Optimization
Abstract: Modeling the combustion characteristics in a multi-fuel compression ignition engine, under varying operating conditions is a challenging problem. Physics-based models can be developed but tend to be quite extensive or limited to certain operating conditions. To achieve reliable combustion under these conditions, the number of actuators required can be high, further increasing the complexity of the model and in turn the difficulty of control design based on it. To simplify the control, feedforward (FF) control is developed by inverting steady state models, built based on data collected at various operating points. Use of data driven models for capturing these steady state characteristics has gained a lot of attraction in the recent years due to the available computational resources and ease of model development. For developing the FF control, data-driven models are inverted by numerically searching for desired control inputs. The time taken for this inversion grows with the complexity of the model and the complexity of the model increases with the number of operating conditions and actuators. In this paper, use of scalable Gaussian process (GP) methods for building computationally efficient models to reduce the time taken for generating FF maps is proposed. The performance of these models and control design is validated using computational fluid dynamics (CFD) and experimental data.

Keywords: Automotive systems, Emerging control applications, Identification for control
Abstract: Advancements in Vehicle-to-Everything (V2X) technologies have opened new avenues for enhancing fuel efficiency in long-haul trucks through ecological (eco-) driving initiatives. These initiatives are commonly executed via a Model Predictive Control (MPC) framework, relying on lookahead information like road grade and speed limits. However, the performance of this framework relies on a precise model of the vehicle’s longitudinal dynamics, which can be challenging due to the inherent nonlinearities in the vehicle’s behavior. Nonlinear MPC (NLMPC) is often impractical for real-time, embedded implementations of eco-driving programs. To address this challenge, we employ the principles of Koopman operator theory and Extended Dynamic Mode Decomposition (EDMD) to construct a linear dynamical system in an augmented state space. This linear model, known as the Koopman Linear Predictor (KLP), approximates the vehicle’s longitudinal dynamics, providing a valuable tool for designing optimal speed profiles and trajectories that minimize fuel consumption. Numerical simulation results show the computational advantages of the proposed Koopman MPC (KMPC) framework over NLMPC. Moreover, this approach proves to be particularly effective in executing eco-driving programs over long routes. Keywords—Eco-driving, Model Predictive Control, Koopman operator, Extended Dynamic Mode Decomposition.

Keywords: Traffic control, Distributed control, Optimal control
Abstract: In this paper, an extension of a linear control design for hyperbolic linear partial differential equations is presented for a first-order traffic flow model. Starting from the Lighthill-Whitham-Richards (LWR) model, variable speed limit control (VSL) is applied through a modification of Greenshield's equilibrium flow model. Then, an optimal linear quadratic (LQ) controller is designed on the linear LWR model. The LQ state feedback function is found via the solution of a Riccati differential equation. Unlike previous studies, the control input is the rate of change of the input, not the input itself. The proposed controller is then verified on both the linear and nonlinear models. In both cases, the controller is able to drive the system to a desired density profile. In the nonlinear application, a higher control gain is needed to achieve similar results as in the linear case.

Keywords: Predictive control for nonlinear systems, Neural networks, Nonlinear systems identification
Abstract: This paper addresses the control of diesel engine nitrogen oxides (NOx) and Soot emissions through the application of Model Predictive Control (MPC). The developments described in the paper are based on a high-fidelity model of the engine airpath and torque response in GT-Power, which is extended with a feedforward neural network (FNN)-based model of engine out (feedgas) emissions identified from experimental engine data to enable the controller co-simulation and performance verification. A Recurrent Neural Network (RNN) is then identified for use as a prediction model in the implementation of a nonlinear economic MPC that adjusts intake manifold pressure and EGR rate set-points to the inner loop airpath controller as well as the engine fueling rate. Based on GT-Power engine model and FNN emissions model, the closed-loop simulations of the control system and the plant model, over different driving cycles, demonstrate the capability to shape engine out emissions response by adjusting weights and constraints in economic MPC formulation.

Keywords: Transportation networks, Smart grid
Abstract: This paper studies the problem of designing workplace electric vehicle (EV) charging tariffs (i.e., fee schedules) while considering their impact to the transportation-electricity nexus. In particular, we consider the morning commute problem where a collection of commuters who drive EV to work must go through a common traffic bottleneck. Individual commuters determine when to leave for work and whether to charge their EV at work by optimizing a payoff function accounting for their generalized travel cost and payoff from charging. As an arrival time dependent charging tariff can directly impact the commuter decisions at the user equilibrium, we tackle the problem of designing tariffs that optimize (a) only the transportation component of the social cost, (b) only the electricity component of the social cost, and (c) the total social cost for the coupled transportation and electricity system. Tariffs incentivizing user equilibria that achieve the same performance as centralized social cost minimization are derived for the first two settings. For the last setting, we establish a tight condition under which it is possible to decentralize social optimal decisions via tariffs, and design optimal and suboptimal tariffs when the condition holds and fails, respectively.

Keywords: Control applications, Optimization algorithms, Linear systems
Abstract: This work presents the use of the area of Allan VARiance (AVAR) as an alternate measure for Mean Squared Error (MSE) to select an optimal Moving Average (MA) filter that minimizes MSE between noisy and filtered signals. MSE is a standard performance index that quantifies the performance of MA filters. However, for signals with non-white noise characteristics - a category that includes nearly all real-world signals - the calculation of MSE is not quickly done with one but typically requires multiple experiments. This work shows that the area of AVAR estimates noise properties from one iteration of measured data and achieves the same optimization results. While AVAR methods are typically used to analyze the variance of static window averages of data, prior recent work extends this to include moving average calculations. In this work, these results are extended further to illustrate that the time-correlation window in the area of AVAR calculations relates to the window size used in the MA filter. This relationship is then utilized to show that the discrete integration of the AVAR curve yields a performance index that quickly identifies the MSE-optimal filter for input with drift (random walk) corrupted by white noise. AVAR is compared against the MSE to show that both the performance indices give similar results when choosing the optimal MA filter, but with only one iteration of AVAR calculations versus significant iterations (hundreds or more) for MSE calculations.

Keywords: Formal verification/synthesis, Control applications, Agents-based systems
Abstract: We propose a distributed differentially private receding horizon control (RHC) approach for multi-agent systems (MAS) with metric temporal logic (MTL) specifications. In the MAS considered in this paper, each agent privatizes its sensitive information from other agents using a differential privacy mechanism. In other words, each agent adds privacy noise (e.g., Gaussian noise) to its output to maintain its privacy. We define two types of MTL specifications for the MAS: agent-level specifications and system-level specifications. Agents should collaborate to satisfy the system-level MTL specifications while each agent must satisfy its own agent-level MTL specifications at the same time. In the proposed distributed RHC approach, each agent communicates with its neighboring agents to acquire their estimate of the system-level trajectory and updates its estimate of the system-level trajectory. Then, each agent synthesizes its own control inputs such that the system-level specifications are satisfied with a probabilistic guarantee while the agent-level specifications are also satisfied with a deterministic guarantee. In the proposed optimization formulation of RHC, we directly incorporate Kalman filter equations to calculate the system-level trajectory estimates. We use mixed-integer linear programming (MILP) to encode the MTL specifications as optimization constraints. Finally, we implement the proposed distributed RHC approach in two scenarios.

Keywords: Control applications, Hybrid systems, Mechatronics
Abstract: Peristaltic pumps are used for transporting liquids within disposable tubes, and are commonly found in medical devices. The peristaltic pump principle, however, introduces disturbances, thereby distorting the desired rotational speed of the pump. Proportional plus double integral (PI2) control is commonly used to reject these disturbances, but at the cost of deteriorated transient response and robustness margins. To balance these trade-offs in a more desirable manner, in this paper we propose a hybrid PI2 control strategy that allows for reducing the steady-state error while maintaining robustness margins similar to linear PI2 control. Experiments on a representative setup demonstrate up to 45% improvement in disturbance rejection capabilities.

Keywords: Control applications, Materials processing, Optimal control
Abstract: In this paper, we consider the optimal control of material micro-structures. Such material micro-structures are modeled by the so-called phase field model. We study the underlying physical structure of the model and propose a data based approach for its optimal control, along with a comparison to the control using a state of the art Reinforcement Learning (RL) algorithm. Simulation results show the feasibility of optimally controlling such micro-structures to attain desired material properties and complex target micro-structures.

Keywords: Control applications, Mechatronics, MEMs and Nano systems
Abstract: Atomic force microscopy (AFM) has found wide application in various fields, including nanotechnology, nano manipulation, and bioscience. Nevertheless, traditional raster or non-raster trajectories do not allow for speed variations in specific regions but are predetermined, resulting in an efficiency shortfall. Addressing this limitation, this paper introduces a novel scanning strategy with online detection of critical regions during the backward scan. This allows for self-adjustment of scanning speed during the forward scan, ensuring the continuity of acceleration throughout the scanning process as well. The proposed online smoothing variable-speed (OSVS) method let the AFM meticulously scan recognized critical regions at a relatively low speed while swiftly traversing uninteresting areas at a much higher speed. This approach reduces scanning time while maintaining imaging performance. In experiments, the developed method efficiently scans a grating sample with higher sidewalls using an AFM equipped with a sample rotating stage, resulting in high-precision scan results.

Keywords: Control applications, Adaptive control, Optimization
Abstract: Particle accelerators, complex machines crucial for various scientific endeavors, require regular tuning due to time-varying beams and components. Extremum seeking control proves to be an ideal strategy for this tuning process. Fine-tuning the beam involves modifying electric and magnetic fields within the beampipe to alter the shape or trajectory of the particle bunch. Yet, safety remains paramount, considering the substantial costs associated with particle collisions with components resulting in damage. Like the cost function, the safety of the system with respect to the tuning parameters is analytically unknown. In this study, we showcase the efficacy of our Safe Extremum Seeking (Safe ES) algorithm in particle accelerator applications. Our initial demonstration involves employing the Kapchinsky Vladimirsky (KV) equations to model a beam dominated by so called ``space-charge'' forces. We formulate a beam loss model and conduct a simulation illustrating the capability of Safe ES on the KV equations to tune the beam spot size while ensuring that beam loss remains below a specified threshold. In a second example, we present data obtained from an experimental implementation of Safe ES on the ion beam at the Los Alamos Neutron Science Center.

Keywords: Constrained control, Linear systems, Predictive control for linear systems
Abstract: The maximal admissible set (MAS) of a stable LTI system characterizes the set of all initial conditions and constant inputs for which the output satisfies pre-specified state/output constraints for all time. The MAS (or its finitely-determined, polytopic approximations) is often employed in set-theoretic methods in control and for constraint management, for example in the Reference Governor (RG) algorithm. The existing MAS (and consequently RG) formulations require a state-space model of the dynamics to characterize the MAS. In this paper, we offer an alternative, data-driven perspective: we leverage output predictors from the behavioral system theory and subspace predictive control literature to formulate a data-driven version of the MAS. As we show, the proposed set is polytopic and has finite complexity, similar to its model-based counterpart, but resides in a higher dimensional space and may have higher complexity. We present the properties of the data-driven MAS including its admissibility index, and compare the data-driven MAS against its model-based formulation, where we show that the two sets are related via a linear map under mild assumptions. Finally, we use the data-driven MAS to introduce a data-enabled RG for constraint management of closed-loop control systems. Numerical simulations are presented to illustrate the results.

Keywords: Linear systems, Output regulation, Subspace methods
Abstract: Over the past two decades, there has been a growing interest in control systems research to transition from model-based methods to data-driven approaches. In this study, we aim to bridge a divide between conventional model-based control and emerging data-driven paradigms grounded in Willems' ``fundamental lemma". Specifically, we study how input/output data from two separate systems can be manipulated to represent the behavior of interconnected systems, either connected in series or through feedback. Using these results, this paper introduces the Internal Behavior Control (IBC), a new control strategy based on the well-known Internal Model Control (IMC) but viewed under the lens of Behavioral System Theory. Similar to IMC, the IBC is easy to tune and results in perfect tracking and disturbance rejection but, unlike IMC, does not require a parametric model of the dynamics. We present two approaches for IBC implementation: a component-by-component one and a unified one. We compare the two approaches in terms of filter design, computations, and memory requirements.

Keywords: Computational methods, Numerical algorithms, Machine learning
Abstract: We present a Bayesian Optimization (BO) framework for optimizing the performance of batch dynamical systems. A key distinctive aspect of this framework is that it uses a parametric machine learning model (a recurrent neural network - RNN) to learn the system dynamics directly from data. The use of a parametric model provides more flexibility to capture complex dynamics and to propose batches of experiments, compared to traditional BO frameworks based on non-parametric Gaussian process (GP) models. However, the use of parametric models introduces challenges in deriving and computing an information measure that can be embedded in the BO acquisition function. The proposed framework uses the expected information gain (EIG) as information measure; we argue that this enables more scalable computations compared to the use of the Fisher Information (FI) measure used in classical design of experiments. We provide a bioreactor case study to illustrate the behavior and benefits of the proposed framework.

Keywords: Autonomous robots
Abstract: This paper considers the problem of controlling a team of camera-equipped robots to ensure a mobile human target is observed by at least one robot at all times. We focus on determining team trajectories over a fixed time horizon such that the human target is in at least one robot's field of view even while the line of sight to the target can be obstructed by obstacles. Our approach to solving this problem lies in using a particle-based Belief Propagation method to estimate the most likely poses for each robot over time such that the visual tracking requirement is satisfied. Our approach is validated in simulation studies and an experimental trial where a human target must be tracked by a pair of miniature autonomous robot blimps.

Keywords: Optimization algorithms, Machine learning, Learning
Abstract: This paper delves into the challenging problem of one-pass learning, where the objective is to learn each streamed datapoint without revisiting past data while not forgetting them. A prominent prior approach in this context for overparameterized models is ORFit (short for Orthogonal Recursive Fitting), which maintains predictions on previous datapoints by enforcing the orthogonality of parameter updates with respect to past output gradients. For overparameterized linear models, ORFit identifies the parameter that perfectly fits the data and has the minimum ell^2-norm, among the infinitely many such parameters. To generalize this and gain control over the selection of desired parameters, in this paper, we introduce Projected Orthogonal Recursive Fitting (Pi-ORFit). We begin by characterizing all parameters that can precisely fit data in general vector-output linear models, employing a formalism based on nullspace projector matrices. This framework yields an alternative derivation of ORFit. We further extend ORFit to learn a desired parameter by incorporating Bregman projection into the update rule. Importantly, we show that the resulting parameter minimizes the potential function that defines the Bregman projection at each update step. This property enables the selection of a desired parameter among multiple candidates consistent with the data. We provide numerical experiments that not only validate our analytical findings but also underscore the practical significance of this generalized approach.

Keywords: Vision-based control, Learning, Autonomous robots
Abstract: We study active perception from first principles to argue that an autonomous agent performing active perception should maximize the mutual information that past observations posses about future ones. Doing so requires (a) a representation of the scene that summarizes past observations and the ability to update this representation to incorporate new observations (state estimation and mapping), (b) the ability to synthesize new observations of the scene (a generative model), and (c) the ability to select control trajectories that maximize predictive information (planning). This motivates a neural radiance field (NeRF)-like representation which captures photometric, geometric and semantic properties of the scene grounded. This representation is well-suited to synthesizing new observations from different viewpoints. And thereby, a sampling-based planner can be used to calculate the predictive information from synthetic observations along dynamically-feasible trajectories. We use active perception for exploring cluttered indoor environments and employ a notion of semantic uncertainty to check for the successful completion of an exploration task. We demonstrate these ideas via simulation in realistic 3D indoor environments.

Keywords: Adaptive systems, Robotics, Intelligent systems
Abstract: Long decaying memory is a trademark of fractional calculus operations. These can be incorporated in the feedback and training laws of neural-adaptive controllers; the adaptive laws for feedforward and transform matrix artificial neural networks (ANNs) inherit historical errors. Thus, requiring an analysis of such a scheme on different control problems over prolonged executions; this enables the ability to observe the interactions between ANNs (feedforward and transform matrices) and fractional-order integral (FOI), as both are adaptive memory functions. Moreover, Lyapunov stability methods paved the way to incorporate FOI in feedback and adaptive laws for nonlinear input-affine dynamical systems. A planar 2-degree-of-freedom serial manipulator executes two control problems: task-space trajectory tracking and hybrid force-position control, in separate simulations. The proposed FOI-based method provides significantly better results than a non-FOI baseline method while remaining stable over prolonged cycles.

Keywords: Adaptive systems, Time-varying systems, Simulation
Abstract: This paper addresses the challenge of achieving stable This paper addresses the challenge of achieving stable adaptive teleoperation and improving the convergence rate in the presence of high communication time delays. We employ a passivity-based formalism to establish stability using wave variables and wave scattering techniques, and we enhance the convergence rate by combining it with predictor-based approaches. The elevated time delay within the teleoperated communication layer is known to induce an oscillatory behavior, which reduces the convergence rate and increases the settling time in the convergence of power variables. This issue is addressed in this paper by utilizing a Smith predictor on the operator end and Minimum Jerk (MJ) predictors on the remote end. We present experimental and simulation results to demonstrate the improvements, ensuring stable teleoperation under high communication time delays.

Keywords: Adaptive systems, Uncertain systems, Direct adaptive control
Abstract: Unknown effector degradation and model uncertainties risk weakening the performance of any system. Model reference adaptive control and adaptive control allocation methods are effective solutions for over-actuated uncertain vehicles to overcome these phenomena because of their ability to estimate unknown effects. Thus, this work proposes a joint structure of adaptive control allocation and model reference adaptive control solutions for compensating the effects of unknown effector degradation and model uncertainties on attitude performance, respectfully. Specifically, Lyapunov stability analysis is provided to prove closed-loop system stability, and simulation results are presented on a multi-rotor to show that the proposed adaptive method improves command tracking performance on attitude dynamics in the presence of unknown effector degradation and uncertain center of gravity location.

Keywords: Kalman filtering, Adaptive systems, Identification
Abstract: Recursive least squares (RLS) is derived as the recursive minimizer of the least-squares cost function. Moreover, it is well known that RLS is a special case of the Kalman filter. This work presents the Kalman filter least squares (KFLS) cost function, whose recursive minimizer gives the Kalman filter. KFLS is an extension of generalized forgetting recursive least squares (GF-RLS), a general framework which contains various extensions of RLS from the literature as special cases. This then implies that extensions of RLS are also special cases of the Kalman filter. Motivated by this connection, we propose an algorithm that combines extensions of RLS with the Kalman filter, resulting in a new class of adaptive Kalman filters. A numerical example shows that one such adaptive Kalman filter provides improved state estimation for a mass-spring-damper with intermittent, unmodeled collisions. This example suggests that such adaptive Kalman filtering may provide potential benefits for systems with non-classical disturbances.

Keywords: Neural networks, Kalman filtering
Abstract: Multi-class multi-object tracking (MCMOT) is crucial for risk perception in autonomous vehicles. However, the complex environment and intense camera movement exacerbate false detections and trajectory interruptions. Therefore, an MCMOT algorithm based on feature decoupling for detection and adaptive motion association for online tracking, named DATrack, is proposed. Firstly, we introduce TSCODE to decouple the learned representation into classification-specific and localization-specific features to alleviate the contradiction between the two branches in YOLOX, enhancing the multi-class object detection accuracy. Additionally, an adaptive motion prediction (AMP) module is proposed to enhance the accuracy of trajectory state estimation in ByteTrack from two aspects: (1) adaptively adjusting the process and observation noise in the Kalman filter according to the matching cost and object detection confidence; (2) estimating and mitigating the impact of camera motion through the positional deviation of the initial matching results. The experimental results on the BDD100K MOT validation dataset demonstrate that, compared with other state-of-the-art methods, our approach achieves higher tracking accuracy (MOTA 58.6%, IDF1 63.5%) while maintaining real-time performance (27.6 FPS on an NVIDIA RTX 2080Ti).

Keywords: Optimization, Adaptive systems, Vision-based control
Abstract: This work presents a real-time time-delay filtering approach for reference shaping for high precision motion control of vibratory systems. The motion of the system is initiated with a judicious (arbitrary) step command and the acquired motion data is used to estimate the modal parameters in real-time. The modal data is subsequently used to synthesize the subsequent step commands to mitigate the residual vibrations. The proposed control algorithm is tested on a gantry crane structure with a suspended payload. Our method estimates the system parameters based on computer vision while tracking a ArUco fiducial marker which is integral with the payload. Computational efficiency is ensured by using C++ to deploy the algorithm. The goal is to minimize the residual energy at the terminal displacement for rest-to-rest maneuvers of a suspended payload with unknown dynamics. An inertial measurement unit is used to track angular velocity at the end of the maneuver and is not used in the model identification process.

Keywords: Network analysis and control, Optimization
Abstract: We consider the problem of optimizing the interconnection graphs of complex networks to promote synchronization. When traditional optimization methods are inapplicable, due to uncertain or unknown node dynamics, we propose a data-driven approach leveraging datasets of relevant examples. We analyze two case studies, with linear and nonlinear node dynamics. First, we show how including node dynamics in the objective function makes the optimal graphs heterogeneous. Then, we compare various design strategies, finding the best either use data samples close to a specific Pareto front or combine a neural network and a genetic algorithm, performing statistically better than the best examples in the datasets.

Keywords: Network analysis and control, Cooperative control, Agents-based systems
Abstract: This paper introduces the ``Predator-Swarm-Guide" (PSG) model, a hybrid approach for modeling crowd dynamics by considering pairwise repulsive and attractive interactions among individuals. Extending the predator-swarm model, PSG specifically addresses the behavior of individuals during a shooting event within a zoned environment. It accounts for individuals' simultaneous efforts to evade the shooter while seeking guidance from a trusted agent. The guiding agent's movements during evacuation are influenced by two factors: its orientation towards the safe zone, where individuals are protected from the shooter, and the shooter's location. The PSG model incorporates crucial environmental factors, including impermeable walls, psychological elements leading to significant social friction, and a termination procedure to track casualties. Outputs of the PSG model underscore the significance of coordinated cooperation between individuals and the guiding agent in minimizing casualties during an active shooting scenario. Therefore, the objective is to reduce casualties through a hybrid motion optimization approach for both individuals and the guiding agent. Additionally, an equilibrium analysis, based on the continuum-limit version of the PSG model, is conducted to predict the crowd's equilibrium configuration in specific scenarios.

Keywords: Control of networks, Biological systems, Networked control systems
Abstract: The paper deals with the spread of two competing viruses over a network of population nodes, accounting for pairwise interactions and higher-order interactions (HOI) within and between the population nodes. We study the competitive networked bivirus susceptible-infected-susceptible (SIS) model on a hypergraph introduced in Cui et al. We show that the system has, in a generic sense, a finite number of equilibria, and the Jacobian associated with each equilibrium point is nonsingular; the key tool is the Parametric Transversality Theorem of differential topology. Since the system is also monotone, it turns out that the typical behavior of the system is convergence to some equilibrium point. Thereafter, we exhibit a tri-stable domain with three locally exponentially stable equilibria. For different parameter regimes, we establish conditions for the existence of a coexistence equilibrium (both viruses infect separate fractions of each population node).

Keywords: Network analysis and control, Large-scale systems, Markov processes
Abstract: We study stochastic interaction network models whereby a finite population of agents, identified with the nodes of a graph, update their states in response to pairwise interactions with their neighbors as well as spontaneous mutations. These include the main epidemic models, such as the Susceptible-Infected-Susceptible, the Susceptible-Infected-Recovered, and the Susceptible-Infected-Recovered-Susceptible models. We analyze the asymptotic behavior of such systems on Erdos-Renyi random graphs, in the limit as the population size grows large. Our approach is based on the use of (approximate) Lyapunov functions for Markov chains through which we can obtain stability results in terms of the corresponding invariant probabilities and on specific concentration results for Erdos-Renyi random graphs.

Keywords: Network analysis and control, Emerging control applications
Abstract: The basic reproduction number of a networked epidemic model, denoted R0, can be computed from a network’s topology to quantify epidemic spread. However, disclosure of R0 risks revealing sensitive information about the underlying network, such as an individual’s relationships within a social network. Therefore, we propose a framework to compute and release R0 in a differentially private way. First, we provide a new result that shows how R0 can be used to bound the level of penetration of an epidemic within a single community as a motivation for the need of privacy, which may also be of independent interest. We next develop a privacy mechanism to formally safeguard the edge weights in the underlying network when computing R0. Then we formalize tradeoffs between the level of privacy and the accuracy of values of the privatized R0. To show the utility of the private R0 in practice, we use it to bound this level of penetration under privacy, and concentration bounds on these analyses show they remain accurate with privacy implemented. We apply our results to real travel data gathered during the spread of COVID-19, and we show that, under real-world conditions, we can compute R0 in a differentially private way while incurring errors as low as 7.6% on average.

Keywords: Networked control systems, Agents-based systems
Abstract: We present and analyze an actively controlled SIS (actSIS) model of interconnected populations to study how risk aversion strategies affect network epidemics. A population using a risk aversion strategy reduces its contact rate with other populations when it perceives an increase in infection risk. The network actSIS model relies on two distinct networks. One is a physical network that defines which populations come into contact with which others, thus how infection spreads. The other is a communication network, such as an online social network, that defines which populations observe the infection level of which others, thus how information spreads. We prove that the system exhibits a transcritical bifurcation where an endemic equilibrium (EE) emerges. For regular graphs, we prove that the endemic infection level is uniform across populations and reduced by the risk aversion strategy, relative to the network SIS endemic level. We show that when communication is sufficiently sparse, this initially stable EE loses stability in a secondary bifurcation. Simulations show that a new stable solution emerges with nonuniform infection levels.

Keywords: Chemical process control, Optimization, Modeling
Abstract: A semicontinuous distillation process is effectively used in the separation of a multi-component mixture with low to medium production rates. This work focuses on building a data-driven model predictive control (MPC) framework to optimize the performance of a semicontinuous process by reducing total annualized cost (TAC) per tonne of feed processed while meeting the specified product quality. A data-driven modeling technique is considered in this work because of the unavailability of a highly complex and accurate first-principle model. An Aspen Plus Dynamics simulation is used as a test bed to collect the data from the process. A multi-model framework developed by modifying the traditional subspace algorithm is adapted in the shrinking horizon MPC (SHMPC) scheme to minimize TAC per tonne of feed processed. Visual Basic for Application (VBA) is used as a third tool to communicate the inputs from MPC developed in MATLAB to the process in Aspen Plus Dynamics. The simulation results illustrate that the MPC reduced the TAC/tonne of feed by 11.4% compared to the existing PI control configuration.

Keywords: Chemical process control, Process Control, Stochastic systems
Abstract: The escalating demand for producing highly purified proteins, free from contaminants, is paramount in the realm of preparative chromatography. To effectively mitigate crystal impurities and establish optimal operational strategies for crystallization processes, it becomes imperative to comprehensively understand the influence of surface morphology on protein crystals. In the present study, we introduce a novel microscopic kinetic Monte Carlo (kMC) model, specifically designed to account for various growth regimes by incorporating surface thermodynamic effects related to different growth mechanisms. This innovation centers on an adaptive adsorption rate that redefines the driving force behind crystallization. To ensure the model's precision and relevance, we validate it with experimental findings. Subsequently, the confirmed kMC model, which forecasts kink density changes, surface morphology, and crystal growth rates under disturbances, is incorporated into a model-based control strategy. This method calculates an optimal input trajectory that facilitates the achievement of the desired kink density, thereby significantly reducing impurities during the crystallization process. This research offers a novel approach for controlling the growth of protein crystals. Furthermore, the stochastic model presents a valuable framework for enhancing the purity of proteins through tunable kink density of crystals, critical for the biotechnology and pharmaceutical industries.

Keywords: Machine learning, Chemical process control, Variational methods
Abstract: Modern industrial production requires real-time control of critical quality variables that are hard to measure, which leads to the development of soft sensors that infer the quality variables online. In this paper, a parsimonious and compact soft-sensor modelling method is proposed based on information-bottleneck (IB) theory. The new method is in the form of a trade-off between model complexity and inferential accuracy. It is notable that this method integrates decoupled representation learning, relevant feature selection, and soft-sensor modelling into one model that can be optimised as a whole using a single cost function. Using a case study on the sulphur recovery unit, soft sensors are obtained with and without the proposed IB module. It is shown that adding the IB module in the model improves R2 from 55.6% to 80.9% and decreases the MSE from 0.039 to 0.026 on the test dataset.

Keywords: Networked control systems, Chemical process control, Communication networks
Abstract: This study proposes an approach to enhance the operational safety and cybersecurity of large-scale nonlinear processes by implementing a combination of traditional and advanced controllers through a two-tier control architecture with encrypted networked communication channels. Within this framework, the lower-tier control system utilizes a set of proportional-integral (PI) controllers to stabilize the process, while the upper-tier control system employs a Lyapunov-based model predictive controller (LMPC) to further improve the closed-loop system performance. To implement encryption, the input data must be presented as integers. Accordingly, signals to be encrypted within this framework are mapped from floating-point numbers to an integer subset through quantization, followed by bijective mapping. Different encryption schemes are implemented for the lower-tier and upper-tier control systems, accounting for the linear and nonlinear nature of the respective control systems. This study further delves into the impact of quantization on the closed-loop performance and an in-depth stability analysis of the two-tier control structure, establishing error bounds associated with quantization and sample-and-hold controller implementations. The approach is applied to a large-scale, nonlinear chemical process network example.

Keywords: Process Control, Chemical process control, Optimization
Abstract: Model predictive control (MPC) has been widely used to control and operate complex systems. However, the efficient implementation of MPC depends on the efficient solution of the underlying optimization problem. In this work, we propose a machine learning (ML) based warm start initialization strategy for Generalized Benders Decomposition (GBD) to be used for the solution of mixed integer MPC problems. Specifically, the mixed integer MPC problem is first solved using an ML-based branch and check GBD algorithm, which provides a set of high-quality integer feasible solutions. These solutions are subsequently used to compute the exact Benders cuts, which are used to warm start the GBD algorithm. We apply the proposed approach to a case study on the operation of chemical processes where a mixed integer MPC problem is solved to compensate for disturbances. The results show that the proposed approach leads to 39% reduction in solution time compared to the standard application of GBD.

Keywords: Optimization, Optimization algorithms, Chemical process control
Abstract: This work addresses the discrete-time simultaneous scheduling and open-loop control (SSOC) of network batch processes with variable processing times through a tailored Generalized Benders Decomposition (GBD) framework. This SSOC problem is a challenging mixed-integer nonlinear programming (MINLP) problem because variable processing times introduce more binary variables to a discrete-time scheduling formulation and may generate new infeasibilities if those variables are poorly selected. Variable processing times are key in SSOC since they affect both the flexibility of the schedule, and the dynamic performance of batch systems. The key novelty of the proposed GBD approach is the addition of initial and auxiliary feasibility cuts to facilitate the handling of infeasibilities generated by variable processing times. The performance of the proposed GBD framework is tested using a case study adapted from the literature. A GBD methodology that implements traditional feasibility cuts is used as a benchmark. While the conventional GBD method was unable to converge to a feasible solution, the proposed GBD framework found a feasible solution within the first two interactions and then converged by closing the absolute MINLP gap. Therefore, the proposed GBD framework is a promising strategy to solve SSOC problems involving batch processes often found in the pharmaceutical, energy, and food industries.

Keywords: Manufacturing systems, Predictive control for linear systems, Estimation
Abstract: Humans are an essential part of Smart Manufacturing systems. While modeling machines based on real-time data and knowledge from subject matter experts has been widely explored, modeling humans has not. Modeling humans presents significant challenges due to the heterogeneity of individuals and the stochasticity that may be introduced through individual decisions based on events. However, we hypothesize that human behavior within a controlled environment and task will lie within a predictable scope that can give insight into future behavioral states of humans, such as fatigue. Human fatigue affects workers' productivity, safety, and performance in manufacturing systems. We define fatigue as measurable tiredness resulting from physical exertion. If we can predict when a human worker will become fatigued, breaks or task changes can be preemptively incorporated into system planning to maintain desired levels of productivity and safety. In this paper, we propose a modeling structure to describe fatigue in humans performing repetitive, manufacturing-like tasks. Using first order modeling techniques the model incorporates task context and physiological sensor data. A case study in which the participant completes a repetitive cable assembly task provides a demonstration of model development. A trial in this case study includes both working and resting periods, during which the participant wore weights of varying amounts to provide variation in task context. We derived linear time-invariant state space models that are capable of predicting fatigue levels with high accuracy over a 20 minute time horizon.

Keywords: Manufacturing systems and automation, Delay systems, Control applications
Abstract: A control framework that optimizes registration accuracy while ensuring safety in roll-to-roll processes is presented. A primary controller using a modified algebraic Riccati equation is designed to reduce registration errors. This is complemented by a safety-critical controller based on a control barrier functional to maintain tension within safe limits. Our method is supported by numerical simulations, offering great potential to enhance existing industrial controllers.

Keywords: Vision-based control, Embedded systems, Manufacturing systems
Abstract: The high-precision and high-speed positioning systems require position feedback with high accuracy at a higher frequency. As reported in recent literature, high accuracy and high operating frequency can be achieved by fusing multiple position sensor data, e.g., the linear encoder (less robust/accurate, but fast) and object detection using camera images (accurate, but slow due to heavy processing load). Typically, image-based object detection incurs a significant computational delay due to computationally intensive processes and is the main performance bottleneck. Moreover, the computation delay varies when implemented on industrial platforms and degrades the performance of the closed-loop control system. In this paper, we present scheduling techniques such as parallelism and pipelining considering predictable multi-core platforms for such a multi-sensor positioning system. On the one hand, the predictable platform nearly removes the variation in execution time, making the delay constant. On the other hand, the parallel and pipeline schedules reduce the computation delay, translating to a shorter sampling period and better closed-loop performance. Furthermore, we perform a design space exploration on various parameters and control performance considering an industrial case study of semiconductor die-bonding equipment.

Keywords: Electrical machine control, Energy systems, Optimal control
Abstract: This work presents a strategy to design an optimal efficiency controller for a complete water pumping system, aiming for both high dynamic performance and high efficiency. The novelty of the developed model is based on an optimisation strategy where a compromise is made between minimizing the electric motor power losses and accurate adjustment of flow rate by balancing efficiency and reliability through adjusting the operation point of the pump. To accomplish this goal, this paper presents the design of an optimal controller which integrates both the Minimum Electric Loss (MEL) control strategy, and the Linear Quadratic Regulator (LQR), augmented by adding integral action and tuned using an adaptive Genetic Algorithm optimization tool (GA). In order to further verify the accuracy of the proposed technique, three performance indices as compared to the conventional PI controller in terms of control input and disturbance rejection. Finally, simulation tests performed show that the proposed optimal can effectively improve the adaptability and flexibility of the water pumping system to several complex working conditions and also has the ability to reduce energy conversion efficiency, leading to a significant impact on energy savings.

Keywords: Optimization, Manufacturing systems, Modeling
Abstract: Micro-additive manufacturing techniques pertaining to material jetting have demonstrated strong applicability in the fields of printed electronic and photonic devices. Nano-scale patterning has been achieved using electrohydrodynamic jet (e-jet) printing, which utilizes a series of high voltage pulses to precisely deposit ink in the form of printed patterns. Previous studies have successfully implemented learning control frameworks to achieve desired printing performance by adjusting the magnitude and timing of the voltage pulse. However, optimization of the input shape from a process-oriented perspective has not been analyzed, and the risks of nozzle clogging and printing regime fluctuations remain as challenges in maintaining stable performance. Additionally, a knowledge gap persists in characterizing the effects of modulating the baseline voltage on temporal and volumetric dynamics of the jetting process, which serve to provide critical time constants in the design of the input shape. This work implements data-driven modelling techniques to quantify the effects of varying the pulsed and baseline voltages while developing a process-oriented optimization algorithm for promoting stable jetting, furthering the foundation for implementation of control strategies for e-jet printing.

Keywords: Biotechnology, Control applications, Manufacturing systems
Abstract: A model-based control system is developed for continuous countercurrent tangential chromatography. The mechanistic model is formulated as a distributed parameter system. The computational cost of the mechanistic model is reduced by reformulating the partial differential equations as ordinary differential equations via the method of characteristics. The model parameters are fit to experimental data for the capture of a monoclonal antibody from clarified bioreactor material. A control problem is formulated for the objective of maximizing system productivity subject to a constraint on the protein recovery, and analyzed to provide insight into the process parameters that strongly affect the closed-loop performance.

Keywords: Healthcare and medical systems, Identification, Modeling
Abstract: This letter examines the Fisher identifiability of two coupled transport processes with substantially different transport coefficients. This examination is motivated by the problem of estimating the efficacy of a novel life support technology for respiratory failure patients. The idea is to circulate an oxygen carrier through the patient’s abdomen, thereby utilizing abdominal gas diffusion for life support. The letter presents a third-order nonlinear model of the coupled dynamics of gas transport in the lungs and abdomen during this treatment. We linearize this model, reduce its order, and analyze its parameter identifiability. The main insight is that the stronger transport process in the lungs acts as a feedback mechanism that weakens the identifiability of the parameter governing the weaker abdominal transport process. Manipulating the stronger transport process through active control and/or passive design can, therefore, improve identifiability. The letter illustrates these insights using Monte Carlo simulation, showing a fourfold improvement in abdominal transport coefficient estimation accuracy through simple experimental redesign.

Keywords: Human-in-the-loop control, Machine learning, Robotics
Abstract: Optimal human-robot interaction (HRI) necessitates the ability to track and compensate nonlinear neuromuscular and biomechanical dynamics that are challenging to identify online during movement. Model-free reinforcement learning approaches are well-suited to identifying such system dynamics through stochastic exploration and subsequent exploitation of learned low-dimensional probabilistic models to maximize reward. However, achieving safe and efficient stochastic exploration in HRI environments is an unsolved challenge. This work presents the development and experimental validation of a Neuromechanical Model-Free Epistemic Risk-Guided Exploration (NeuroMERGE) algorithm for stochastic iterative identification of HRI dynamics, a novel approach which integrates a measurement model of neuromechanical impedances to dynamically constrain the exploration-exploitation tradeoff. We validate NeuroMERGE in the control of a simulated cart-pole system as well as in a soft robotic hand exoskeleton in a case study with three participants. The results demonstrate safe and efficient convergence to stable control policies, achieving performance competitive with model- and learning-based control schemes.

Keywords: Biomedical, Modeling, Human-in-the-loop control
Abstract: This study employs intersection point height frequency analysis to quantitatively assess the balance control strategies used by individuals with Parkinson's disease (PD) during quiet stance. The changes in balance strategy are quantified using a triple inverted pendulum human model with a linear quadratic regulator as the neural balance controller. By considering both translational and angular body accelerations, we extract intersection point frequency curves that contain crucial information about the neuromuscular balance strategy of the PD patients. To contextualize our findings, we compare the observed frequency behavior with previous studies examining quiet stance in individuals without PD. This comprehensive investigation furnishes valuable insights into the disparities between the balance strategies of the PD patients and the healthy counterparts, shedding light on the influence of PD on balance control dynamics. The findings hold promising potential for applications in PD diagnostics and the development of robotic assistive devices for PD patient rehabilitation.

Keywords: Biomedical, Computational methods, Modeling
Abstract: Deep Brain Stimulation (DBS) is an established and powerful treatment method in various neurological disorders. It involves chronically delivering electrical pulses to a certain stimulation target in the brain in order to alleviate the symptoms of a disease. Traditionally, the effect of DBS on neural tissue has been modeled based on the geometrical intersection of the static Volume of Tissue Activated (VTA) and the stimulation target. Recent studies suggest that the Dentato-Rubro-Thalamic Tract (DRTT) may serve as a potential common underlying stimulation target for tremor control in Essential Tremor (ET). However, clinical observations highlight that the therapeutic effect of DBS, especially in ET, is strongly influenced by the dynamic DBS parameters such as pulse width and frequency, as well as stimulation polarity. This study introduces a computational model to elucidate the effect of the stimulation signal shape on the DRTT under neural input. The simulation results suggest that achieving a specific pulse amplitude threshold is necessary before eliciting the therapeutic effect through adjustments in pulse widths and frequencies becomes feasible. Longer pulse widths proved more likely to induce firing, thus requiring a lower stimulation amplitude. Additionally, the modulation effect of bipolar configurations on neural traffic was found to vary significantly depending on the chosen stimulation polarity and the direction of neural traffic. Further, bipolar configurations demonstrated the ability to selectively influence firing patterns in different fiber tracts.

Keywords: Adaptive control, Biomedical, Biological systems
Abstract: The use of electrical current to modulate neurons for autonomic regulation requires the ability to both up-regulate and down-regulate the nervous system. An implanted system employing this electrical neuromodulation would also need to adapt to changes in autonomic state in real-time. Stimulation of autonomic nerves at frequencies in the range 1-30 Hz has been a well-established technique for increasing neural activity. Vagus nerve stimulation (VNS) has been shown to be sensitive to frequency adjustments, which can be used to more precisely control the effect as compared to amplitude modulation. Kilohertz frequency alternating current (KHFAC) is a proven technique for blocking action potential conduction to reduce neural activity. Additionally, KHFAC can be reliably modulated by simple amplitude modulation. Although there are many types of commonly used closed-loop controllers, many conventional methods do not respond well to long system delays or discontinuities. Fuzzy logic control (FLC) is a state-based controller that can describe the discontinuities of the system linguistically and then translate the state transition to a continuous output signal. In our preparation, a single bipolar electrode was placed on the vagus nerve and controlled by a fuzzy logic controller to deliver both stimulation and KHFAC to control heart rate. The FLC was able to both change the heart rate to selected values and maintain the heart rate at a constant value in response to a physiological perturbation.

Keywords: Biomedical, Constrained control, Control applications
Abstract: Mechanical ventilation is a life-saving device for patients who are unable to breathe on their own. In the pressure-controlled ventilation mode, a mechanical ventilator frequently increases and decreases the pressure at the patient's airway; this process induces a flow in an out of the patient's lungs. Prior work has shown that a poor pressure tracking performance can lead to lung injury, and might contribute significantly to the morbidity and mortality of critically ill patients. Also, a large overshoot in the induced flow can cause false ventilator-induced triggered breaths and tachypnoea. Thus, any control scheme designed for mechanical ventilators should ensure that not only the reference pressure profile is tracked, but also the induced flow does not exceed the maximum allowable overshoot. In general, these two objectives are conflicting, and addressing them is challenging due to the unknownness of the system parameters. This paper uncouples the problem of addressing tracking performance from that of guaranteeing safety of patients and proposes a two-level control scheme to tackle the challenge, wherein a low-level controller addresses pressure tracking performance and a high-level controller guarantees safety of patients. Effectiveness of the proposed scheme is evaluated via extensive simulation studies.

Keywords: Fault diagnosis, Identification for control, Fault tolerant systems
Abstract: In this work, we solve the problem of quantifying and mitigating control authority degradation in real time. Here, our target systems are controlled nonlinear affine-in-control evolution equations with finite control input and finite- or infinite-dimensional state. We consider two cases of control input degradation: finitely many affine maps acting on unknown disjoint subsets of the inputs and general Lipschitz continuous maps. These degradation modes are encountered in practice due to actuator wear and tear, hard locks on actuator ranges due to over-excitation, as well as more general changes in the control allocation dynamics. We derive sufficient conditions for identifiability of control authority degradation, and propose a novel real-time algorithm for identifying or approximating control degradation modes. We demonstrate our method on a nonlinear distributed parameter system, namely a one-dimensional heat equation with a velocity-controlled moveable heat source, motivated by autonomous energy-based surgery.

Keywords: Distributed parameter systems, Delay systems, Stability of linear systems
Abstract: Partial Integral Equations (PIEs) have been used to represent both systems with delay and systems of Partial Differential Equations (PDEs) in one or two spatial dimensions. In this paper, we show that these results can be combined to obtain a PIE representation of any suitably well-posed 1D PDE model with constant delay. In particular, we represent these delayed PDE systems as coupled systems of 1D and 2D PDEs, obtaining a PIE representation of both subsystems. Taking the feedback interconnection of these PIE subsystems, we then obtain a 2D PIE representation of the 1D PDE with delay. Next, based on the PIE representation, we formulate the problem of stability analysis as convex optimization of positive operators which can be solved using the PIETOOLS software suite. We apply the result to PDE examples with delay in the state and boundary conditions.

Keywords: Distributed parameter systems, Computational methods
Abstract: We consider Linear Quadratic Regulation (LQR) for the boundary control of the one dimensional, undamped, linear wave equation under Neumann actuation. We present a Riccati partial differential equation, the derivation of which is by the simple and explicit techniques of integration by parts and completing the square. The Fourier expansion of the solution of the Riccati PDE leads to an infinite dimensional algebraic Riccati equation that can be approximately solved by policy iteration. Since the system is undamped, all the open loop eigenvalues lie on the imaginary axis. Under suitable assumptions a Neumann LQR feedback moves all these eigenvalues into the open left half plane. The closed loop eigenvalues converge to the open loop eigenvalues as the wave number increases so the closed loop system is asymptotically stable but not exponentially stable. An interesting fact is that the closed loop modal shapes are complex sinusoids and they appear to converge to real sinusoids as the wave number increases.

Keywords: Reduced order modeling, Nonlinear systems identification, Fluid flow systems
Abstract: This paper proposes a new model reduction method that improves the prediction accuracy of dynamic modes decomposition with control (DMDc), DMD is a data-driven technique that extracts low-order models from high-dimensional complex dynamic systems with actuation. With DMDc, an input-output reduced-order model can be obtained for system identification and prediction. In this work, in order to better capture the nonlinear behavior, an adaptive clustering method is introduced to group the snapshots obtained by experimental data or numerical simulation into several sub-regions that display similar behavior to construct a reduced-order model. Cluster methods with DMDc are combined to construct the local reduced-order model. Furthermore, with the prediction process, new incoming data is fed into the clusters to update the cluster-DMDc reduced order model to obtain more accurate predictions. Time clustering is applied to the snapshots generated by the Burgers' equations with boundary actuation, and the adaptive cluster DMDc reduced-order model outperforms the standard DMD.

Keywords: Differential-algebraic systems, Optimal control, Optimization
Abstract: We study the linear-quadratic (LQ) control problem on a finite-horizon for linear differential-algebraic equations (DAEs) of arbitrary index. By means of a projection, we derive a differential Riccati equation whose solution yields the optimal control. No index reduction is performed. Numerical simulations are given to illustrate the theoretical findings.

Keywords: Optimal control, Stability of linear systems, Linear systems
Abstract: In this paper we investigate the turnpike property for constrained LQ optimal control problem in connection with dissipativity of the control system. We determine sufficient conditions to ensure the turnpike property in the case of a turnpike reference possibly occurring on the boundary of the state constraint set.

Keywords: Optimal control, Stochastic optimal control, Automotive control
Abstract: In this paper, a stochastic Model Predictive Control (S-MPC) approach is developed to efficiently optimize the thermal management of electric vehicles and accommodate scenarios with multiple routes. To account for the uncertainties, the cost function is modified to minimize the expected (average) cost across all possible routes over the prediction horizon. Thermal constraints are treated as soft constraints using slack variables. This approach allows for flexibility in satisfying the constraints while optimizing the performance. Through simulations, the performance of the proposed method is evaluated using a fleet of vehicles. We demonstrate that the proposed method achieves a good trade-off between multiple competing performance metrics. Furthermore, an adaptation strategy is introduced, which dynamically adjusts the penalty weight value. This adaptive approach eliminates the need for offline calibration and further enhances performance. The results indicate that the time-varying penalty weight significantly reduces the total constraint violations by up to 20% without impacting the performance on energy consumption.

Keywords: Modeling, Simulation, Control applications
Abstract: Pumped Two-phase Cooling (PTC) systems use the evaporation and condensation of a refrigerant to provide isothermal, high-heat flux, cooling using minimal pumping power. A basic PTC system consists of a pump to drive refrigerant flow, an evaporator to absorb the heat load, a condenser to reject heat from the system, and a separator to ensure that only liquid refrigerant returns to the pump. Control-oriented dynamic models of these systems are needed to develop model-based controllers capable of safely maximizing the performance and efficiency of the systems. However, existing first-principles modeling approaches are typically not well suited to be directly used in model-based control design. Therefore, this paper proposes a dynamic modeling approach for PTC systems with several key features that result in a model that can be simulated using a fixed-step size numerical solver with a relatively large timestep size. Additionally, a new separator model is proposed that captures the complex mass and energy dynamics within this component that significantly affect the overall behavior of the system. A laboratory-scale experimental PTC system is used to demonstrate the accuracy of this modeling framework and the impact of the key features of the proposed approach. The simulation and experimental results show that a model with only nine dynamic states is able to accurately capture the steady-state and transient pressure and temperature dynamics of the system while using the first-order forward Euler method with a fixed step size of 0.01 seconds to simulate the system.

Keywords: Energy systems, Constrained control, Control applications
Abstract: This paper presents a novel multi-agent-based approach for safety-aware control of energy systems while accounting for sub-system coupling. The proposed method employs graph modeling to represent the dynamics of each sub-system and its control objectives in the energy domain. This unified representation in the energy domain allows for defining each sub-system with an independent control objective as an energy agent. The interactions among energy agents exhibit either collaboration on energy transfer or conflict over energy resource usage. For collaborative scenarios, a control barrier function (CBF)-based quadratic programming approach is utilized to achieve collective energy objectives while respecting individual safety constraints. On the other hand, decision-making in conflicting scenarios is resolved locally through a min-max problem with a CBF payoff function, ensuring the feasibility of a safe solution for all agents under worst-case conditions. The effectiveness of the proposed approach is demonstrated through its application in an electro-thermal system comprising both collaborative and conflicting agents.

Keywords: Network analysis and control, Optimization, Energy systems
Abstract: The need to handle cooling loads more efficiently from geographically near locations has brought attention to the use of district cooling networks. District cooling networks can provide significant energy and economic benefits but only if designed and operated correctly. The location of thermal energy storage (TES) can impact both the operation and performance of the system. We formulate an optimization framework for a simplified cooling network for which we solve for the optimal TES location and system open loop control that reduces the 2-norm of the chiller energy consumption, serving as a surrogate for flattening the energy demand. The benefit of considering storage location is captured using the centrality of the TES in the network. The centrality metric allows us to present the benefit of reducing the centrality of the storage in the optimization objective. It shows that there exists a coupling between the optimal storage location, system operation, and power consumption objective.

Keywords: Energy systems, Machine learning, Kalman filtering
Abstract: Physics-based computational models of vapor compression systems (VCSs) enable high-fidelity simulations but typically require a high-dimensional state representation. Furthermore, the underlying VCS dynamics are stiff, constrained by conservation laws, and only a small fraction of the states can be measured online. While recent advances on constrained extended Kalman filtering (EKF) have provided a systematic framework for estimating states of VCSs using simulation models, two major bottlenecks to efficient implementation include: (i) expensive forward predictions requiring customized stiff solvers; and, (ii) frequent and computationally expensive linearization operations on high-dimensional nonlinear models. In this paper, we circumvent these bottlenecks by constructing neural state-space models (SSMs) from simulation data for which both forward predictions and linearization operations via automatic differentiation can be performed efficiently. In addition, we incorporate physical constraints based on pressure gradients explicitly into the neural SSM architecture, and demonstrate that the physics-constrained model improves the estimation performance compared to an neural SSM that does not enforce the physics information. We integrate the proposed physics-constrained neural SSM within an EKF framework and show that we can accurately reconstruct the states of a Julia-based high-fidelity VCS simulator with high efficiency, outperforming baselines and ablations.

Keywords: Variable-structure/sliding-mode control, Stability of nonlinear systems, Control applications
Abstract: In this letter, a smooth sliding control for robustly regulating a set of identical oscillatory systems, interconnected in parallel and with only one common input for all, is discussed. Our focus is primarily on oscillators resembling the Van der Pol type. To achieve this goal, a control strategy for synchronizing the oscillators is evaluated, using their phase response curve (PRC), thereby aligning them under identical conditions. The proposed control law, the combined synchronization plus regulation control actions, is applied to a flow micro-thermal-fluid cooling system in the two-phase regime, which has similarities to Van der Pol oscillators. In this application, the idea is to control the mass flow rate of the refrigerant fluid circulating in the microchannels and, consequently, the temperature at the walls of these channels, achieving better performance in heat transfer. Simulation results are presented to validate the proposed control strategy.

Keywords: Modeling, Networked control systems, Optimal control
Abstract: Maintaining productivity in computer networks under virus threats has been an ongoing research. Existing works have adopted epidemiological-based ordinary differentiation equations (ODEs) to model virus and antivirus propagation. However, these models tend to oversimplify by not accounting for the heterogeneity among different computer network clusters and ignoring real-world protocol constraints, e.g., nodes cannot communicate simultaneously with nodes in different groups. In this work, we develop a novel model that acknowledges these constraints and incorporates heterogeneity. We first propose a single-cluster ODE model in which both the virus and antivirus propagate. We then generalize this single-cluster model to a model for networks with heterogeneous clusters. Leveraging these models, we formulate the maximum productivity objective as an optimization problem that could be solved using quasi-Newton methods. We also numerically formalize the optimal control's validity in the single-cluster model through Pontryagin's Maximum Principle (PMP). By experimentation and simulation, we find that the optimal control policy follows a bang-bang structure and performs guided prioritization for the heterogeneity of clusters.

Keywords: Modeling, Nonlinear systems identification, Neural networks
Abstract: This paper proposes a method for uncertainty quantification of an autoencoder-based Koopman operator. The main challenge of using the Koopman operator is to design the basis functions for lifting the state. To this end, this paper builds an autoencoder to automatically search the optimal lifting basis functions with a given loss function. We approximate the Koopman operator in a finite-dimensional space with the autoencoder, while the approximated Koopman has an approximation uncertainty. To resolve the problem, we compute a robust positively invariant set for the approximated Koopman operator to consider the approximation error. Then, the decoder of the autoencoder is analyzed by robustness certification against approximation error using the Lipschitz constant in the reconstruction phase. The forced Van der Pol model is used to show the validity of the proposed method. From the numerical simulation results, we confirmed that the trajectory of the true state stays in the uncertainty set centered by the reconstructed state.

Keywords: Modeling, Large-scale systems, Biologically-inspired methods
Abstract: We introduce a model for multi-agent interaction problems to understand how a heterogeneous team of agents should organize its resources to tackle a heterogeneous team of attackers. This model is inspired by how the human immune system tackles a diverse set of pathogens. The key property of this model is a “cross-reactivity” kernel which enables a particular defender type to respond strongly to some attacker types but weakly to a few different types of attackers. We show how due to such cross-reactivity, the defender team can optimally counteract a heterogeneous attacker team using very few types of defender agents, and thereby minimize its resources. We study this model in different settings to characterize a set of guiding principles for control problems with heterogeneous teams of agents, e.g., sensitivity of the harm to sub-optimal defender distributions, and competition between defenders gives near-optimal behavior using decentralized computation of the control. We also compare this model with existing approaches including reinforcement-learned policies, perimeter defense, and coverage control.

Keywords: Identification, Time-varying systems, Modeling
Abstract: This paper presents a novel approach for the identification of linear time-periodic (LTP) systems in continuous time. This method is based on harmonic modeling and consists in converting any LTP system into an equivalent LTI system with infinite dimension. Leveraging specific harmonic properties, we demonstrate that solving this infinite-dimensional identification problem can be reduced to solving a finite-dimensional linear least-squares problem. The result is an approximation of the original solution with an arbitrarily small error. Our approach offers several significant advantages. The first one is closely tied to the inherent LTI characteristic of the harmonic system, along with the Toeplitz structure exhibited by its elements. The second advantage is related to the regularization property achieved through the integral action when computing the phasors from input and state trajectories. Finally, our method avoids the computation of signals' derivative. This sets our approach apart from existing methods that rely on such computations, which can be a notable drawback, especially in continuous-time settings. We provide numerical simulations that convincingly demonstrate the effectiveness of the proposed method, even in scenarios where signals are corrupted by noise.

Keywords: Modeling
Abstract: Minimising cell thermal gradients and the average temperature rise requires an optimal combination of tab and surface cooling methods to leverage their unique advantages. This work presents a computationally efficient two dimensional (2D) thermal model for cylindrical lithium-ion battery cells that is developed based on the Chebyshev Spectral-Galerkin method and allows the independent control of tab and surface cooling channels for effective thermal performance optimisa- tion. This obtained model is validated against a high-fidelity finite element model under the worldwide harmonised light vehicle test procedure (WLTP). Results show that the reduced- order model with as few as two states can predict the spatially resolved temperature distribution throughout the cell, and that in aggressive cooling scenarios, a model order of nine states can improve accuracy by about 84%. It is also shown that even though cooling all sides of the cylindrical cell achieves the lowest average temperature rise, cooling only the top and bottom sides provides minimum radial thermal gradients.

Keywords: Hybrid systems, Automata
Abstract: Barrier certificates enable a deductive approach to safety verification by characterizing an over-approximation of the reachable state space via their level sets. Dual to verification, falsification approaches often rely on a smart search by simulating the system for different operating conditions in the search of an unsafe behavior. While falsification approaches are effective in discovering shallow bugs, they fail to uncover deep counterexamples due to “plateaus” in the search space. For this purpose, we present two characterizations of barrier certificates to provide a deductive approach to falsification. We show these two characterizations are incomparable, i.e, for a fixed template one may falsify the system using one kind but not the other. Finally, we demonstrate the effectiveness of the proposed approaches in our case studies.

Keywords: Hybrid systems, Constrained control
Abstract: This paper proposes a switched reference governor (RG) algorithm to achieve rapid and non-oscilliatory convergence to a given reference signal while satisfying the imposed constraints by switching between a fast controller and a slow controller. The proposed algorithm computes the set of state and admissible reference pairs for both controllers offline. At each iteration, it computes the admissible reference sets for each controller at the current state and activates one of the controllers based on the distance between the state and the reference. After a controller is activated, a lightweight optimization problem is solved to find an admissible reference that is closest to the reference signal. The solution, which is referred to as the virtual reference, is used as the reference signal. Recursive feasibility and convergence of the virtual reference to the given reference signal, among other key properties of the proposed switched RG, are shown and illustrated in a system

Keywords: Hybrid systems, Distributed control, Power systems
Abstract: The broad deployment of phasor measurement units has enabled effective wide-area damping control for enhancing small-signal stability of large and interconnected power systems. However, this requires networked communication between systems that may be subjected to intermittent, noisy, and delayed feedback measurements. In this paper, we present a distributed wide-area damping controller that applies local power injections via a sample-and-hold mechanism to synchronize the states of the interconnected power systems, thereby damping inter-area oscillations. We model the nomi- nal closed-loop system as a hybrid system. Then, leveraging analytical hybrid systems tools, we apply sufficient conditions that guarantee that the set characterizing synchronization is globally exponentially stable. Moreover, due to the hybrid system construction, we show that this set is robust to certain classes of perturbations, which include both perturbations and delays on the communication between the power systems. We demonstrate the damping controller’s performance in a numerical example that considers interconnected heterogeneous nonlinear systems with intermittent communication that is subjected to significant noise and time-delays.

Keywords: Hybrid systems, Estimation, Optimization
Abstract: We consider the problem of estimating a vector of unknown constant parameters for a class of hybrid dynamical systems with bounded delays in the detection of jumps. Using a hybrid systems framework, we propose an algorithm that estimates the jump times of the trajectories and uses stored data to update the parameter estimate at jumps. We show that the algorithm guarantees convergence of the parameter estimate to the true value, except possibly on the intervals wherein detection of jumps is delayed. Simulation results show the merits of the proposed approach.

Keywords: Control over communications, Hybrid systems, Networked control systems
Abstract: We consider the problem of output feedback stabilization of LTI systems under event-triggering implementation. In particular, we assume that both the plant output and the control input are both transmitted over the network in an asynchronous manner. To that end, two independent event-triggering rules are constructed to generate the transmission instants of the submitted signals. The proposed approach is dynamic in the sense that the triggering rules involve internal dynamical variables to allow for further reduction in the communication load. Moreover, the inter-transmission times for both sides of the channel are lower bounded by enforced dwell times to prevent the occurrence of Zeno phenomena. The problem is challenging due to mutual interactions between the sampling errors of the plant output and the control input, which requires careful handling to ensure the closed-loop stability. The triggering mechanisms are designed by emulation as we first ignore the effect of the network and stabilize the plant in continuous-time. Then, the communication constraints are taken into account to derive the triggering conditions such that the stability of the networked control system is preserved. The required conditions are formulated in terms of a linear matrix inequality. The effectiveness of the technique is demonstrated by numerical simulations.

Keywords: Fault tolerant systems, Hybrid systems, Linear systems
Abstract: This study presents a methodology to enhance the operating safety of hybrid unmanned aerial vehicles by employing an active fault-tolerant control technique. The idea is to incorporate the weighted control allocation scheme with integral-sliding mode control law to attain accurate tracking performance while accounting for the impact of actuator faults and failures. One notable benefit of this methodology lies in its ability to attain tracking accuracy in all operational modes of hybrid UAVs through the careful creation of a suitable weighting matrix. The efficiency of the suggested system is demonstrated by numerical simulations conducted on a longitudinal model of an octoplane aircraft. The proposed controller demonstrates satisfactory performance both in nominal conditions and under faults occurring in the elevator and rotors 1, 2, 7, and 8 at 20s and 40s.

Keywords: Stochastic systems, Computational methods, Machine learning
Abstract: The solution of the path structured multimarginal Schr"{o}dinger bridge problem (MSBP) is the most-likely measure-valued trajectory consistent with a sequence of observed probability measures or distributional snapshots. We leverage recent algorithmic advances in solving such structured MSBPs for learning stochastic hardware resource usage by control software. The solution enables predicting the time-varying distribution of hardware resource availability at a desired time with guaranteed linear convergence. We demonstrate the efficacy of our probabilistic learning approach in a model predictive control software execution case study. The method exhibits rapid convergence to an accurate prediction of hardware resource utilization of the controller. The method can be broadly applied to any software to predict cyber-physical context-dependent performance at arbitrary time.

Keywords: Stochastic systems, Cooperative control, Network analysis and control
Abstract: In the study of convergence property of infinite products of stochastic matrices, a pivotal concern revolves around the characterization of a subset from the family of stochastic, indecomposable and aperiodic (SIA) matrices such that the subset is closed under matrix multiplication. Historically, the collection of Sarymsakov matrices stood as the most expansive subset known to possess such a closure property. Consequently, an infinite product involving Sarymsakov matrices guarantees convergence toward a rank-one matrix. In recent times, a subset larger than the Sarymsakov matrix collection has been proposed, demonstrating an equivalent closure property. In this exposition, we establish that an even more extensive col- lection possessing the aforementioned property can be devised utilizing a similar yet generalized approach. During the formulation of our subset, we also address the unresolved quandary of verifying a scrambling matrix by scrutinizing the powers of an SIA matrix. We offer a solution to this quandary by providing a sharp upper bound for the powers required for verification. This particular outcome streamlines the construction process of our extended set. Numerical examples are provided to illustrate our work.

Keywords: Stochastic optimal control, Uncertain systems, Networked control systems
Abstract: In this paper, we develop distributionally robust controllers and observers for Markov Jump Linear Systems (MJLS) with observable Markov modes and unknown transition probabilities that must be inferred from observations. We introduce the notation of distributionally robust stabilizability and detectability, and propose design procedures for both the controller and observer, so that the resulting closed-loop system is mean-square stable with high confidence, by using an empirical estimate of the Markov transition matrix. The second part of the paper deals with networked control systems that are representable as MJLS. The paper closes with a numerical example of a distance controller for a platoon of cars to highlight the benefits of our approach.

Keywords: Stochastic systems, Stability of nonlinear systems, Biological systems
Abstract: The COVID-19 pandemic has reinvigorated mathematical analysis of epidemic spread dynamics. We analytically investigate a partial differential equation (PDE) based, compartmental model of spatiotemporal epidemic spread, incorporating nonlinear infection forces accounting for saturation effects in the infection transmission mechanism. Using higher-order perturbation analysis and computing the local Lyapunov exponent, we find the emergence of dynamic instabilities induced both by the saturation parameter and stochastic environmental forces driving the epidemic spread. Notably, a second-order perturbation is found to be essential to uncover the noise-induced instabilities since they are not observed under first-order perturbations. We also analyze the effects of saturation and noise on such instabilities. Finally, using numerical, stationary solutions of the governing PDEs, we study the formation of spatial patterns of the infection spread corresponding to the instabilities. We find the emergence of diffusion-driven patterns in the deterministic case and noise-induced patterns in cases when diffusion alone does not induce steady-state patterns.

Keywords: Stochastic systems, Stochastic optimal control, LMIs
Abstract: We present new results regarding the stability properties of a stochastic nonlinear quadratic system (NLQS). The paper extends to the stochastic context a previous work concerning the domain of attraction (DA) of the zero equilibrium point of a nonlinear quadratic system. A stabilizing control law is designed by considering the concept of (Omega,alpha)-stability in probability. The devised procedure requires the solution of a convex optimization problem. An example based on a stochastic epidemic model illustrates how to implement the developed approach.

Keywords: Stochastic systems, Stochastic optimal control, Uncertain systems
Abstract: Schrödinger bridge is a stochastic optimal control problem to steer a given initial state density to another, subject to controlled diffusion and deadline constraints. A popular method to numerically solve the Schrödinger bridge problems, in both classical and in the linear system settings, is via contractive fixed point recursions. These recursions can be seen as dynamic versions of the well-known Sinkhorn iterations, and under mild assumptions, they solve the so-called Schrödinger systems with guaranteed linear convergence. In this work, we study a priori estimates for the contraction coefficients associated with the convergence of respective Schrödinger systems. We provide new geometric and control-theoretic interpretations for the same. Building on these newfound interpretations, we point out the possibility of improved computation for the worst-case contraction coefficients of linear SBPs by preconditioning the endpoint support sets.

Keywords: Observers for nonlinear systems, Estimation, Nonlinear output feedback
Abstract: Feedback control typically relies on an estimate of the system state provided by an estimation scheme. These estimates, however, are always affected by errors that have non-negligible impacts on control performance. Various stabilizing and safety-critical control frameworks address this issue, but all require some characterization of the current estimation error to determine when to apply more or less conservative control inputs. Current methods of bounding these errors either take a very coarse worst-case bound or employ computationally expensive time-varying set-valued methods.

This paper fills the missing gap in these works, presenting new deterministic worst-case error bounds for a state estimation scheme for generic nonlinear systems. Crucially, these error bounds can be efficiently computed in real-time and shrink or grow depending on the current system behavior and the current measurement quality. These new, lightweight, ``online'' error bounds can directly interface with the aforementioned measurement-robust control frameworks, resulting in less conservative control actions while retaining safety and stability guarantees.

Keywords: Lyapunov methods, Observers for nonlinear systems
Abstract: Observers for PDEs are themselves PDEs. Therefore, producing real time estimates with such observers is computationally burdensome. For both finite-dimensional and ODE systems, moving-horizon estimators (MHE) are operators whose output is the state estimate, while their inputs are the initial state estimate at the beginning of the horizon as well as the measured output and input signals over the moving time horizon. In this paper we introduce MHEs for PDEs which remove the need for a numerical solution of an observer PDE in real time. We accomplish this using the PDE backstepping method which, for certain classes of both hyperbolic and parabolic PDEs, produces moving-horizon state estimates explicitly. Precisely, to explicitly produce the state estimates, we employ a backstepping transformation of a hard-to-solve observer PDE into a target observer PDE, which is explicitly solvable. The MHEs we propose are not new observer designs but simply the explicit MHE realizations, over a moving horizon of arbitrary length, of the existing backstepping observers. Our PDE MHEs lack the optimality of the MHEs that arose as duals of MPC, but they are given explicitly, even for PDEs. In the paper we provide explicit formulae for MHEs for both hyperbolic and parabolic PDEs, as well as simulation results that illustrate theoretically guaranteed convergence of the MHEs.

Keywords: Observers for nonlinear systems, Fuzzy systems, Biological systems
Abstract: In this paper, a two-stage state interval estimation method is proposed for the basic process of microbial growth in wastewater treatment based on an L_∞ observer and set-membership technique. Firstly, the continuous-time nonlinear microbial growth model is converted to a discrete time Takagi-Sugeno (T-S) fuzzy system to deal with nonlinearities. Next, an L_∞ T-S fuzzy observer is designed for the generated T-S fuzzy uncertain system to generate the state point estimation, then the interval bounds of state estimation error is calculated by combining with ellipsoidal analysis. Furthermore, the interval estimation of the state for the bioprocess in wastewater treatment can be derived from the point estimate of the state and the range of error in state estimation. Ultimately, the effectiveness of the proposed approach of the interval state estimation for wastewater treatment bioprocess is confirmed through simulation.

Keywords: Observers for nonlinear systems, Neural networks, Autonomous systems
Abstract: Accurately estimating the lateral velocity of automatic ground vehicles is a complex task, especially when faced with sensor-sampled measurements and unfamiliar mathematical models. In order to overcome these difficulties, the study presented here proposes a novel approach that makes use of a sampled-data neural network observer. In order to fill in the information gap between successive samples, a compensating injector is introduced to the continuous state observer on which the observer is based. In order to replicate unknown dynamic vehicle systems, a radial basis function neural network is also implemented. A special weight update mechanism is used to update the weights continually. The Lyapunov methodology is used to demonstrate the stability of the suggested method. Experimental findings validate the effectiveness of the sampled-data neural network observer, providing promising insights for improving lateral velocity estimation and enhancing the control and stability of autonomous vehicle systems.