Keywords: Automotive systems, Automotive control, Predictive control for nonlinear systems
Abstract: We propose an integral action nonlinear model predictive controller (NMPC) for trajectory tracking of an articulated vehicle with an uncertain hitching offset. The controller is intended for complex parking maneuvers including forward and backward movement with tight specifications on the lateral positional tracking error of the trailer. In order to assess performance with uncertain hitching offsets, disturbances, and sensor noise, we conduct extensive hardware-in-the-loop simulations using a dSPACE Scalexio unit. With high-grade sensing, we demonstrate that the closed-loop control system achieves a lateral tracking error of <3 [cm] in expectation, and an absolute terminal error of <15 [cm] with high probability p>0.97. The proposed integral action is shown to be essential in achieving this performance, and the efficacy of the proposed NMPC is evaluated by comparison to previously reported MPCs.

Keywords: Automotive control, Traffic control, Optimal control
Abstract: Coordinating the flow of traffic through urban areas with multiple intersections is a complex problem whose solution has the potential to improve safety, increase throughput, and optimize energy efficiency. In addition to controlling traffic lights, the introduction of connected and automated vehicles (CAVs) offers opportunities in terms of additional sensing and actuation points within the traffic network. This paper proposes a centralized and a decentralized implementation for the joint coordination and control of both traffic signals and mixed traffic, including CAVs and human driven vehicles (HDVs), in a network of multiple connected traffic intersections. Mixed-integer linear programming (MILP) is used to compute safe control trajectories for both CAVs and traffic light signals, which minimize overall congestion and fuel consumption. Our approaches are validated using extensive traffic simulations on the SUMO platform and they are shown to provide improvements of around 32-60%, 90-96% and 40-60% in travel time, waiting time and fuel consumption, respectively, when compared to gap-based adaptive and timed traffic lights.

Keywords: Automotive systems, Identification
Abstract: When a heavy-duty vehicle (HDV) operates at the nominal highway speed, over two-thirds of its total resistive force comes from the air drag, contributing to more than half of its fuel consumption. One effective countermeasure to reduce the fuel consumption of HDVs is platooning, which employs connectivity and automated driving technologies to link two or more HDVs in convoy. Platooning allows HDVs to drive closer together and yields improved fuel economy and less CO2 emission thanks to the reduced air drag. Maximizing the energy benefits of an HDV platoon requires quantifying the drag interaction between vehicles. In practice, modeling the drag reduction in a platoon boils down to identifying the relationship between the air drag coefficient and the inter-vehicle distance. Existing approaches to identify the air drag coefficient include vehicle field test, wind tunnel experiment, and computational fluid dynamics simulation, which can howbeit be time-consuming and cost prohibitive. In contrast, this paper proposes an algebraic approach, which relies on onboard-measurable variables, to estimate the air drag coefficient of an HDV in a platoon. Its algebraic nature avoids the classical persistence of excitation condition for parameter identification and can yield the identified parameter almost instantaneously. Simulation results demonstrate its effectiveness and the improved estimation speed over a recursive least squares identifier.

Keywords: Modeling, Automotive control
Abstract: Understanding wet tire/road interactions is critical for predicting unstable operating conditions such as hydroplaning and, therefore, for vehicle safety operation. We present an analytical method to compute water film pressure distribution on the viscous hydrodynamic region between the tire and the ground. The hydrodynamic models and analysis are obtained for the smooth tire surface and tires with transverse tread elements. We present analytical conditions to predict the hydroplaning occurrence. The impact of the wet ground condition on tire/road friction forces is also discussed through the effective length of the contact patch and a LuGre friction model. Simulation results are presented to demonstrate the modeling development. Comparison results with other existing models illustrate the advantage of the proposed model and analysis.

Keywords: Automotive control, Emerging control applications, Optimal control
Abstract: This paper analyzes the xyz-motion planning problem for autonomous vehicles with active suspension systems. A generic nonlinear optimization problem based on a 3D quarter car model is formulated, where vertical motion planning and the knowledge of road surface data are taken into consideration for planning the motion of the vehicle body in 3D space. A novel z-motion planning methodology is proposed and integrated with a sampling-based xyz-motion planning framework. Finally, simulated driving scenarios are presented to illustrate the advantages of using the proposed planning framework.

Keywords: Automotive systems, Learning, Automotive control
Abstract: Advanced driver assistance systems improve the driving comfort and contribute to enhance safety and energy efficiency in automotive traffic. However, whether these systems are actually used, depends on the driver's satisfaction with the system's way of driving. A promising approach to met the driver's individual preferences, is to personalize the assistance system. This paper presents a recursive Gaussian Process based analysis to determine the driver's preferences, during manual vehicle guidance, separately for various driving maneuvers. The recursive process enables an online-capable analysis where no maneuver data has to be stored. In addition, an event detection approach to identify relevant driving situations is proposed. The gained information about the driver's preferences can be accessed by modern assistance systems to individually parameterize the driving behavior for example in curves or for general velocity adjustments at speed limit changes.

Keywords: Learning, Constrained control, Automotive control
Abstract: Evaluating the safety of an autonomous vehicle (AV) depends on the behavior of surrounding agents which can be heavily influenced by factors such as environmental context and informally-defined driving etiquette. A key challenge is in determining a minimum set of assumptions on what constitutes reasonable foreseeable behaviors of other road users for the development of AV safety models and techniques. In this paper, we propose a data-driven AV safety design methodology that first learns "reasonable" behavioral assumptions from data, and then synthesizes an AV safety concept using these learned behavioral assumptions. We borrow techniques from control theory, namely high order control barrier functions and Hamilton-Jacobi reachability, to provide inductive bias to aid interpretability, verifiability, and tractability of our approach. In our experiments, we learn an AV safety concept using demonstrations collected from a highway traffic-weaving scenario, compare our learned concept to existing baselines, and showcase its efficacy in evaluating real-world driving logs.

Keywords: Autonomous robots, Automotive control, Optimal control
Abstract: Path-constrained trajectory optimization research normally focuses on time or energy optimality. However, some applications seek trajectories that satisfy other constraints. In this paper, we formulate a control-minimal time-assigned path-constrained trajectory optimization problem: a mobile ground robot must traverse a given path in a specific amount of time using minimal control effort. Through a nonlinear change of variables, we solve this problem using convex optimization. We evaluate our solution on a scenario from the intelligent transportation domain. An autonomous vehicle must cross an intersection in a specific amount of time while following the turn lane's geometric center.

Keywords: Autonomous robots, Automotive systems, Optimization
Abstract: Safety-guaranteed motion planning is critical for self-driving cars to generate collision-free trajectories. A layered motion planning approach with decoupled path and speed planning is widely used for this purpose. This approach is prone to be suboptimal in the presence of dynamic obstacles. Spatial-temporal approaches deal with path planning and speed planning simultaneously; however, the existing methods only support simple-shaped corridors like cuboids, which restrict the search space for optimization in complex scenarios. We propose to use trapezoidal prism-shaped corridors for optimization, which significantly enlarges the solution space compared to the existing cuboidal corridors-based method. Finally, a piecewise Bézier curve optimization is conducted in our proposed corridors. This formulation theoretically guarantees the safety of the continuous-time trajectory. We validate the efficiency and effectiveness of the proposed approach in numerical and CommonRoad simulations.

Keywords: Automotive control, Robust adaptive control, Multivehicle systems
Abstract: A distributed robust adaptive control framework is proposed for an adaptive cruise control system. The proposed approach is designed based on the model reference adaptive control approach. A robust control term is employed to make the system robust to any bounded disturbances, and a concurrent learning framework is leveraged to ensure the convergence of estimated parameters. The main feature of the developed robust adaptive cruise controller is that it does not require the speed of the lead vehicle. It also considers uncertainties in both position and speed in the double integrator model. The string stability notion of the proposed approach is also investigated, and the performance of the control framework is evaluated in simulations in the presence of parametric uncertainties, disturbances, and noise.

Keywords: Autonomous robots, Control applications, Stochastic optimal control
Abstract: For automated vehicles operating in off-road environments, there is substantial uncertainty in their energy needs and utilization. To account for this uncertainty, we propose a high-confidence global planner that obtains the path with the highest-confidence energy constraints are met. We outline a sampling-based method to approximate the energy stage cost uncertainty as a normal random variable, and then transform the uncertain optimal control problem to a deterministic one that can be solved using standard methods. We couple this with a local nominal model predictive controller that employs a dynamics model of the off-road vehicle on deformable terrains. We show through Monte-Carlo simulations that the framework is robust in the face of uncertainty in terms of energy consumption and outperforms approaches that simply plan for the minimum expected energy consumption.

Keywords: Control applications, Automotive control, Identification for control
Abstract: Spark ignition engines are often calibrated to operate as close to its knock borderline as possible when MBT (maximum brake torque) cannot be achieved. However, the existing combustion cycle-to-cycle variations result in a relative conservative borderline knock control. To reduce these variations, a real-time cycle-wised knock variation control is proposed in this paper using measured exhaust temperature as feedback. Q-Markov COVER (COVariance Equivalent Realization) system identification was used to obtain a linearized engine exhaust system model from spark timing deviation to associated exhaust temperature and knock intensity variations. Accordingly, a Linear–Quadratic–Gaussian (LQG) controller is designed, based on the identified model, to minimizing the knock fluctuations based on exhaust temperature deviations. Note that the cycle-based compensation adds spark timing deviation control to the baseline so that knock combustion variations can be reduced. With the help of the LQG control, the engine bench test shows a significant reduction of knock combustion variations with its variance reduced by 28%.

Keywords: Control applications, Autonomous systems, Modeling
Abstract: A novel approach to the modeling and control of a subactuated aircraft is performed based on Geometric Algebra (GA). The selected platform for analysis is a quad rotorcraft. The derived model leverages objects from GA, such as the rotor, to perform rotations, replacing the need for Euler angles and quaternions. Controllers, which operate exclusively on GA objects, are developed to regulate the altitude, attitude, and translation of the quad rotorcraft. Numerical examples, including way-point navigation and trajectory tracking, illustrate the feasibility of the GA approach.

Keywords: Control applications, Biomedical, Biological systems
Abstract: A widely studied susceptible S(t), infectious I(t), and removed R(t) (SIR) family of deterministic, lumped-parameter models of directly transmitted infectious diseases is considered to estimate the transmission rate assumed to be piecewise constant via a linear, extended-state observer. Then, although the transmission rate is not a control signal in the traditional sense, the application of feedback control design offers guidance in implementing mitigating actions that curb the disease spread. A linearized model at each measurement point is used for offline observer design with the transmission rate treated as an unknown but constant disturbance. The observer-based controller simulations in discrete time explore heuristic policies that may be implemented by public health and government organizations.

Keywords: Control applications, Energy systems, Uncertain systems
Abstract: Power buffers are DC-DC converters where a large capacitor helps shield the DC grid from abrupt load changes. While point of load converters (PoLC)s are mainly tasked with meeting the terminal load requirements, power buffers add inertia to the DC grid during transients. The stochastic behaviour of loads could necessitate an adaptive optimal control strategy for power buffers. The optimal control of power buffers is usually formulated as a nonzero-sum differential game. The load behaviour can be captured using a multivariate probabilistic collocation method (MPCM) to sample its uncertainty. An integral reinforcement learning (IRL) algorithm, applied to the multiplayer differential game, finds the optimal control policy. Simulation studies demonstrate the performance of the IRL-based stochastic optimal control of power buffers in a DC microgrid.

Keywords: Control applications, Materials processing, Chemical process control
Abstract: Inorganic semiconducting quantum dots (QDs) have emerged as a promising alternative to silicon with widespread applications in next-generation displays and highefficiency solar cells. Generally, the optoelectronic properties of QDs are majorly dictated by their bandgap energy (related to their size), which makes it important to accurately predict and control size of QD crystals. Unfortunately, unlike protein or sugar crystallization, there are very few models that describe QD crystallization. Moreover, the existing QD models are either based on computationally demanding multiscale modeling approaches making them unsuitable for direct implementation in a controller framework or based on black-box modeling providing little insight into crystallization kinetics. To address this knowledge gap, we present a population balance equation (PBE)-based model for QD crystallization. Specifically, the PBE along with mass and energy balance equations, growth and nucleation kinetics are decomposed into first-order ordinary differential equations (ODEs) that can be easily solved using present-day python solvers. Further, a model predictive controller (MPC) is demonstrated for set-point tracking of crystal size and distribution (CSD). Also, given the high computational efficiency of the developed simulation it can be directly incorporated within the MPC without the requirement of a surrogate model, thereby reducing the plant-model mismatch. Further, the case study of CdTe QDs, which are widely utilized in displays and solar cells, has been investigated. The simulation results are in good agreement with experimental observations, and the proposed MPC demonstrates effective size-control of CdTe QDs by manipulating the solute-concentration using a semi-batch addition operation. Overall, to the best of our knowledge, the current work is the first instance of utilizing well-established PBE-based crystallization model for accurate modeling and MPC-based control of QDs, and will serve as a foundation for modeling other QD systems.

Keywords: Control applications, Materials processing, Modeling
Abstract: Optical sorting is a key technology for the circular economy and is widely applied in the food, mineral, and recycling industries. Despite its widespread use, one typically resorts to expensive means of adjusting the accuracy, e.g., by reducing the mass flow or changing mechanical or software parameters, which typically requires manual tuning in a lengthy, iterative process. To circumvent these drawbacks, we propose a new layout for optical sorters along with a controller that allows re-feeding of controlled fractions of the sorted mass flows. To this end, we build a dynamic model of the sorter, analyze its static behavior, and show how material recirculation affects the sorting accuracy. Furthermore, we build a model predictive controller (MPC) employing the model and evaluate the closed-loop sorting system using a coupled discrete element–computational fluid dynamics (DEM–CFD) simulation, demonstrating improved accuracy.

Keywords: Control applications, Model/Controller reduction, Modeling
Abstract: Lithium-metal batteries (LMB) are attractive for energy-storage applications because of their high specific energy and energy density. Unlike lithium-ion batteries (LIB), LMB have metallic lithium anodes which introduce complications to modeling their long-term behavior. In particular, a dead-lithium layer grows over time, and this must be described in any battery-management-system (BMS) model to enable producing good long-term estimates of state-of-charge, state-of-health, and power limits. This paper shows how to convert an LMB PDE model from the literature into a reduced-order control-oriented format suitable for implementation in BMS algorithms.

Keywords: Control applications, Modeling, Optimal control
Abstract: We address the challenge of controlling the density of particles in two dimensions by manipulating the electric field acting on the particles immersed in a dielectric fluid. An array of electrodes is used to control the electric field, which applies dielectrophoretic forces to achieve the desired pattern of particle density. To model the motion of a particle, we use a lumped, 2D, capacitive-based, and nonlinear model. We estimate the spatial dependence of the capacitances using electrostatic COMSOL simulations. We formulate an optimal control problem to determine the electrode potentials that will produce the desired particle density pattern. The loss function is defined in terms of the difference between the target density and the particle density at a specific final time. To estimate the particle density, we use a kernel density estimator (KDE) computed from the particle positions that vary with the electrode potentials. The effectiveness of our approach is demonstrated through numerical simulations that illustrate how the particle positions and electrode potentials change when shaping the particle density from a uniform to a Gaussian distribution.

Keywords: Control applications, Predictive control for linear systems, Optimal control
Abstract: The tokamak, a potential candidate for realizing nuclear fusion energy on Earth, uses strong magnetic fields to confine a hot ionized gas (plasma) in a toroidal vacuum chamber. The ability of tokamaks to run in high-performance modes of operation demands advanced control capabilities to regulate the spatial distribution (profile) of several plasma properties such as the safety factor q. A model predictive control (MPC) approach has been followed to further advance such control capabilities for the EAST tokamak. The proposed controllers have the capability of simultaneously regulating the q-profile and the plasma stored energy W by controlling the plasma current I_p, the individual powers of four neutral beam injectors (NBI_{1L}, NBI_{1R}, NBI_{2L}, NBI_{2R}), and the powers of two lower hybrid wave sources with different frequencies (2.45~GHz, 4.60~GHz). An active-set algorithm has been employed to solve the Quadratic Programming (QP) problem arising from the MPC formulation. Initial experimental tests of the MPC show that the real-time optimization is successfully carried out within the time constraints imposed by the dynamics of the plasma.

Keywords: Autonomous robots, Feedback linearization, Optimization
Abstract: Controller design for bipedal walking on dynamic rigid surfaces (DRSes), which are rigid surfaces moving in the inertial frame (e.g., ships and airplanes), remains largely underexplored. This paper introduces a hierarchical control approach that achieves stable underactuated bipedal walking on a horizontally oscillating DRS. The highest layer of our approach is a real-time motion planner that generates desired global behaviors (i.e., center of mass trajectories and footstep locations) by stabilizing a reduced-order robot model. One key novelty of this layer is the derivation of the reduced-order model by analytically extending the angular momentum based linear inverted pendulum (ALIP) model from stationary to horizontally moving surfaces. The other novelty is the development of a discrete-time foot-placement controller that exponentially stabilizes the hybrid, linear, time-varying ALIP. The middle layer translates the desired global behaviors into the robot's full-body reference trajectories for all directly actuated degrees of freedom, while the lowest layer exponentially tracks those reference trajectories based on the full-order, hybrid, nonlinear robot model. Simulations confirm that the proposed framework ensures stable walking of a planar underactuated biped under different swaying DRS motions and gait types.

Keywords: Autonomous robots, Flight control, Intelligent systems
Abstract: Reinforcement learning (RL) may enable fixed-wing unmanned aerial vehicle (UAV) guidance to achieve more agile and complex objectives than typical methods. However, RL has yet struggled to achieve even minimal success on this problem; fixed-wing flight with RL-based guidance has only been demonstrated in literature with reduced state and/or action spaces. In order to achieve full 6-DOF RL-based guidance, this study begins training with imitation learning from classical guidance, a method known as warm-staring (WS), before further training using Proximal Policy Optimization (PPO). We show that warm starting is critical to successful RL performance on this problem. PPO alone achieved a 2% success rate in our experiments. Warm-starting alone achieved 32% success. Warm-starting plus PPO achieved 57% success over all policies, with 40% of policies achieving 94% success.

Keywords: Autonomous robots, Statistical learning, Uncertain systems
Abstract: Autonomous marine vehicles are deployed in oceans and lakes to collect spatio-temporal data. GPS is often used for localization, but is inaccessible underwater. Poor localization underwater makes it difficult to pinpoint where data are collected, to accurately map, or to autonomously explore the ocean and other aquatic environments. This paper proposes the use of multifidelity Gaussian process regression to incorporate data associated with uncertain locations. With the proposed approach, an adaptive sampling algorithm is developed for exploration and mapping of unknown scalar fields. The reconstruction performance based on the multifidelity model is compared to that based on a single-fidelity Gaussian process model that only uses data with known locations, and to that based on a single-fidelity Gaussian process model that ignores the localization error. Numerical results show that the proposed multifidelity approach outperforms both single-fidelity approaches in terms of the reconstruction accuracy.

Keywords: Autonomous robots, Stochastic systems, Optimization
Abstract: This paper explores minimum sensing navigation of robots in environments cluttered with obstacles. The general objective is to find a path plan to a goal region that requires minimal sensing effort. In [1], the information-geometric RRT* (IG-RRT*) algorithm was proposed to efficiently find such a path. However, like any stochastic sampling-based planner, the computational complexity of IG-RRT* grows quickly, impeding its use with a large number of nodes. To remedy this limitation, we suggest running IG-RRT* with a moderate number of nodes, and then using a smoothing algorithm to adjust the path obtained. To develop a smoothing algorithm, we explicitly formulate the minimum sensing path planning problem as an optimization problem. For this formulation, we introduce a new safety constraint to impose a bound on the probability of collision with obstacles in continuous-time, in contrast to the common discrete-time approach. The problem is amenable to solution via the convex-concave procedure (CCP). We develop a CCP algorithm for the formulated optimization and use this algorithm for path smoothing. We demonstrate the efficacy of the proposed approach through numerical simulations.

Keywords: Autonomous robots, Hybrid systems, Machine learning
Abstract: A Cognitive Hybrid Autonomous Motion Planner (CHAMP) is developed for autonomous driving applications in challenging driving scenarios. The proposed hybrid planner unifies a hierarchical rule-based decision-making architecture with Reinforcement Learning (RL). For challenging intersection scenarios, RL agents are trained to replace a subset of the rules in the logical planner. The hybrid planner is systematically tested and benchmarked to demonstrate its effectiveness in handling challenging road scenario with congested and chaotic traffic conditions.

Keywords: Autonomous robots, Vision-based control, Autonomous systems
Abstract: The generation of 3D bounding boxes from a combination of RGB images and depth data is an important area of research for autonomous systems. Additional constraints must be considered in order for any method to be implemented in a small form factor unmanned aerial vehicle (UAV) or other robotic system. In this work, an ``ultra-lightweight'' pipeline is developed and used to generate 3D bounding boxes from aligned RGB-LiDAR images. Different from current implementations, the design of this pipeline was made to maintain a similar performance to more computationally intensive algorithms while also being implementable onboard low SWaP-C systems. The pipeline is demonstrated in a computationally restricted indoor environment by a small rover to navigate around obstacles while searching for a target object.

Keywords: Constrained control, Autonomous systems, Predictive control for nonlinear systems
Abstract: In this paper, we introduce a class of future-focused control barrier functions (ff-CBF) aimed at improving traditionally myopic CBF based control design and study their efficacy in the context of an unsignaled four-way intersection crossing problem for collections of both communicating and non-communicating autonomous vehicles. Our novel ff-CBF encodes that vehicles take control actions that avoid collisions predicted under a zero-acceleration policy over an arbitrarily long future time interval. In this sense the ff-CBF defines a virtual barrier, a loosening of which we propose in the form of a relaxed future-focused CBF (rff-CBF) that allows a relaxation of the virtual ff-CBF barrier far from the physical barrier between vehicles. We study the performance of ff-CBF and rff-CBF based controllers on communicating vehicles via a series of simulated trials of the intersection scenario, and in particular highlight how the rff-CBF based controller empirically outperforms a benchmark controller from the literature by improving intersection throughput while preserving safety and feasibility. Finally, we demonstrate our proposed ff-CBF control law on an intersection scenario in the laboratory environment with a collection of 5 non-communicating AION ground rovers.

Keywords: Estimation, Optimization algorithms, Markov processes
Abstract: Mixed-Observable Markov Decision Processes (MOMDPs) are used to model systems where the state space can be decomposed as a product space of a set of state variables, and the controlling agent is able to measure only a subset of those state variables. In this paper, we consider the setting where we have a set of potential sensors to select for the MOMDP, where each sensor measures a certain state variable and has a selection cost. We formulate the problem of selecting an optimal set of sensors for MOMDPs (subject to certain budget constraints) to maximize the expected infinite-horizon reward of the agent and show that this sensor placement problem is NP-Hard, even when one has access to an oracle that can compute the optimal policy for any given instance. We then study a greedy algorithm for approximate optimization and show that there exist instances of the MOMDP sensor selection problem where the greedy algorithm can perform arbitrarily poorly. Finally, we provide experimental results for the greedy algorithm for randomly generated MOMDP instances and show that, in practice, the greedy algorithm provides near-optimal solutions for many cases, but one cannot provide general theoretical guarantees for its performance. In total, our work establishes fundamental complexity results for the problem of optimal sensor placement for MOMDPs.

Keywords: Optimization algorithms, Optimal control, Energy systems
Abstract: Rising complexity of engineered systems, increasing needs for coordination among specialized design teams, and the emergence of component-based design modalities have created a need for component-based design optimization tools. Further, many modern systems are dynamic, and dynamic performance is a core component of the design objective. This work builds on a hybrid methodology for component-based design optimization by expanding the formulation to dynamic systems. The method is applied to select a planar quadrotor’s components and input trajectory to minimize the to complete a dynamic mission.

Keywords: Agents-based systems, Autonomous systems, Game theory
Abstract: This paper is concerned with the reconnaissance game that involves two mobile agents: the Intruder and the Defender. The Intruder is tasked to reconnoiter a territory of interest (target region) and then return to a safe zone (retreat region), where the two regions are disjoint half-planes, while being chased by the faster Defender. This paper focuses on the scenario where the Defender is not guaranteed to capture the Intruder before the latter agent reaches the retreat region. The goal of the Intruder is to minimize its distance to the target region, whereas the Defender's goal is to maximize the same distance. The game is decomposed into two phases based on the Intruder's myopic goal. The complete solution of the game corresponding to each phase, namely the Value function and state-feedback equilibrium strategies, is developed in closed-form using differential game methods. Numerical simulation results are presented to showcase the efficacy of our solutions.

Keywords: Autonomous robots, Game theory, Autonomous systems
Abstract: We consider a perimeter defense problem in a planar conical environment comprising a turret that has a finite range and non-zero startup time. The turret seeks to defend a concentric perimeter against N>1 intruders. Upon release, each intruder moves radially towards the perimeter with a fixed speed. To capture an intruder, the turret’s angle must be aligned with that of the intruder’s angle and must spend a specified startup time at that orientation. We address offline and online versions of this optimization problem. Specifically, in the offline version, we establish that in general parameter regimes, this problem is equivalent to solving a Travelling Repairperson Problem with Time Windows (TRP-TW). We then identify specific parameter regimes in which there is a polynomial time algorithm that maximizes the number of intruders captured. In the online version, we present a competitive analysis technique in which we establish a fundamental guarantee on the existence of at best (N-1)-competitive algorithms. We also design two online algorithms that are provably 1 and 2-competitive in specific parameter regimes.

Keywords: Robotics, Human-in-the-loop control, Optimization
Abstract: To achieve a safe and seamless human-robot collaboration in intelligent remanufacturing, robot agents should be able to understand human behaviors, predict human future motion, and incorporate motion prediction into their planning process. While most existing human prediction algorithms suffer from poor generalization and huge training data requirements, this paper models the human agent as a rational model seeking to minimize an unknown cost function along the motion trajectory. With such modeling, we design a set of features, such as collision avoidance, maintaining comfort during the motion, and reaching the goal point without too much detour, that could capture human intents during HRC. Maximum-Entropy inverse reinforcement learning is then leveraged to learn the underlying cost function from noisy human demonstrations. The human motion prediction is obtained by solving an optimization problem with a learned cost function. We particularly build an HRC dataset for human-robot-collaborative disassembly tasks and applied the proposed algorithm to this new dataset. Experimental studies are extensively conducted to validate our human motion prediction model.

Keywords: Optimal control, Learning, Predictive control for linear systems
Abstract: We develop a policy iteration-based model-free reinforcement learning (RL) control for nonlinear systems with single input. First, Carleman linearization, a commonly used linearization technique in the Hilbert space, is applied to express the nonlinear system as an infinite-dimensional Carleman state-space model, followed by derivation of an online state-feedback RL controller using state and input data in this infinite-dimensional space. Next, the practicality of using {it any} finite-order truncation of this controller, and the corresponding closed-loop stability of the nonlinear plant is established. Results are validated using two numerical examples, where we show how our proposed method provides solutions close to the optimal control resulting from the model-based Carleman controllers. We also compare our controller to alternative data-driven methods, showing its advantage in terms of shorter learning time.

Keywords: Optimal control, Lyapunov methods, Predictive control for nonlinear systems
Abstract: Safety is one of the fundamental challenges in control theory. Recently, multi-step optimal control problems for discrete-time dynamical systems were formulated to enforce stability, while subject to input constraints as well as safety-critical requirements using discrete-time control barrier functions within a model predictive control (MPC) framework. Existing work usually focus on the feasibility or the safety for the optimization problem, and the majority of the existing work restrict the discussions to relative-degree one control barrier functions. Additionally, the real-time computation is challenging when a large horizon is considered in the MPC problem for relative-degree one or high-order control barrier functions. In this paper, we propose a framework that solves the safety-critical MPC problem in an iterative optimization, which is applicable for any relative-degree control barrier functions. In the proposed formulation, the nonlinear system dynamics as well as the safety constraints modeled as discrete-time high-order control barrier functions (DHOCBF) are linearized at each time step. Our formulation is generally valid for any control barrier function with an arbitrary relative-degree. The advantages of fast computational performance with safety guarantee are analyzed and validated with numerical results.

Keywords: Variational methods, Algebraic/geometric methods, Hybrid systems
Abstract: In this paper, the theory of smooth action-dependent Lagrangian mechanics (also known as contact Lagrangians) is extended to a non-smooth context appropriate for collision problems. In particular, we develop a Herglotz variational principle for non-smooth action-dependent Lagrangians which leads to the preservation of energy and momentum at impacts. By defining appropriately a Legendre transform, we can obtain the Hamilton equations of motion for the corresponding non-smooth Hamiltonian system. We apply the result to a billiard problem in the presence of dissipation.

Keywords: Optimal control, Machine learning, Neural networks
Abstract: Discretized dynamics is widespread in numerical optimization and optimal control. However, the physical system is inherently continuous at the macroscopic scale, thus handling the original continuous-time problem is desirable. In this paper, we focus on learning an optimal policy under the continuous-time finite-horizon optimal control setting. We introduce continuous-time policy optimization (CTPO), which employs the adjoint method to calculate the policy gradient, then implements optimization by gradient descent. The nature of CTPO is to minimize the integral of Hamiltonian over the time horizon to approach optimality, which fits the framework of Pontryagin's minimum principle. We further reveal that the intrinsic connection to its discrete-time counterpart lies in the different order of differentiation and discretization operations. Finally we conduct experiments on a linear quadratic regulator (LQR) and a nonlinear vehicle trajectory tracking task. The results demonstrate that the trained policy retains continuous-time system information and achieves high accuracy.

Keywords: Optimal control, Model/Controller reduction, Nonlinear systems identification
Abstract: In this paper, we introduce a reduced order Iterative Linear Quadratic Regulator (RO-ILQR) approach for the optimal control of nonlinear Partial Differential Equations (PDE). The approach proposes a novel modification of the ILQR technique: it uses the Method of Snapshots to identify a reduced order Linear Time Varying (LTV) approximation of the nonlinear PDE dynamics around a current estimate of the optimal trajectory, utilizes the identified LTV model to solve a time varying reduced order LQR problem to obtain an improved estimate of the optimal trajectory along with a new reduced basis, and iterates till convergence. The proposed approach is tested on the viscous Burger's equation and two phase field models for microstructure evolution in materials, and the results show that there is a significant reduction in the computational burden over the standard ILQR approach, without sacrificing performance.

Keywords: Optimal control, Neural networks, Learning
Abstract: This study provides a lifelong integral reinforcement learning (LIRL)-based optimal tracking scheme for uncertain nonlinear continuous-time (CT) systems using multilayer neural network (MNN). In this LIRL framework, the optimal control policies are generated by using both the critic neural network (NN) weights and single-layer NN identifier. The critic MNN weight tuning is accomplished using an improved singular value decomposition (SVD) of its activation function gradient. The NN identifier, on the other hand, provides the control coefficient matrix for computing the control policies. An online weight velocity attenuation (WVA)-based consolidation scheme is proposed wherein the significance of weights is derived by using Hamilton-Jacobi-Bellman (HJB) error. This WVA term is incorporated in the critic MNN update law to overcome catastrophic forgetting. Lyapunov stability is employed to demonstrate the uniform ultimate boundedness of the overall closed-loop system. Finally, a numerical example of a two-link robotic manipulator supports the theoretical claims.

Keywords: Markov processes, Stochastic optimal control, Stochastic systems
Abstract: We consider the control of a Markov decision process (MDP) that undergoes an abrupt change in its transition kernel (mode). We formulate the problem of minimizing regret under control switching based on mode change detection, compared to a mode-observing controller, as an optimal stopping problem. Using a sequence of approximations, we reduce it to a quickest change detection (QCD) problem with Markovian data, for which we characterize a state-dependent threshold-type optimal change detection policy. Numerical experiments illustrate various properties of our control-switching policy.

Keywords: Markov processes, Optimization algorithms, Stochastic systems
Abstract: There are no computationally feasible algorithms that provide solutions to the finite horizon Risk-sensitive Constrained Markov Decision Process (Risk-CMDP) problem, even for problems with moderate horizon. With an aim to design the same, we derive a fixed-point equation such that the optimal policy of Risk-CMDP is also a solution. We further provide two optimization problems equivalent to the Risk-CMDP. These formulations are instrumental in designing a global algorithm that converges to the optimal policy. The proposed algorithm is based on random restarts and a local improvement step, where the local improvement step utilizes the solution of the derived fixed-point equation; random restarts ensure global optimization. We also provide numerical examples to illustrate the feasibility of our algorithm for inventory control problem with risk-sensitive cost and constraint. The complexity of the algorithm grows only linearly with the time-horizon.

Keywords: Markov processes, Game theory, Control applications
Abstract: This paper studies the deployment of joint moving target defense (MTD) and deception against multi-stage cyberattacks. Given the system equipped with MTD that randomizes between different configurations, we investigate how to allocate a bounded number of sensors in each configuration to optimize the probability of detecting the attack before the attacker achieves its objective. Specifically, two types of sensors are considered: intrusion detectors that are observable by the attacker and stealthy sensors that are not observable to the attacker. We propose a two-step optimization-based approach: Firstly, the defender allocates intrusion detectors assuming the attacker will best respond to evade detection. Secondly, the defender will allocate stealthy sensors, given the best response attack strategy computed in the first step, to further reduce the attacker's chance of success. We illustrate the effectiveness of the proposed methods using a cyber defense example.

Keywords: Markov processes, Optimization algorithms, Optimal control
Abstract: The partially observable Markov decision process with continuous observations has emerged as a popular model for system modeling and sequential decision-making for many real-world problems. The main challenge induced by continuous observations is its high computational complexity in the planning process because it is impossible to enumerate all observations in a continuous space. In this paper, we propose a static observation space partitioning approach to solve a continuous-observation POMDP approximately. Although observation space partitioning approaches have been investigated in the literature, a formal analysis of the partitioning effect on the system performance is still missing. We aim to fill this gap by providing a formal analysis of the approximation error. For this, the belief update function is shown to be Lipschitz continuous for the observation when the observation function satisfies certain properties. With this property, we formally prove that the approximation error of each value iteration is bounded. Meanwhile, we show that the proposed approach can be integrated into the heuristic search value iteration algorithm with performance guarantees. Finally, the advantage of using the static partitioning approach rather than the Monte Carlo sampling approach is validated by experimental results.

Keywords: Fault tolerant systems, Markov processes, H-infinity control
Abstract: This paper investigates the finite-region asynchronous fault-tolerant control problem for 2-D Markov jump systems with sensor faults. Considering the system mode and controller mode are asynchronized, we aim to derive a suitable asynchronous fault-tolerant controller such that the closed-loop 2-D Markov jump systems be finite-region stabilizable and satisfies the given H_{infty} performance index. Applying the stochastic Lyapunov-Krasovskii functional methods, some sufficient conditions are given to obtain the finite-region controller. Finally, a numerical example is used to show the feasibility and validity of the main results.

Keywords: Computational methods, Uncertain systems, Optimal control
Abstract: In multirotor systems, guaranteeing safety while considering unknown disturbances is essential for robust trajectory planning. The Forward reachable set (FRS), the set of feasible states subject to bounded disturbances, can be utilized to identify robust and collision-free trajectories by checking the intersections with obstacles. However, in many cases, the FRS is not calculated in real time and is too conservative to be used in actual applications. In this paper, we address these issues by introducing a nonlinear disturbance observer (NDOB) and an adaptive controller to the multirotor system. We express the FRS of the closed-loop multirotor system with an adaptive controller in augmented state space using Hamilton-Jacobi reachability analysis. Then, we derive a closed-form expression that over-approximates the FRS as an ellipsoid, allowing for real-time computation. By compensating for disturbances with the adaptive controller, our over-approximated FRS can be smaller than other ellipsoidal over-approximations. Numerical examples validate the computational efficiency and the smaller scale of our proposed FRS.

Keywords: Computational methods, Modeling, Robotics
Abstract: We consider the problem of synthesis of safe controllers for nonlinear systems with unknown dynamics using Control Barrier Functions (CBF). We utilize Koopman operator theory (KOT) to associate the (unknown) nonlinear system with a higher dimensional bilinear system and propose a data-driven learning framework that uses a learner and a falsifier to simultaneously learn the Koopman operator based bilinear system and a corresponding CBF. We prove that the learned CBF for the latter bilinear system is also a valid CBF for the unknown nonlinear system by characterizing the ell^2-norm error bound between these two systems. We show that this error can be partially tuned by using the Lipschitz constant of the Koopman based observables. The CBF is then used to formulate a quadratic program to compute inputs that guarantee safety of the unknown nonlinear system. Numerical simulations are presented to validate our approach.

Keywords: Computational methods, Reduced order modeling, Materials processing
Abstract: The rising need for reducing the usage and wastage of paper has mandated the production of mechanically superior papers, and it is known that maintaining a high degree of polymerization (DP) for cellulose microfibers ensures the high tensile strength of the pulp. To mitigate the cellulose degradation and establish the optimum operating strategies of the pulping processes, it is necessary to understand the effect of the operation conditions on cellulose DP. In this sense, we proposed a novel multiscale model which can predict the mesoscopic properties (e.g., Kappa number, and fiber morphology) alongside the microscopic properties (e.g., cellulose DP). The model incorporates a multi-layered kinetic Monte Carlo (kMC) framework that allows us to capture the temporal evolution of Kappa number, fiber morphology, and cellulose DP in a computationally tractable fashion. Furthermore, the model predictions are validated with the experimental results, which are then used to find an optimal operation profile to achieve desired Kappa number and cellulose DP.

Keywords: Computational methods, Control applications, Process Control
Abstract: The process monitoring and control of post-combustion CO2 capture plants (PCCPs) is crucial. In this work, we consider the problem of placing sensors for PCCPs and propose a computationally efficient method to perform sensor placement. The objective is to find the (near-)optimal set of sensors that gives the maximum degree of observability for state estimation while satisfying certain budget constraint. Specifically, we resort to the information contained in the sensitivity matrix calculated around the operating region of a PCCP to quantify the degree of observability of the states corresponding to the placed sensors. The sensor placement problem is formulated as an optimization problem and is efficiently solved by a one-by-one removal approach through orthogonalization. The proposed approach is demonstrated to be applicable and efficient through simulations.

Keywords: Switched systems, Lyapunov methods, Computational methods
Abstract: We study the stability of an equilibrium of arbitrarily switched, autonomous, continuous-time systems through the computation of a common Lyapunov function (CLF). The switching occurs between a finite number of individual subsystems, each of which is assumed to be linear. We present a linear programming (LP) based approach to compute a continuous and piecewise affine (CPA) CLF and compare this approach with different methods in the literature. In particular we compare it with the prevalent use of linear matrix inequalities (LMIs) and semidefinite optimization to parameterize a quadratic common Lyapunov function (QCLF) for the linear subsystems.

Keywords: Control of networks, Numerical algorithms, Biological systems
Abstract: We propose a computational framework for optimal control design of oscillator networks. We first introduce a new system representation to eliminate challenges arising from the periodic nature of oscillators. The representation allows us to consider the general problem of pattern formation for oscillators as a classical point-to-point steering. We then develop a novel control design technique that offers the flexibility to blend the time-optimal and energy-optimal considerations with a parameter of choice. We demonstrate the applicability of the proposed framework to a variety of neuroscience applications.

Keywords: Network analysis and control, Power systems, Control of networks
Abstract: The disturbance response of the angle dynamics for a droop-controlled islanded microgrid is characterized. Specifically, a notion of propagation stability is defined, which is concerned with spatial attenuation vs amplification of input-output responses in the network in a H-infty or H-2 sense. Criteria for propagation stability are developed, phrased in terms of the microgrid's inverter control parameters. The input frequency range over which the network is susceptible to amplification is also characterized, in the case that the criteria are not met. Based on the formal analysis, the design of resilient controls that trade off coherence and disturbance propagation goals is briefly conceptualized. Finally, the propagation stability analysis is illustrated using a 15-bus example microgrid network.

Keywords: Estimation, Cooperative control, Sensor networks
Abstract: In this paper, we study the problem of parameter estimation in a sensor network, where the measurements and updates of some sensors might be arbitrarily manipulated by adversaries. Despite the presence of such misbehaviors, normally behaving sensors make successive observations of an unknown d-dimensional vector parameter and aim to infer its true value by cooperating with their neighbors over a directed communication graph. To this end, by leveraging the so-called dynamic regressor extension and mixing procedure, we transform the problem of estimating the vector parameter to that of estimating d scalar ones. For each of the scalar problem, we propose a resilient combine-then-adapt diffusion algorithm, where each normal sensor performs a resilient combination to discard the suspicious estimates in its neighborhood and to fuse the remaining values, alongside an adaptation step to process its streaming observations. With a low computational cost, this estimator guarantees that each normal sensor exponentially infers the true parameter even if some of them are not sufficiently excited.

Keywords: Transportation networks, Learning, Traffic control
Abstract: We investigate the resilience of learning-based textit{Intelligent Navigation Systems} (INS) to informational flow attacks, which exploit the vulnerabilities of IT infrastructure and manipulate traffic condition data. To this end, we propose the notion of textit{Wardrop Non-Equilibrium Solution} (WANES), which captures the finite-time behavior of dynamic traffic flow adaptation under a learning process. The proposed non-equilibrium solution, characterized by target sets and measurement functions, evaluates the outcome of learning under a bounded number of rounds of interactions, and it pertains to and generalizes the concept of approximate equilibrium. Leveraging finite-time analysis methods, we discover that under the mirror descent (MD) online-learning framework, the traffic flow trajectory is capable of restoring to the Wardrop non-equilibrium solution after a bounded INS attack. The resulting performance loss is of order tilde{mathcal{O}}(T^{beta}) (-frac{1}{2} leq beta < 0 )), with a constant dependent on the size of the traffic network, indicating the resilience of the MD-based INS. We corroborate the results using an evacuation case study on a Sioux-Fall transportation network.

Keywords: Stochastic optimal control, Kalman filtering, Large-scale systems
Abstract: When multiple agents solve cooperatively a joint optimal control problem, it is generally beneficial for them to coordinate their control signals. However, such strategies require that the agents share their local measurements, which may be privacy-sensitive. Motivated by this issue, this paper considers the Linear Quadratic Gaussian (LQG) control problem subject to differential privacy constraints. Differential privacy ensures that the published signals of an algorithm are not too sensitive to the data of any single participating agent. We propose a two-stage architecture for differentially private LQG control and show how to optimize it by leveraging a solution that we previously developed for the Kalman filtering problem. The first stage of this architecture is most easily implemented by a coordinator aggregating and perturbing the agents’ measurements appropriately, but it can also be implemented without a trusted aggregator by using a secure sum protocol. Numerical simulations illustrate the performance improvement of this architecture over simpler alternatives such as directly perturbing the agents' measurements.

Keywords: Model Validation, Randomized algorithms, Traffic control
Abstract: Traffic systems are multi-agent cyber-physical systems whose performance is closely related to human welfare. They work in open environments and are subject to uncertainties from various sources, making their performance hard to verify by traditional model-based approaches. Alternatively, statistical model checking (SMC) can verify their performance by sequentially drawing sample data until the correctness of a performance specification can be inferred with desired statistical accuracy. This work aims to verify traffic systems with privacy, motivated by the fact that the data used may include personal information (e.g., daily itinerary) and get leaked unintendedly by observing the execution of the SMC algorithm. To formally capture data privacy in SMC, we introduce the concept of expected differential privacy (EDP), which constrains how much the algorithm execution can change in the expectation sense when data change. Accordingly, we introduce an exponential randomization mechanism for the SMC algorithm to achieve the EDP. Our case study on traffic intersections by Vissim simulation shows the high accuracy of SMC in traffic model verification without significantly sacrificing computing efficiency. The case study also shows EDP successfully bounding the algorithm outputs to guarantee privacy.

Keywords: Estimation, Fault detection, Uncertain systems
Abstract: Abstract— This paper proposes a novel distributed interval-valued simultaneous state and input observer for linear time-invariant (LTI) systems that are subject to attacks or unknown inputs, injected both on their sensors and actuators. Each agent in the network leverages a singular value decomposition (SVD) based transformation to decompose its observations into two components, one of them unaffected by the attack signal, which helps to obtain local interval estimates of the state and unknown input and then uses intersection to compute the best interval estimate among neighboring nodes. We show that the computed intervals are guaranteed to contain the true state and input trajectories, and we provide conditions under which the observer is stable. Furthermore, we provide a method for designing stabilizing gains that minimize an upper bound on the worst-case steady-state observer error. We demonstrate our algorithm on an IEEE 14-bus power system.

Keywords: Formal verification/synthesis, Autonomous robots, Fault tolerant systems
Abstract: Linear temporal logic (LTL) with the knowledge operator, denoted as KLTL, is a variant of LTL that incorporates what an agent knows or learns at run-time into its specification. Therefore it is an appropriate logical formalism to specify tasks for systems with unknown components that are learned or estimated at run-time. In this paper, we consider a linear system whose system matrices are unknown but come from an a priori known finite set. We introduce a form of KLTL that can be interpreted over the trajectories of such systems. Finally, we show how controllers that guarantee satisfaction of specifications given in fragments of this form of KLTL can be synthesized using optimization techniques. Our results are demonstrated in simulation and on hardware in a drone scenario where the task of the drone is conditioned on its health status, which is unknown a priori and discovered at run-time.

Keywords: Formal verification/synthesis, Optimization
Abstract: This paper considers the design of a planner/tracker for a dynamical system with complex mission specifications expressed as a Signal Temporal Logic (STL) formula. The design consists of two parts: (i) a high-level planner to generate a reference trajectory to satisfy the desired STL formula, and (ii) a low-level controller to generate the control inputs to track the given reference trajectory. Traditionally, these two parts are often designed in a decoupled fashion. Moreover, the planner is often designed using an open-loop plant model that neglects (or only loosely accounts for) the low-level controller. We propose a control synthesis framework in which the high-level planner and the low-level controller are designed simultaneously in an iterative process. We demonstrate our results using a quadcopter scenario and benchmark our results with existing methods in the literature.

Keywords: Formal verification/synthesis, Machine learning, Autonomous systems
Abstract: As neural networks become more integrated into the systems that we depend on for transportation, medicine, and security, it becomes increasingly important that we develop methods to analyze their behavior to ensure that they are safe to use within these contexts. The methods used in this paper seek to certify safety for closed-loop systems with neural network controllers, i.e., neural feedback loops, using backward reachability analysis. Namely, we calculate backprojection (BP) set over-approximations (BPOAs), i.e., sets of states that lead to a given target set that bounds dangerous regions of the state space. The system's safety can then be certified by checking its current state against the BPOAs. While over-approximating BPs is significantly faster than calculating exact BP sets, solving the relaxed problem leads to conservativeness. To combat conservativeness, partitioning strategies can be used to split the problem into a set of sub-problems, each less conservative than the unpartitioned problem. We introduce a hybrid partitioning method that uses both target set partitioning (TSP) and backreachable set partitioning (BRSP) to overcome a lower bound on estimation error that is present when using BRSP. Numerical results demonstrate a near order-of-magnitude reduction in estimation error compared to BRSP or TSP given the same computation time.

Keywords: Formal verification/synthesis, Cooperative control, Optimal control
Abstract: We consider the problem of controlling a heterogeneous multi-agent system required to satisfy temporal logic requirements. Capability Temporal Logic (CaTL) was recently proposed to formalize such specifications for deploying a team of autonomous agents with different capabilities and cooperation requirements. In this paper, we extend CaTL to a new logic CaTL+, which is more expressive than CaTL and has semantics over a continuous workspace shared by all agents. We define a novel robustness metric for CaTL+, which is sound, differentiable almost everywhere and eliminates masking, which is one of the main limitations of existing traditional robustness metrics. We formulate a control synthesis problem to maximize CaTL+ robustness and propose a two-step optimization method to solve this problem. Simulation results are included to illustrate the increased expressivity of CaTL+ and the efficacy of the proposed control synthesis approach.

Keywords: Formal verification/synthesis, Model Validation, Predictive control for linear systems
Abstract: In this paper, we propose a runtime assurance mechanism for online verification of a control system given a signal temporal logic (STL) specification that, at each time step, must hold for the remaining state trajectory. Given a nominal control input, we propose a mechanism that minimally adjusts the input at each time step in order to ensure existence of future inputs that maintain satisfaction of the STL specification. Because STL constraints generally impose requirements on future states, the runtime assurance mechanism also enforces continued satisfaction of the STL constraint evaluated at all past time steps. Lastly, to ensure a feasible input is always available, we provide a novel characterization of a persistently feasible set and require that the system state is always able to reach this set. We formulate this approach as a mixed integer convex program and demonstrate it on examples.

Keywords: Formal verification/synthesis, Markov processes, Stochastic systems
Abstract: Preferences play a key role in determining what goals/constraints to satisfy when not all constraints can be satisfied simultaneously. In this paper, we study how to synthesize preference-satisfying plans in a stochastic system modeled as an MDP, given a (possibly incomplete) combinative preference model over temporally extended goals. We start by introducing new semantics to interpret preferences over infinite plays of the stochastic system. Then, we introduce a new notion of `improvement' to enable comparison between two prefixes of an infinite play. Based on this, we define two solution concepts called Safe and Positively Improving (SPI) and Safe and Almost-Sure Improving (SASI) that enforce improvements with a positive probability and with probability one, respectively. We construct a model called an improvement MDP, in which the synthesis of SPI and SASI strategies that guarantee at least one improvement, reduces to computing positive and almost-sure winning strategies in an MDP. We present an algorithm to synthesize the SPI and SASI strategies that induce multiple sequential improvements. We demonstrate the proposed approach using a robot motion planning problem.

Keywords: Hybrid systems
Abstract: For a broad class of nonlinear systems, we formulate the problem of guaranteeing safety with optimality under constraints. Specifically, we define controlled safety for differential inclusions with constraints on the states and the inputs. Through the use of nonsmooth analysis tools, we show that a continuous optimal control law can be selected from a set-valued constraint capturing the system constraints and conditions guaranteeing safety using control barrier functions. Our results guarantee optimality and safety via a continuous state-feedback law designed using nonsmooth control barrier functions. An example pertaining to obstacle avoidance with a target illustrates our results and the associated benefits of using nonsmooth control barrier functions.

Keywords: Hybrid systems, Optimization, Optimization algorithms
Abstract: This paper proposes global accelerated nonconvex geometric (GANG) optimization algorithms for optimizing a class of nonconvex functions on a compact Lie group, i.e., SO(3). Nonconvex optimization is a challenging problem because the objective function may have multiple critical points, including saddles points. We propose two accelerated geometric algorithms to escape maxima and saddle points using random perturbations. The first algorithm uses the value of the Hessian of the objective functions and random perturbations to escape the undesired critical points. In contrast, the second algorithm uses only the gradient information and random perturbation to escape maxima and saddle points. The results of these geometric algorithms are verified in simulations.

Keywords: Hybrid systems, Identification, Estimation
Abstract: We consider the problem of estimating a vector of unknown constant parameters for a linear regression model whose inputs and outputs are discretized hybrid signals – that is, they are samples of hybrid signals that exhibit both continuous (flow) and discrete (jump) evolution. Using a hybrid systems framework, we propose a hybrid gradient descent algorithm that operates during both flows and jumps. We show that this algorithm guarantees exponential convergence of the parameter estimate to the unknown parameter under a new notion of discretized hybrid persistence of excitation that relaxes the classical discrete-time persistence of excitation condition. Simulation results validate the properties guaranteed by the new algorithm.

Keywords: Hybrid systems, Switched systems, Optimal control
Abstract: This paper presents the jump law of co-states in optimal control for state-dependent switched systems. The number of switches and the switching modes are assumed to be known a priori. A proposed jump law is rigorously derived by theoretical analysis and illustrated by simulation results. An algorithm is then proposed to solve optimal control for state-dependent hybrid systems. Through numerical simulations, we further show that the proposed approach is more efficient than existing methods in solving optimal control for state-dependent switched systems.

Keywords: Hybrid systems, Biological systems, Modeling
Abstract: The impulsive Goodwin's oscillator (IGO) is a hybrid model composed of a third-order continuous linear part and a pulse-modulated feedback. This paper introduces a design problem of the IGO to admit a desired periodic solution. The dynamics of the continuous states represent the plant to be controlled, whereas the parameters of the impulsive feedback constitute design degrees of freedom. The design objective is to select the free parameters so that the IGO exhibits a stable 1-cycle with desired characteristics. The impulse-to-impulse map of the oscillator is demonstrated to always possess a positive fixed point that corresponds to the desired periodic solution; the closed-form expressions to evaluate this fixed point are provided. Necessary and sufficient conditions for orbital stability of the 1-cycle are presented in terms of the oscillator parameters and exhibit similarity to the problem of static output control. An IGO design procedure is proposed and validated by simulation. The nonlinear dynamics of the designed IGO are reviewed by means of bifurcation analysis. Applications of the design procedure to dosing problems in chemical industry and biomedicine are envisioned.

Keywords: Quantized systems, Hybrid systems, Stability of hybrid systems
Abstract: This paper studies the stability and stabilization problems for discrete-time piecewise-affine (PWA) systems with single input and state quantization. The PWA controller is considered to have dependence on the controlled PWA system modes; the adopted logarithmic quantization scheme is in a piecewise form, which is synchronized with the operating mode of the PWA system. A piecewise Lyapunov function that is dependent on the sector-bounded uncertainties of both the control input and the state-feedback signal is constructed. Then, the stability and the stabilization criteria are derived based on the constructed Lyapunov function. The proposed quantized control strategy is illustrated via an application to a simulated temperature control system.

Keywords: Large-scale systems, Network analysis and control, Stability of nonlinear systems
Abstract: This paper investigates the stability of large-scale systems (LSSs) in the presence of subsystems that amplify the perturbations propagated by their neighborhood, possibly leading to undesired behaviors of the overall interconnected system. Then, sufficient conditions ensuring the system trajectories boundedness and the subsequent LSS asymptotic stability in the sense of scalable Mesh Stability are proven to exist. The theoretical results show that there exists a dependence between the stability and the topology of the interconnected system. The obtained framework is then exploited for the stability analysis of a network of electrical microgrids, showing the effectiveness of the theoretical results.

Keywords: Control of networks, Networked control systems, Network analysis and control
Abstract: Minimal Laplacian Controllability problem plays an important role in the field of network control. A new way to construct the Minimum Leader Set is proposed. For S(|S|=4), this work proved that there are two and only two types of MPCSs of tree graphs. To illustrate how to use MPCSs to find all of the Minimum Leader Sets, three examples are given.

Keywords: Networked control systems, Predictive control for linear systems, Optimal control
Abstract: We analyze a cost-minimization problem in which the controller relies on an imperfect timeseries forecast. Forecasting models generate imperfect forecasts because they use anonymization noise to protect input data privacy. However, this noise increases the control cost. We consider a scenario where the controller pays forecasting models incentives to reduce the noise and combines the forecasts into one. The controller then uses the forecast to make control decisions. Thus, forecasting models face a trade-off between accepting incentives and protecting privacy. We propose an approach to allocate economic incentives and minimize costs. We solve a biconvex optimization problem on linear quadratic regulators and compare our approach to a uniform incentive allocation scheme. The resulting solution reduces control costs by 2.5 and 2.7 times for the synthetic timeseries and the Uber demand forecast, respectively.

Keywords: Cooperative control, Network analysis and control, Neural networks
Abstract: The central pattern generator (CPG) is a group of interconnected neurons, existing in biological systems as a control center for oscillatory behaviors. We propose a new approach based on the multivariable harmonic balance to characterize the relationship between the oscillation profile (frequency, amplitude, phase) and interconnections within the CPG, modeled as weakly coupled oscillators. In particular, taking advantage of the weak coupling, we formulate a low-dimensional matrix whose eigenvalue/eigenvector capture the perturbation in the oscillation profile due to the coupling. Then we develop an algorithm to estimate the perturbed oscillation profile of a given CPG, and suggest an optimization to synthesize the interconnections to produce a given oscillation profile.

Keywords: Networked control systems
Abstract: The aim of this paper is to investigate the fixed-time consensus problems of cooperative and antagonistic multi-agent systems (CAMSs) with both antagonistic interactions and external disturbances under directed topologies. Toward this end, a nonlinear control protocol is constructed according to the nearest neighbor information. With the aid of the properties of improved Laplacian potentials, the associated convergence analyses can be developed from the viewpoint of Lyapunov stability theory. It is shown that all the agents can accomplish the bipartite consensus (respectively, state stability) objective within a fixed time under structurally balanced (respectively, unbalanced) signed digraphs in spite of the existing external disturbances. Additionally, simulations are included to validate the developed results.

Keywords: Adaptive control, Neural networks, Uncertain systems
Abstract: In this study, we propose a novel adaptive control architecture, which provides dramatically better performance compared to conventional methods. What makes this architecture unique is the synergistic employment of a traditional, Adaptive Neural Network (ANN) controller and a Long Short-Term Memory (LSTM) network. LSTM structures, unlike the standard feed-forward neural networks, take advantage of the dependencies in an input sequence, which helps predict the evolution of an uncertainty. Through a training method we introduced, the LSTM network learns to compensate for the deficiencies of the ANN controller. This substantially improves the transient response by allowing the controller to quickly react to unexpected events. Through careful simulation studies, we demonstrate that this architecture can improve the estimation accuracy on a diverse set of unseen uncertainties. We also provide an analysis of the contributions of the ANN controller and LSTM network, identifying their individual roles in compensating low and high frequency error dynamics. This analysis provides insight into why and how the LSTM augmentation improves the system's transient response.

Keywords: Adaptive control, Predictive control for linear systems, Estimation
Abstract: In this paper, we propose a combined Magnitude Saturated Adaptive Control (MSAC)-Model Predictive Control (MPC) approach to linear quadratic tracking optimal control problems with parametric uncertainties and input saturation. The proposed MSAC-MPC approach first focuses on a stable solution and parameter estimation, and switches to MPC when parameter learning is accomplished. We show that the MSAC, based on a high-order tuner, leads to parameter convergence to true values while providing stability guarantees. We also show that after switching to MPC, the optimality gap is well-defined and proportional to the parameter estimation error. We demonstrate the effectiveness of the proposed MSAC-MPC algorithm through a numerical example based on a linear second-order, two input, unstable system.

Keywords: Adaptive control, Robust control, Predictive control for linear systems
Abstract: We present Self-Tuning Tube-based Model Predictive Control (STT-MPC), an adaptive robust control algorithm for uncertain linear systems with additive disturbances based on the least-squares estimator and polytopic tubes. Our algorithm leverages concentration results to bound the system uncertainty set with prescribed confidence, and guarantees robust constraint satisfaction for this set, along with recursive feasibility and input-to-state stability. Persistence of excitation is ensured without compromising the algorithm's asymptotic performance or increasing its computational complexity. We demonstrate the performance of our algorithm using numerical experiments.

Keywords: Adaptive control, Switched systems, Identification for control
Abstract: This work proposes a switched model reference adaptive control (S-MRAC) architecture for a multi-input multi-output (MIMO) switched linear system with memory for enhanced learning. A salient feature of the proposed method that separates it from most previous results is the use of memory that store the estimator states at switching and facilitate parameter learning during both active and inactive phases of a subsystem, thereby improving the tracking performance of the overall switched system. Specifically, the learning experience from the previous active duration of a subsystem is retained in the memory and reused when the subsystem is inactive and when the subsystem becomes active again. Parameter convergence is shown based on an intermittent initial excitation (IIE), which is significantly relaxed than the classical persistence of excitation (PE) condition. A common Lyapunov function is considered to ensure closed-loop stability with S-MRAC. Further under IIE, the exponential stability of tracking and parameter estimation error dynamics are guaranteed.

Keywords: Adaptive control, Switched systems, Lyapunov methods
Abstract: Motorized functional electrical stimulation (FES) induced cycling is a rehabilitation intervention and exercise strategy that can benefit people with movement disorders. Power tracking is an objective in which leg muscles are artificially activated to track an active torque trajectory while an electric motor achieves a desired speed (cadence). Technical challenges remain to enhance muscle torque tracking performance since muscles experience saturation, which can induce error build-up. Further, the electric motor controller needs to account for the cross muscle torque input in the kinematic tracking loop and thus reduce potential cycling fluctuations. In this paper, a FES muscle torque tracking controller is designed with an anti-windup term in an integral torque error signal to mitigate the effect of muscle saturation. Then, an adaptive-based concurrent learning controller is developed for the electric motor to track cadence and estimate uncertain constant parameters of the cycle-rider system. The adaptive motor controller embeds the muscle torque (since the muscle controller is implementable) in the regressor and exploits it as a feedforward term in the cadence loop, rather than canceling the muscle torque input as it is usually performed in robust control designs. Globally uniformly ultimately bounded (GUUB) tracking is obtained for the torque tracking objective and exponential cadence tracking and parameter convergence is obtained by the learning controller after a finite excitation condition is satisfied.

Keywords: Spacecraft control, Constrained control, Autonomous systems
Abstract: This tutorial paper discusses the rising need for safe and constrained spacecraft Rendezvous, Proximity Operations, and Docking (RPOD). This class of problems brings with it i) a unique set of equations of motion, ii) a variety of constraints and objectives that are specialized to RPOD, and iii) a number of traditional and current Guidance, Navigation, and Control (GNC) considerations. There are strong connections between the work done in RPOD and a variety of other research domains that have synergistically aided in pushing forward the state-of-the-art. This tutorial paper discusses the above, provides an entry point into the field of spacecraft RPOD, and highlights a selection of open problems that still exist in the field.

Keywords: Constrained control, Adaptive control, Uncertain systems
Abstract: This work applies universal adaptive control to control barrier functions to achieve safe control of dynamical systems with parametric model uncertainties. The proposed approach utilizes the certainty equivalence principle to methodically select a model-parameterized control barrier function and corresponding safety controller from an allowable set with instantaneous parameter estimates. While such a combination does not necessarily yield forward invariance without additional requirements on the barrier function, we show that safety can indeed be established by simply adjusting the adaptation gain online. Simulation results demonstrate the approach.

Keywords: Constrained control, Fault detection, Uncertain systems
Abstract: The barrier function method for safety control typically assumes the availability of full state information. Unfortunately, in many scenarios involving uncertain dynamical systems, full state information is often unavailable. In this paper, we aim to solve the safety control problem for an uncertain single-input single-output system with partial state information. First, we develop a synthesis method that simultaneously creates a barrier function and a dynamic output feedback safety controller. This safety controller guarantees that the unit sub-level set of the barrier function is an invariant set under the uncertain dynamics and disturbances of the system. Then, we build an identifier-based estimator that provides a state estimate affine to the uncertain model parameters of the system. To detect the potential risks of the system, a fault detector uses the state estimate to find an upper bound for the barrier function. The fault detector triggers the safety controller when the system's original action leads to a potential safety issue and resumes the original action when the potential safety issue is resolved by the safety controller.

Keywords: Constrained control, Learning, Neural networks
Abstract: Control barrier functions (CBFs) have been widely used for synthesizing controllers in safety-critical applications. When used as a safety filter, a CBF provides a simple and computationally efficient way to obtain safe controls from a possibly unsafe performance controller. Despite its conceptual simplicity, constructing a valid CBF is well known to be challenging, especially for high-relative degree systems under nonconvex constraints. Recently, work has been done to learn a valid CBF from data based on a handcrafted CBF (HCBF). Even though the HCBF gives a good initialization point, it still requires a large amount of data to train the CBF network. In this work, we propose a new method to learn more efficiently from the collected data through a novel prioritized data sampling strategy. A priority score is computed from the loss value of each data point. Then, a probability distribution based on the priority score of the data points is used to sample data and update the learned CBF. Using our proposed approach, we can learn a valid CBF that recovers a larger portion of the true safe set using a smaller amount of data. The effectiveness of our method is demonstrated in simulation on a two-link arm.

Keywords: Constrained control, Observers for nonlinear systems, Uncertain systems
Abstract: This work presents a safe control design approach that integrates the disturbance observer (DOB) and the control barrier function (CBF) for systems with external disturbances. Different from existing robust CBF results that consider the “worst case” of disturbances, this work utilizes a DOB to estimate and compensate for the disturbances. DOB-CBF-based controllers are constructed with provably safe guarantees by solving convex quadratic programs online, to achieve a better tradeoff between safety and performance. Two types of systems are considered individually depending on the magnitude of the input and disturbance relative degrees. The effectiveness of the proposed methods is illustrated via numerical simulations.

Keywords: Constrained control
Abstract: This paper presents a methodology for ensuring that the composition of multiple Control Barrier Functions (CBFs) always leads to feasible conditions on the control input, even in the presence of input constraints. In the case of a system subject to a single constraint function, there exist many methods to generate a CBF that ensures constraint satisfaction. However, when there are multiple constraint functions, the problem of finding and tuning one or more CBFs becomes more challenging, especially in the presence of input constraints. This paper addresses this challenge by providing tools to 1) decouple the design of multiple CBFs, so that a CBF can be designed for each constraint function independently of other constraints, and 2) ensure that the set composed from all the CBFs together is a viability domain. Thus, a quadratic program subject to all the CBFs simultaneously is always feasible. The utility of this methodology is then demonstrated in simulation for a nonlinear orientation control system.

Keywords: Observers for Linear systems, Sensor networks, Linear systems
Abstract: This paper considers the problem of real-time reconstruction of ocean wave field with a network of discrete wave height sensors. Being able to predict incoming wave characteristics helps individual or collections of wave energy converters to increase the amount of energy that they can capture. In this paper, the wave field is modeled to consist of a frequency spectrum of monotone Airy waves with unknown strengths and phases. Kalman filter based observers are then designed to estimate the wave fields. The observers' performance in reconstructing the wave field accurately is validated in simulation for 1-D and 2-D linear and nonlinear waves. Wave tank experiments have also been performed to validate its ability to reconstruct a wave field in real-time using noisy data obtained from a vision-based wave height sensor.

Keywords: Modeling, Energy systems, Computer-aided control design
Abstract: In this paper, a six-degree-of-freedom tethered rigid kite with a kite-mounted turbine is modeled using Newtonian and Lagrangian formulations supplemented with corresponding kinematic analysis and an Euler-angle representation. In addition, to capture the coupled effects of kite and tether dynamics, the Euler-Bernoulli bending equations are taken into their weak form to be spatially discretized into N-segments utilizing a Galerkin Finite Element Method (FEM) strategy. Consequently, the infinite-dimensional beam governing equations become a finite set of 5(N +1) ordinary time differential equations. The kite and tether dynamics are placed into their state-space form and their interactions are characterized by the force balance at the tip of the tether at which the kite is attached. The formulations obtained in this work provide a baseline for the study of the effect of the tether loads on the energy generation of the kite.

Keywords: Modeling, Lyapunov methods, Computer-aided control design
Abstract: This paper studies passivity-based control of a tethered underwater kite used for energy generation. The mathematical formulation of the motion of a 6-degee-of-freedom (DOF) rigid kite is coupled with the continuous governing equations of a flexible tether. The tether is spatially discretized as N-frame elements so that the intrinsic infinitedimensional set of partial differential equations (PDEs) is reduced to a finite second-order set of ordinary differential equations (ODEs). Using this formulation, a Lyapunov stability analysis is conducted to establish operational conditions on the system parameters and states to achieve a certain level of internal and input-output stability and to provide proof of system trajectory boundedness. Previous passivity-based control schemes on tethered kite systems are used to establish a baseline scheme for the control logic that can accommodate the previously defined tether dynamics. A Lyapunov-based feedback linearization control is imposed on the rotational dynamics of the rigid kite according to overall stability and boundness conditions. Baseline simulation results that compare energy generation levels for decoupled-rigid kite dynamics, tether drag influenced-kite dynamics, and the tether-kite full dynamics are presented.

Keywords: Energy systems, Mechanical systems/robotics, Machine learning
Abstract: This paper presents a reinforcement learning (RL) framework applied for an autonomous underwater vehicle (AUV) path planning, focusing on a specific type of energy-harvesting AUV, entitled marine current turbine (MCT). The proposed RL-based approach improves a classical path planning to adopt with an underwater environment prone to spatiotemporal uncertainties. The path planning problem is formulated to achieve the goal of maximizing the harnessed energy from the MCT subject to the agent dynamics and the spatiotemporal environment constraints. Three RL algorithms, including Q-learning, deep Q-network (DQN), and proximal policy optimization (PPO), are nominated to deal with the path planning over both discrete gridded and continuous underwater environments modeling. The experimental results demonstrate the efficiency of the RL-based approaches in seeking the optimal path in the underwater environment, where further discussion is presented to generalize the proposed approach to other energy-harvesting autonomous vehicles operating in the spatiotemporally varying environment, such as airborne wind turbines.

Keywords: Energy systems, Optimization, Power systems
Abstract: Ocean wave energy has the potential to play a crucial role in the shift to renewable energy. In order to improve wave energy conversion techniques, it is necessary to recognize the sub-optimal nature of traditional sequential design processes due to the interconnectedness of subsystems. A codesign optimization in this paper seeks to include effects of all subsystems within one optimization loop in order to reach a fully optimal design. A width and height sweep serves as a brute force geometry optimization while optimizing the power take-off components and controls using a pseudo-spectral method for each geometry. An investigation of electrical power and mechanical power maximization also outlines the contrasting nature of the two objectives to illustrate electrical power maximization's importance for identifying optimality. The codesign optimization leads to an optimal design with a width of 12 m and a height of 10 m. Ultimately, the codesign optimization leads to a 62% increase in the objective function over the optimal design from a sequential design process while also requiring only about half the power take-off torque.

Keywords: Energy systems, Optimal control, Optimization
Abstract: Control co-design (CCD) explores physical and control design spaces simultaneously to optimize a system’s performance. A commonly used CCD framework aims to achieve open-loop optimal control (OLOC) trajectory while optimizing the physical design variables subject to constraints on control and design parameters. In this study, in contrast with the conventional CCD methods based on OLOC schemes, we present a CCD formulation that explicitly considers a feedback controller. In the formulation, we consider two control laws based on proportional linear and quadratic state feedback, where the control gain is optimized. The simulation results show that the OLOC trajectory could be approximated by a feedback controller. While the total energy generated from the CCD with a feedback controller is slightly lower than that of the CCD with OLOC, it results in a much simpler control structure and more robust performance in the presence of uncertainties and disturbances, making it suitable for real-time control. The study in this paper investigates the performance of optimal hydrokinetic turbine design with a feedback controller in the presence of uncertainties and disturbances to demonstrate the benefits and highlight challenges associated with incorporating the feedback controller explicitly in the CCD stage.

Keywords: Machine learning, Grey-box modeling, Neural networks
Abstract: Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering domains. As opposed to purely data-driven methods, PIML models can be trained from additional information obtained by enforcing physical laws such as energy and mass conservation. More broadly, PIML models can include abstract properties and conditions such as stability, convexity, or invariance. The basic premise of PIML is that the integration of ML and physics can yield more effective, physically consistent, and data-efficient models. This paper aims to provide a tutorial-like overview of the recent advances in PIML for dynamical system modeling and control. Specifically, the paper covers an overview of the theory, fundamental concepts and methods, tools, and applications on topics of: 1) physics-informed learning for system identification; 2) physics-informed learning for control; 3) analysis and verification of PIML models; and 4) physics-informed digital twins. The paper is concluded with a perspective on open challenges and future research opportunities.

Keywords: Computational methods, Control software, Control applications
Abstract: This paper presents a tutorial on the elements of computation in a real-time control system. Unlike conventional computation or even computation in digital signal processing systems, computation in a feedback loop must be sensitive to issues of latency and noise around the loop. This presents some fundamental requirements, limitations, and design constraints not seen in other computational applications. The logic of presenting such a tutorial is that while the computer technology changes at a rapid pace, the principles of how we match that technology to the constraints of a feedback loop remain consistent over the years. We will discuss the different computational chains in a feedback system, ways to conceptualize the effects of time delay and jitter on the system, and present a three-layer-model for programming real-time computations. The tutorial also presents some filter and state-space structures that are useful for real-time computation. It concludes with an overview of the different sample rate ranges currently used in some typical control problems and a short discussion of how business models affect our choices in real-time computation.

Keywords: Process Control, Chemical process control
Abstract: In this study, a learning model predictive control (MPC) algorithm for process dynamic working condition change (DWCC) tasks is proposed. The algorithm continuously compensates for model–plant mismatch (MPM) and improves dynamic performance by predicting multi-step-ahead disturbance from similar DWCC tasks. First, a state-space model augmented by disturbance variables ensures offset-free control for MPM. Second, a dynamic autoencoder is constructed to extract private features from process sequences based on long short-term memory and fully connected networks. DWCC scenarios similar to the current scenario are located from the historical database by calculating the distance between extracted features. Finally, the multi-step-ahead disturbance and its uncertainty representation are predicted through multi-output Gaussian process regression based on the located scenarios. The obtained multi-step-ahead disturbance is incorporated into the state-space MPC framework. A nonlinear case is conducted to demonstrate the effectiveness of the proposed method.

Keywords: Process Control, Chemical process control
Abstract: Recent cyberattacks targeting process control systems have motivated the need for operational technology-based approaches, such as detection schemes that monitor processes for attacks. Chemical processes are normally operated at/near the steady-state for extended periods. To account for this, attack detection schemes may be designed to monitor the process operated near the steady-state. Attack-free transient operation (e.g., during process start-up and set point changes) may render detection schemes designed for steady-state operation ineffective by generating false alarms. In this work, a reachable set-based detection scheme is proposed to monitor the process during transient operation. Additive and multiplicative false data injection attacks (FDIAs) that alter data communicated over the sensor-controller and controller-actuator communication links are considered. Based on the ability of the proposed detection scheme to detect an FDIA, an approach to classify attacks is presented. The reachable set-based detection scheme and attack classification are applied to two illustrative processes.

Keywords: Process Control, Control applications, Chemical process control
Abstract: Fast yet health-conscious and safe optimal charging for lithium-ion batteries is essential for resource efficiency, increased battery lifetime, and overall usability. While quick and resource-efficient charging can be formulated as an optimal control problem, it often cannot be solved in real-time on computationally limited, embedded systems. We build upon a mathematical reformulation of the constrained optimal control problem into hybrid simulations, which allows for computationally efficient solutions and provides operation modes beyond existing charging profiles. We analyze under which conditions this mathematical reformulation can lead to the optimality of the resulting charging protocols. Physics-based battery models are analyzed from a systems theory perspective using controllability and flatness properties, necessary optimality conditions for the charging protocols are established.

Keywords: Process Control, Control applications, Predictive control for nonlinear systems
Abstract: Monitoring the water quality and controlling the feeding are essential functions in balancing fish productivity and shaping fish’s life history in the fish growth process. Currently, most fish feeding processes are conducted manually in different phases and not optimized. The feeding technique influences fish growth through the feed conversion rate. In addition, the high concentration level of ammonia affects the water quality, resulting in fish survival and mass death. Therefore, there is a crucial need to develop control strategies to determine optimal, efficient, and reliable feeding processes and to monitor water quality at the same time. In this paper,We revisit the representative fish growth model describing the total biomass change by incorporating the fish population density and mortality. We specifically focus on relative feeding as a manipulated variable to design traditional and optimal control to track the desired weight reference within the sub-optimal temperature and Disolved Oxygen (DO) profiles under different levels of unionized ammonia (UIA) exposures. Then, we propose an optimal algorithm that optimizes the feeding and water quality of the dynamic fish population growth process. We also show that the model predictive control decreases fish mortality and also reduces food consumption in all different cases by an average of 26.9% compared to the bang-bang controller, 22.6% compared to the PID controller.

Keywords: Process Control, Energy systems, Control applications
Abstract: Electrification and deploying distributed energy systems are two integral strategies to decarbonize buildings. However, integrating buildings to intermittent on-site distributed energy systems and power grids with dynamic carbon intensity requires a much more intelligent building energy management (BEM) system than the current reactive-control-based BEM practice. This study proposed an electricity-mix-responsive model predictive control (MPC) framework for integrated control of building and distributed energy systems considering the dynamics of electricity carbon intensity and prices. A novel linear integrated model, including sub-models of adaptive thermal comfort, building thermodynamics, humidity, space heating, space cooling, water heating, renewable energy system, electric energy storage, and electric vehicle, is developed. A linear MPC controller is developed based on the linear integrated model. The proposed MPC framework is applied to a simulation case study for integrated control of building energy systems and multiple distributed energy resources (solar photovoltaic, electric energy storage, and electric vehicle charging) in a residential test building. The proposed MPC approach vastly reduces the electricity cost by up to 38.3% and carbon emission by up to 25.1%, for the test building, compared to conventional reactive-based control. Meanwhile, the proposed MPC approach largely enhances the test building's thermal comfort and demand flexibility. The case study results also show that maximizing carbon emission reduction does not necessarily degrade the electricity cost-saving in buildings. Instead, they can be optimized simultaneously with the proposed MPC approach.

Keywords: Process Control, Hierarchical control, Energy systems
Abstract: A renewable microgrid using green ammonia and hydrogen for energy storage is proposed in the work. Wind and solar energy are captured as power inputs for water electrolysis to produce hydrogen which can be further transformed to ammonia through the Haber-Bosch process. Gensets are dispatched to generate power from hydrogen or ammonia for meeting residential demands. Local control structures are designed for each module in the framework, which takes hourly commands from an upper level dynamic real-time optimization (D-RTO) layer. Case studies in Duluth, MN are conducted for summer and winter in a 24-hour time horizon, demonstrating the stability of system under disturbances in renewable sources. Results confirm that ammonia is more preferred for long-term energy storage.

Keywords: Process Control, Model/Controller reduction, Control system architecture
Abstract: Many large-scale systems are composed of subsystems operated by decentralized controllers, which are fixed in their structure, yet have parameters to tune. Initial tuning or subsequent adjustments dof those parameters ue to varying operating conditions or changes in the network of interconnected systems, while ensuring stability, performance, and security, pose a challenging task due to the overall complexity and size. Subsystems may not be willing or allowed to expose detailed information for safety and privacy reasons. In some cases, a comprehensive system model might not be available for global tuning, or the resulting problem might be computationally infeasible. To enable meaningful global parameter tuning while allowing for data privacy and security, we propose that the subsystems themselves should provide reduced-order models. These models capture the parametric dependency of the subsystem dynamics on the controller parameters. Specifically, we present a method to construct a region in the subsystems’ parameter space in which the deviation of the subsystem and the reduced-order model stays below a specified error bound and in which both systems are stable. A necessary and sufficient condition for such regions is derived using robust control theory. Notably, sufficiency can be expressed in terms of a linear matrix inequality. We demonstrate the approach by considering the temperature control of a large-scale building complex.

Keywords: Process Control, Predictive control for nonlinear systems, Estimation
Abstract: This paper explores data-assisted cyber-attack awareness and resiliency of optimization-based estimation and control of integrated process systems to malicious attacks on measurement sensors. The proposed optimization-based estimation and control architecture consists of an integrated nonlinear moving horizon estimation (MHE) and model predictive control (MPC), where the MHE estimates the unmeasured state variables of the system required by MPC design. In addition, a measured output data-driven cyberattack detection framework is developed by frequently employing a feedforward neural network during the closed-loop process, identifying the cyberattacks from the interactive network-level dynamics. Finally, the integrated process of benzene alkylation with ethylene to produce ethylbenzene is considered a benchmark to demonstrate the application of cyberattack awareness and resiliency of the proposed control architecture in the presence of different types of adversarial cyberattacks interfering with the temperature measurement sensors.

Keywords: Process Control, Nonlinear output feedback, Optimization
Abstract: An impedance matching between the Radio-Frequency (RF) generator and the equipment is required in order to achieve maximum power transfer or minimum reflection. Different architectures of impedance matching control circuits are utilized in this problem depending on the selection of the tunable elements and topological structure. The matching network may not show expected topology behavior due to unknown elements and parameter drifting. Although there exist suggestions for the selection of feedback variables for various impedance matching control schemes, a comprehensive justification for the feedback variable selection on RF impedance matching is still missing in the literature to our best knowledge. To introduce a systematic approach on the feedback variable selection methodology, a coupling analysis for the MIMO impedance matching problem is introduced using Relative Gain Array (RGA) and interaction index analysis. Two most common matching networks are used for demonstration of the procedure namely L-Type up converting and T-Type considering additional inductor due to additional unknown element in the structure. At the end, a novel interaction coefficient is presented to as a metric for the coupling quantification of impedance matching MIMO problem for 6 candidate feedback variable scenarios. Clearly, one should select feedback variables in the impedance matching control so that the coupling effect is as small as possible. Topology changes due to performance degradation or unknown elements can be monitored with predictive maintenance and health monitoring applications. Hence, the selection of feedback variables can be updated to achieve possible error recovery. Results show that the selection of feedback variables with the aid of proposed systematic methodology enables to achieve higher convergence rate within feasible load impedance region.

Keywords: Process Control, Optimization algorithms, Manufacturing systems
Abstract: The industrial drying process consumes approximately 12% of the total energy used in manufacturing, with the potential for a 40% reduction in energy usage through improved process controls and the development of new drying technologies. To achieve cost-efficient and high-performing drying, multiple drying technologies can be combined in a modular fashion with optimal sequencing and control parameters for each. This paper presents a mathematical formulation of this optimization problem and proposes a framework based on the Maximum Entropy Principle (MEP) to simultaneously solve for both optimal values of control parameters and optimal sequence. The proposed algorithm addresses the combinatorial optimization problem with a non-convex cost function riddled with multiple poor local minima. Simulation results on drying distillers dried grain (DDG) products show up to 12% improvement in energy consumption compared to the most efficient single-stage drying process. The proposed algorithm converges to local minima and is designed heuristically to reach the global minimum.

Keywords: Robust control, Optimal control, Linear systems
Abstract: Closed-loop stability of uncertain linear systems is studied under the state feedback realized by a linear quadratic regulator (LQR). Sufficient conditions are presented that ensure the closed-loop stability in the presence of uncertainty, initially for the case of a non-robust LQR designed for a nominal model not reflecting the system uncertainty. Since these conditions are usually violated for a large uncertainty, a procedure is offered to redesign such a non-robust LQR into a robust one that ensures closed-loop stability under a predefined level of uncertainty. The analysis of this paper largely relies on the concept of inverse optimal control to construct suitable performance measures for uncertain linear systems, which are non-quadratic in structure but yield optimal controls in the form of LQR. The relationship between robust LQR and zero-sum linear quadratic dynamic games is established.

Keywords: Robust control, Optimization, Optimal control
Abstract: We study performance of momentum-based accelerated first-order optimization algorithms in the presence of additive white stochastic disturbances. For strongly convex quadratic problems with a condition number , we determine the best possible convergence rate of continuous-time gradient flow dynamics of order n. We also demonstrate that additional momentum terms do not affect the tradeoffs between convergence rate and variance amplification that exist for gradient flow dynamics with n = 2.

Keywords: Robust control, Predictive control for linear systems
Abstract: We present a novel tube-based data-driven predictive control method for linear systems affected by a bounded addictive disturbance. Our method leverages recent results in the reachability analysis of unknown linear systems to formulate and solve a robust tube-based predictive control problem. More precisely, our approach consists in deriving, from the collected data, a zonotope that includes the true state error set. We show how to guarantee the stability of the resulting error zonotope, which can be exploited to increase the computational efficiency of existing zonotopic data-driven MPC formulations. Results on a double-integrator affected by strong adversarial noise demonstrate the effectiveness of the proposed control approach.

Keywords: Robust control, Quantized systems, Sampled-data control
Abstract: The inherent problem with continuous-time robust control synthesis is that it returns a controller which cannot directly be implemented on a numeric device. The discrete-time robust control synthesis does not fully solve this problem, as the sampling rate is considered as an input hyperparameter, without explicitly performing a selection, and the quantization of the controller coefficients is not encompassed in the synthesis procedure. The aim of this paper is to provide rigorous means to efficiently compute the sampling rate and quantization step for a given continuous regulator in order to maintain the robust stability and robust performance specifications guaranteed in the analog domain, assuming a constant rate and fixed-point arithmetic, using the structured singular value framework and global optimization techniques. A numerical example is further presented and discussed, emphasizing practical implications.

Keywords: Robust control, Uncertain systems, Modeling
Abstract: Tremor is a debilitating oscillation of the limbs that affects millions of people worldwide. Functional electrical stimulation (FES) can reduce tremor by artificially activating opposing muscles, and when mediated by repetitive control (RC), has potential to provide complete suppression. However, all previous RC applications have limited performance due to fatigue, spasticity and modelling error. This paper first applies gap metric analysis to derive robust stability margins for RC subject to model uncertainty. It then formulates a multiple model switched repetitive control (MMSRC) scheme with guaranteed robust performance bounds. Simulation results demonstrate that MMSRC effectively suppresses tremor with realistic levels of identification error, fatigue and spasticity, whereas conventional RC FES schemes are unstable.

Keywords: Robust control, Uncertain systems, Smart structures
Abstract: In this paper, we provide results that describe the largest degree of stability that can be achieved using negative imaginary state feedback control. The achievable degree of stability is related to the zero locations of the transfer function from the control input to the disturbance output of the nominal plant being controlled.

Keywords: Robust control, Uncertain systems, Stability of linear systems
Abstract: This paper focuses on analyzing the robust D-stability of fractional-order systems having uncertain coefficients using fractional-order controllers. Robust D-stability means that each polynomial in a family of an uncertain fractional-order system has all its roots in a prescribed region of the complex plane. By employing the concept of the value set, two distinct methodologies are introduced for scrutinizing the robust D-stability of the system. Although the outcomes of both approaches are equivalent, their computational appeal may differ. The first approach entails a graphical technique for the analysis of robust D-stability, while the second approach furnishes a robust D-stability testing function based on the shape properties of the value set, thereby establishing necessary and sufficient conditions for verifying the robust D-stability of fractional-order systems using fractional-order controllers. Finally, a numerical example is provided to validate the results presented in this paper

Keywords: Robust control, Uncertain systems
Abstract: It has been well understood that the estimation error of uncertainty and disturbance estimator (UDE) can be arbitrarily small provided the bandwidth of UDE is chosen to be sufficiently high. Unfortunately, due to many physical constraints, the allowed bandwidth of UDE is always practically limited, the UDE is not so ideal and its actual estimation performance may not be satisfactory. Motivated by this observation, we formulate a simple inequality constraint on the UDE bandwidth and propose an uncertainty and disturbance estimator with phase-lead compensation (UDE-PLC) to improve the estimation performance under such a constraint. The main idea behind the design is to use the cascade of a first-order phase lead compensator and a first-order Butterworth filter, instead of a single Butterworth filter, to build the estimation relationship. By choosing properly the involved three parameters, the obvious phase lag of the non-ideal Butterworth filter is well compensated and both the disturbance estimation error and trajectory tracking error are reduced by the proposed design. The design specifications and the guideline for parameter tuning are provided to make the philosophy behind the UDE-PLC easy to follow. The effectiveness of UDE-PLC is verified by simulation on a 2-DOF AERO attitude control platform.

Keywords: Robust control, Identification for control
Abstract: The Koopman operator is a promising approach for learning nonlinear dynamics using linear operators in high-dimensional function space. However, due to finite-dimensional approximation and imperfect data, model mismatch can arise, resulting in a discrepancy from the actual nonlinear model. As a result, robustness against model mismatch is a critical objective in Koopman-model-based control design. This paper presents a robust dual-loop control scheme for the finite-dimensional Koopman model to address this issue. Firstly, the biased dynamics of the finite-dimensional Koopman model are illustrated by a nonlinear bilinear motor. Multiple trajectory data sets are assumed with measurement noises and used to identify a Koopman model using the extended Dynamic Mode Decomposition (EDMD). The resulting Koopman model is examined to yield biased dynamics from actual nonlinear dynamics. Then, a robust dual-loop control is designed, consisting of an observer-based state-feedback control for the nominal Koopman model and an additional robust loop to improve robustness. The numerical results show that the dual-loop control can improve the robustness of the Koopman operator against model mismatch compared to simply applying nominal control. At low noise levels, both LQG and dual-loop control can regulate the system. However, at higher noise levels, the LQG control strategy fails to regulate the system, but the dual-loop control drives the system to achieve robust performance against the model mismatch.

Keywords: Robust control, Adaptive control, Optimization
Abstract: Adaptive robust control (ARC) has demonstrated its superiority in handling disturbances and parametric uncertainties in the past decades. However, the conventional ARC designs cannot effectively handle the hard state constraints. To deal with the state constraints while maintaining a good tracking performance and robustness, a two-layer constrained adaptive robust control (CARC) strategy is proposed in this paper. In the outer layer, a planner continuously monitors level of tracking errors. When the tracking errors become large, the planner redesigns the reference trajectory by solving a constrained optimization problem. In the inner layer, a Saturated-ARC controller is synthesized to achieve a high tracking performance in the presence of external disturbances and parametric modeling uncertainties. The interaction between the two layers was analyzed to achieve guaranteed performance. The optimization cost function can be arbitrarily selected based on different needs, with time-optimal trajectory tracking re-planning solved in this paper due to its wider potential applications. The focus of this paper is not on solving the optimization problems, but rather incorporating the existing algorithms into our two-layer structure. Unlike model predictive control (MPC) based strategies, the proposed design does not rely on the fast iterative computation of solving the constrained optimization problem to achieve stability and robustness. Comparative simulations were carried out on an unmatched system. The results demonstrate the improvement of the proposed design over the past ones in dealing with hard state constraints.

Keywords: Human-in-the-loop control, Automotive systems, Control applications
Abstract: This paper presents a human-as-advisor architecture for shared human-machine autonomy in dynamic systems. In the human-as-advisor architecture, the human provides suggested control actions to the autonomous system; the system uses a model of the human controller to ascertain the system's state as perceived by the human. The system combines this information with additional sensor measurements, yielding an improved state estimate. We apply this architecture to the problem of lane-centering an autonomous vehicle in the presence of conflicting lane markings that render the true lane center uncertain. We model conflicting lane markings with a multi-component Gaussian mixture model. The human-suggested course of action is interpreted as an additional sensor measurement, which a Kalman filter is designed to combine with a speedometer and camera for improving the state estimate. With human input from our human-as-advisor architecture, the vehicle centers itself in the lane; without human input, the vehicle does not center itself. We also demonstrate the human-as-advisor architecture is robust to additive output matrix uncertainty and non-linear perturbations in the human model used to interpret the human-suggested control actions.

Keywords: Markov processes, Autonomous robots, Supervisory control
Abstract: Using the context of human-supervised object collection tasks, we explore policies for a robot to seek assistance from a human supervisor and avoid loss of human trust in the robot. We consider a human-robot interaction scenario in which a mobile manipulator chooses to collect objects either autonomously or through human assistance; while the human supervisor monitors the robot's operation, assists when asked, or intervenes if the human perceives that the robot may not accomplish its goal. We design an optimal assistance-seeking policy for the robot using a Partially Observable Markov Decision Process (POMDP) setting in which human trust is a hidden state and the objective is to maximize collaborative performance. We conduct two sets of human-robot interaction experiments. The data from the first set of experiments is used to estimate POMDP parameters, which are used to compute an optimal assistance-seeking policy that is used in the second experiment. For most participants, the estimated POMDP reveals that humans are more likely to intervene when their trust is low and the robot is performing a high-complexity task; and that robot asking for assistance in high-complexity tasks can increase human trust in the robot. Our experimental results show that the proposed trust-aware policy yields superior performance compared with an optimal trust-agnostic policy

Keywords: Hybrid systems, Neural networks, Modeling
Abstract: In this paper, a data-driven neural hybrid system modeling framework via the Maximum Entropy partitioning approach is proposed for complex dynamical system modeling such as human motion dynamics. The sampled data collected from the system is partitioned into segmented data sets using the Maximum Entropy approach, and the mode transition logic is then defined. Then, as the local dynamical description for their corresponding partitions, a collection of small-scale neural networks is trained. Following a neural hybrid system model of the system, a set-valued reachability analysis with low computation cost is provided based on interval analysis and a split and combined process to demonstrate the benefits of our approach in computationally expensive tasks. Finally, a numerical examples of the limit cycle and a human behavior modeling example are provided to demonstrate the effectiveness and efficiency of the developed methods.

Keywords: Robotics, Human-in-the-loop control, Optimization
Abstract: Task-invariant control paradigms can enable lower-limb exoskeletons to provide assistance for their users across various locomotor tasks without prescribing to specific joint kinematics. As an energetic control method, energy shaping can alter a human's body energetics in the closed-loop to provide gait benefits. To obtain the energy shaping law for underactuated systems, a set of nonlinear partial differential equations, called the matching condition, needs to be solved to determine the achievable closed-loop dynamics. However, solving matching conditions for high-dimensional nonlinear systems is generally difficult. In addition, how to define parameters for the closed-loop dynamics that render the optimal exoskeleton assistance remains unclear. In this paper, we proposed a two-layer, human-in-the-loop optimization framework for lower-limb exoskeletons to customize their assistance to human users. The inner-layer optimization finds solutions to the matching condition, meanwhile following the energy trajectories of a virtual reference model defined based on the self-selected gaits of humans and a scaled version of their anatomical parameters. The outer-layer incorporates human-in-the-loop Bayesian Optimization to update reference energy's parameters for reducing metabolic costs. Simulation results on two biped models demonstrate that the proposed framework can solve matching conditions numerically at the selected timestamps and the associated energy shaping strategies can reduce human metabolic cost. Moreover, exoskeletons torques calculated using an able-bodied subject's kinematic data well match human biological torques.

Keywords: Human-in-the-loop control, Constrained control, Time-varying systems
Abstract: This paper introduces control barrier functions for viability kernels, where a control input that enforces the safety of a system exists, to address a human assist control problem under input constraints. This paper also introduces a CBF-based human assist controller that satisfies both state and input constraints if an initial state of a system is contained in viability kernels. We lastly demonstrate how viability kernels are represented by system states and confirm the effectiveness of the proposed controller by computer simulation.

Keywords: Human-in-the-loop control, Control applications, Predictive control for linear systems
Abstract: This article considers irrigation canal control problems where human agents are free to move along the canal temporarily overriding the position of actuators, which are considered to be electromechanical gates. To deal with this issue, the centralized controller is robustified against human interventions by following a tube-based model predictive control approach. To decrease conservatism, the controller considers explicitly the different scenarios for human interventions. Also, the ancillary control law implemented by the tube-based MPC controller is computed using a modular feedback gain that is designed to be resilient against the loss of control inputs. To illustrate the effectiveness of the proposed method, the American Society of Civil Engineers (ASCE) Test Canal 2 is used as a case study.

Keywords: Statistical learning, Genetic regulatory systems, Stochastic systems
Abstract: Accurate inference of biological systems, such as gene regulatory networks and microbial communities, is a key to a deep understanding of their underlying mechanisms. Despite several advances in the inference of regulatory networks in recent years, the existing techniques cannot incorporate expert knowledge into the inference process. Expert knowledge contains valuable biological information and is often reflected in available biological data, such as interventions made by biologists for treating diseases. Given the complexity of regulatory networks and the limitation of biological data, ignoring expert knowledge can lead to inaccuracy in the inference process. This paper models the regulatory networks using Boolean network with perturbation. We develop an expert-enabled inference method for inferring the unknown parameters of the network model using expert-acquired data. Given the availability of information about data-acquiring objectives and expert confidence, the proposed method optimally quantifies the expert knowledge along with the temporal changes in the data for the inference process. The numerical experiments investigate the performance of the proposed method using the well-known p53-MDM2 gene regulatory network.

Keywords: Statistical learning, Optimization, Agents-based systems
Abstract: In this paper, we study the problem of feature selection in distributed stochastic multi-arm bandits, in which M agents work collaboratively to choose optimal actions under the coordination of a central server in order to minimize the total regret. We consider a learning situation where there is a set of feature maps, each map is best suited for a a certain state of the system and the best feature map is unknown to the agent at the time of learning. In our model, an adversary chooses a distribution on the set of possible feature maps and the agents observe only the distribution and the true feature map are unknown to the agents. Our goal is to develop a distributed algorithm that selects a sequence of optimal actions to maximize the cumulative reward. By performing a feature vector transformation we propose an elimination algorithm and prove regret and communications bounds for linearly parametrized reward functions. We implement our algorithm and validate the performance of our approach through numerical simulations.

Keywords: Statistical learning, Fault detection, Kalman filtering
Abstract: A novel dynamic probabilistic latent variable model with exogenous variables (DPLVMX) is proposed in this article to capture system dynamics with the existence of random noises. The dynamic auto-regressive relations between current and past latent variables are extracted in a Markov state-space form in the proposed model. Furthermore, to strengthen the utilization of valuable information in the collected data, a composite loading index is designed to select some interested variables as the exogenous variables, which is explicitly incorporated into the model relations of DPLVMX. An improved DPLVM based monitoring scheme is also designed, where a new dynamic monitoring index is proposed to detect dynamic anomalies. The Tennessee Eastman process is used to illustrate the superiority of the proposed algorithm.

Keywords: Statistical learning, Uncertain systems, Constrained control
Abstract: A supervisory safety filter is developed to minimally modify nominal control inputs to a nonlinear control-affine discrete-time system to ensure satisfaction of potentially time-varying state and input constraints, i.e., safety constraints, with high probability. The system model is known while the environment model, i.e., distribution of additive Gaussian process noise, is unknown. State measurements are used to learn the statistics of the process noise. The safety filter employs a robust optimization problem involving tightening of the safety constraints based on the learned statistics and the corresponding confidence.

Keywords: Genetic regulatory systems, Stochastic systems, Statistical learning
Abstract: Gene regulatory networks (GRNs) consist of multiple interacting genes whose activities govern various cellular processes. The limitations in genomics data and the complexity of the interactions between components often pose huge uncertainties in the models of these biological systems. Meanwhile, inferring/estimating the interactions between components of the GRNs using data acquired from the normal condition of these biological systems is a challenging or, in some cases, an impossible task. Perturbation is a well-known genomics approach that aims to excite targeted components to gather useful data from these systems. This paper models GRNs using the Boolean network with perturbation, where the network uncertainty appears in terms of unknown interactions between genes. Unlike the existing heuristics and greedy data-acquiring methods, this paper provides an optimal Bayesian formulation of the data-acquiring process in the reinforcement learning context, where the actions are perturbations, and the reward measures step-wise improvement in the inference accuracy. We develop a semi-gradient reinforcement learning method with function approximation for learning near-optimal data-acquiring policy. The obtained policy yields near-exact Bayesian optimality with respect to the entire uncertainty in the regulatory network model, and allows learning the policy offline through planning. We demonstrate the performance of the proposed framework using the well-known p53-Mdm2 negative feedback loop gene regulatory network.

Keywords: Optimal control, Automotive systems, Fault tolerant systems
Abstract: The ability to guarantee safety for a given controller is becoming more and more important in the field of autonomous driving. In this paper, we design, implement and compare two safety methods, capable of providing safety for an arbitrary input signal. Possible unsafe controllers ranging from learning algorithms to unknown controllers from an OEM can thus be safely applied to the system. The presented robust model predictive safety filter, based upon an MPC framework, searches for a safe and minimally invasive input. Hence, an algorithm certifying whether the desired control signal is safe or must be altered in order to maintain safety is used. By applying the design to a single track model and the scenario of a double lane-change, the filter shows its capability to provide safety for a badly tuned PID controller. The MPC approach is compared to an invariant set filter that employs a safe control set to keep the vehicle within constraints, identifying the main differences. Additionally, the robust model predictive safety filter scheme successfully ensures safe driving under additive disturbances.

Keywords: Optimal control, Control applications, Electrical machine control
Abstract: In this paper,a robust optimale efficience Controller for a Complete water pumping system is designed based on the Fractional order Integral Sliding Surface (FISTSM) with Linear Quadratic Regulator (LQR) related to the Minimum Electric Loss (MEL) condition and tuned using an adaptive Genetic Algorithm optimization tool (GA). The whole control system is simulated in MATLAB SIMULINK workspace and the results show that the optimal controller allows, at the same time, the maximization of the overall efficiency and stabilization of the discharge flow rate for every operation point of the pumping system, offering a suitable operating mode by balancing efficiency and reliability of the Moto Pump Pipline system. A comparative analysis based on control energy, chattering phenomena, and control robustness has been conducted between the conventional PI, LQR, Integral SuperTwisting Sliding Mode Surface (ISTSMC) and the proposed control strategy FISTSM-LQR for moto pump pipline systems based on the simulated results. Finally, we evaluated the performance of the designed controls, including the Integral Absolute Error (IAE). The results of a simulation demonstrate that the proposed controller proves energy efficiency,robustness achievement, and chattering reduction.

Keywords: Optimal control, Decentralized control, Machine learning
Abstract: We study the scalable multi-agent reinforcement learning (MARL) with general utilities, defined as nonlinear functions of the team's long-term state-action occupancy measure. The objective is to find a localized policy that maximizes the average of the team's local utility functions without the full observability of each agent in the team. By exploiting the spatial correlation decay property of the network structure, we propose a scalable distributed policy gradient algorithm with shadow reward and localized policy that consists of three steps: (1) shadow reward estimation, (2) truncated shadow Q-function estimation, and (3) truncated policy gradient estimation and policy update. Our algorithm converges, with high probability, to epsilon-stationarity with widetilde{mc{O}}(epsilon^{-2}) samples up to some approximation error that decreases exponentially in the communication radius. This is the first result in the literature on multi-agent RL with general utilities that does not require the full observability.

Keywords: Optimal control, Hybrid systems
Abstract: A unique feature of hybrid dynamical systems (systems whose evolution is subject to both continuous- and discrete-time laws) is Zeno trajectories. Usually these trajectories are avoided as they can cause incorrect numerical results as the problem becomes ill-conditioned. However, these are difficult to justifiably avoid as determining when and where they occur is a non-trivial task. It turns out that in optimal control problems, not only can they not be avoided, but are sometimes required in synthesizing the solutions. This work explores the pedagogical example of the bouncing ball to demonstrate the importance of "Zeno control executions."

Keywords: Optimal control, Learning, Observers for Linear systems
Abstract: A key challenge in solving the deterministic inverse reinforcement learning problem online and in real-time is the existence of non-unique solutions. Nonuniqueness necessitates the study of the notion of equivalent solutions and convergence to such solutions. While offline algorithms that result in convergence to equivalent solutions have been developed in the literature, online, real-time techniques that address nonuniqueness are not available. In this paper, a regularized history stack observer is developed to generate solutions that are approximately equivalent. Novel data-richness conditions are developed to facilitate the analysis and simulation results are provided to demonstrate the effectiveness of the developed technique.

Keywords: Optimal control, Optimization algorithms, Computational methods
Abstract: We report numerical results on solving linear-quadratic model predictive control (MPC) problems by exploiting graphics processing units (GPUs). The presented method reduces the MPC problem by eliminating the state variables and applies a condensed-space interior-point method to remove the inequality constraints in the KKT system. The final condensed matrix is positive definite and can be efficiently factorized in parallel on GPU/SIMD architectures. In addition, the size of the condensed matrix depends only on the number of controls in the problem, rendering the method particularly effective when the problem has many states but few inputs and moderate horizon length. Our numerical results for PDE-constrained problems show that the approach is an order of magnitude faster than a standard CPU implementation. We also provide an open-source Julia framework that facilitates modeling (DynamicNLPModels.jl) and solution (MadNLP.jl) of MPC problems on GPUs.

Keywords: Stochastic systems, Stability of nonlinear systems, Lyapunov methods
Abstract: In this paper, we address fixed time stability in probability of discrete-time stochastic dynamical systems. Unlike finite time stability in probability, wherein the finite time almost sure convergence behavior of the dynamical system depends on the system initial conditions, fixed time stability in probability involves finite time stability in probability for which the stochastic settling-time is guaranteed to be independent of the system initial conditions. More specifically, we develop Lyapunov theorems for fixed time stability in probability for Ito-type stationary nonlinear stochastic difference equations including a Lyapunov theorem that involves an exponential inequality of the Lyapunov function that gives rise to a minimum bound on the average stochastic settling-time characterized by the primary and secondary branches of the Lambert W function.

Keywords: Stochastic systems, Hybrid systems, Markov processes
Abstract: Automatically synthesizing controllers for continuous-state nonlinear stochastic systems, while giving guarantees on the probability of satisfying (infinite-horizon) temporal logic specifications crucially depends on abstractions with a quantified accuracy. For this similarity quantification, approximate stochastic simulation relations are often used. To handle the nonlinearity of the system effectively, we use finite-state abstractions based on piecewise-affine approximations together with tailored simulation relations that leverage the local affine structure. In the end, we synthesize a robust controller for a nonlinear stochastic Van der Pol oscillator.

Keywords: Stochastic systems, Markov processes
Abstract: Dissipative dynamical systems provide fundamental connections between physics, dynamical systems theory, and control science and engineering. In the deterministic setting, dissipativity theory has been extensively developed in the literature to provide a general framework for the analysis and design of control systems using an input-state-output system description based on generalized system energy considerations that uses a state-space formalism to link engineering systems with memory to well known physical phenomena. Recently, several results have appeared in the literature extending dissipativity notions to the stochastic setting in order to develop an analogous theory for stochastic dynamical systems. However, unlike the deterministic theory, which can involve either an energy balance or a power balance state dissipation inequality for characterizing system dissipativity, in the stochastic case this equivalence is far more nuanced. In this paper, we develop a general theory for stochastic dissipativity and present general conditions on the system drift and diffusion functions as well as the system energy storage and supply rates to provide an equivalence between the sample path dependent energetic (i.e., supermartingale) and the power balance (i.e., algebraic) forms for characterizing stochastic dissipativity.

Keywords: Quantum information and control, Filtering, Stochastic systems
Abstract: In this paper, we consider an open quantum system undergoing imperfect and indirect measurement. For quantum non-demolition (QND) measurement, we show that the system evolves on an appropriately chosen manifold and we express the exact solution of the quantum filter equation in terms of the solution of a lower dimensional stochastic differential equation. In order to further reduce the dimension of the system under study, we consider the projection on the lower dimensional manifold originally introduced in [1] for the case of perfect measurements. An error analysis is performed to evaluate the precision of this approximate quantum filter, focusing on the case of QND measurement. Simulations suggest the efficiency of the proposed quantum projection filter, even in presence of a stabilizing feedback control which depends on the projection filter.

Keywords: Stochastic systems, Uncertain systems
Abstract: This paper focuses on safe control problems for high-dimensional systems with large uncertainties. A major challenge is the computation load to account for long outlook horizons in large-scale systems. This challenge is tackled using an integration of probabilistic forward invariance, the comparison theorem, and PDE techniques. Specifically, we propose a probabilistic certificate for long-term safety that only requires myopically ensuring linear control constraints and evaluating two-dimensional PDEs regardless of the system dimension. The certificate is constructed by obtaining a long-term safe probability bound as a solution of the PDE using the comparison theorem and applying a new notion of probabilistic forward invariance on the probability bound. The use of forward invariance directly on probabilistic reachability allows our method to carry the former’s computation efficiency and the latter’s control over long-term behaviors. Its capability to efficiently ensure long-term safety for high-dimensional systems can be useful in many large-scale distributed autonomous systems operating with limited onboard resources in latency- critical environments.

Keywords: Finance, Stochastic systems, Uncertain systems
Abstract: A trading system is said to be robust if it generates a robust return regardless of market direction. To this end, a consistently positive expected trading gain is often used as a robustness metric for a trading system. In this paper, we propose a new class of trading policies called the double linear policy in an asset trading scenario when the transaction costs are involved. Unlike many existing papers, we first show that the desired robust positive expected gain may disappear when transaction costs are involved. Then we quantify under what conditions the desired positivity can still be preserved. In addition, we conduct heavy Monte-Carlo simulations for an underlying asset whose prices are governed by a geometric Brownian motion with jumps to validate our theory. A more realistic backtesting example involving historical data for cryptocurrency Bitcoin-USD is also studied.

Keywords: Control applications, Process Control, Materials processing
Abstract: A new model is developed to approximate the multivariable nonlinear sputter process with respect to the argon gas flow and the generator power as the inputs and the argon pressure and the self-bias voltage as the outputs. The identification of the process parameters is discussed based on experimental data. A novel control strategy for sputter processes is presented that applies an offset-free predictive controller based on the approximated model. Experiments are shown to validate the control system.

Keywords: Control applications, Process Control
Abstract: Heat pump water heaters (HPWHs) are more energy-efficient than electric resistance water heaters and have inherent load-shifting potential due to their built-in storage tank. Most HPWHs currently employ rule-based control (RBC) strategies that track a temperature setpoint, regardless of the cost of electricity or marginal grid greenhouse gas (GHG) emissions. Economic model predictive control (MPC) can provide automated load flexibility for HPWHs as it can determine in real-time the optimal operation of the HPWH heat sources based on time-varying factors. For example, time-of-use (TOU) rates can be used by the MPC to minimize the cost of operating the HPWH. However, TOU rates do not directly reflect the actual grid GHG emissions associated with electricity generation. In this work, a method for incorporating the marginal grid GHG emissions rate signal into the MPC cost function is proposed to reduce GHG emissions associated with HPWH use. The resulting multi-objective MPC operating cost and expected marginal grid GHG emissions, while maintaining user comfort. Simulation results demonstrate that the MPC approach can reduce operating costs and GHG emissions with no comfort violations compared to a conventional RBC strategy for HPWHs.

Keywords: Control applications, Stability of nonlinear systems, Multivehicle systems
Abstract: This paper studies the problem of using a group of mobile robots to drive a group of humans to an exit for emergency evacuation. The interactions between the robots and the humans are modeled by a social force model. A novel optimization problem is formulated to synthesize a controller with closed-form expression. Sufficient conditions for global asymptotic stability are established for the humans and the robots. Simulation is conducted to evaluate the proposed controller.

Keywords: Control applications, Stability of nonlinear systems, Variable-structure/sliding-mode control
Abstract: The growing interest in green energy and the necessity of reliable electricity in remote areas take the researchers' interest toward DC microgrids. DC microgrids are exposed to small disturbances in their DC sources due to weather uncertainties and ripples resulting from AC/DC converters in their AC sources. These uncertainties may cause instability in microgrids especially in the presence of constant power loads (CPLs). DC microgrids' stability highly depends on DC bus voltage deviation. This paper proposes a new sliding mode control for a DC microgrid to guarantee the stability of the DC bus voltage.

Keywords: Power electronics, Control applications, Stability of nonlinear systems
Abstract: We investigate the design, implementation, and verification of closed-loop DC-DC switching regulators controlled by using field-programmable gate arrays (FPGAs). These converters are designed to stabilize output voltage and guarantee desired reference voltage profiles in expanded operating envelopes. For systems where supplied energy, voltage, and loads vary, practical control laws must be designed and implemented to meet requirements. These regulators are used in many aerial, automotive, communication, electronic and electromechanical systems. We investigate an FPGA based management system to control power modules and interconnected components. This implies solving problems such as sensing and filtering, components aggregation, interfacing, etc. The system requirements imply design and implementation of minimal complexity control laws for high-performance switching converters. FPGAs enable adaptive control, filtering and estimation to guarantee optimal performance, robustness, and interoperability for a broad range of applications. Our findings are experimentally validated.

Keywords: Grey-box modeling, Machine learning, Control applications
Abstract: In order to improve the control performance of vapor compression cycles (VCCs), it is often necessary to construct accurate dynamical models of the underlying thermo-fluid dynamics. These dynamics are represented by complex mathematical models that are composed of large systems of nonlinear and numerically stiff differential algebraic equations (DAEs). The effects of nonlinearity and stiffness may be ameliorated by using physics-based models to describe characteristic system behaviors, and approximating the residual (unmodeled) dynamics using neural networks. In these so-called `physics-augmented' or `physics-informed' machine learning approaches, the learning problem is often solved by jointly estimating parameters of the physics component model and weights of the network. Furthermore, such approaches also often assume the availability of full-state information, which typically are not available in practice for energy systems such as VCCs after deployment. Rather than concurrently performing state/parameter estimation and network training, which often leads to numerical instabilities, we propose a framework for decoupling the network training from the joint state/parameter estimation problem by employing state-constrained Kalman smoothers customized for VCC applications. We show the effectiveness of our proposed framework on a Julia-based, high-fidelity simulation environment calibrated to a model of a commercially-available VCC and achieve an accuracy of 98% calculated over 24 states and multiple initial conditions under realistic operating conditions.

Keywords: Automotive systems, Uncertain systems, Autonomous robots
Abstract: We develop a novel framework to assess the risk of misperception in a traffic sign classification task in the presence of exogenous noise. We consider the problem in an autonomous driving setting, where visual input quality gradually improves due to improved resolution, and less noise since the distance to traffic signs decreases. Using the estimated perception statistics obtained using the standard classification algorithms, we aim to quantify the risk of misperception to mitigate the effects of imperfect visual observation. By exploring perception outputs, their expected high-level actions, and potential costs, we show the closed-form representation of the conditional value-at-risk (CVaR) of misperception. Several case studies support the effectiveness of our proposed methodology.

Keywords: Kalman filtering, Estimation, Observers for Linear systems
Abstract: Adversarially robust training has been shown to reduce the susceptibility of learned models to targeted input data perturbations. However, it has also been observed that such adversarially robust models suffer a degradation in accuracy when applied to unperturbed data sets, leading to a robustness-accuracy tradeoff. Inspired by recent progress in the adversarial machine learning literature which characterize such tradeoffs in simple settings, we develop tools to quantitatively study the performance-robustness tradeoff between nominal and robust state estimation. In particular, we define and analyze a novel adversarially robust Kalman Filtering problem. We show that in contrast to most other problem instances in adversarial machine learning, we can precisely derive the adversarial perturbation in the Kalman Filtering setting. We provide an algorithm to find this optimal adversarial perturbation given data realizations, and develop upper and lower bounds on the adversarial state estimation error in terms of the standard (non-adversarial) estimation error and the spectral properties of the resulting observer. Through these results, we show a natural connection between a filter's robustness to adversarial perturbation and underlying control theoretic properties of the system being observed, namely the spectral properties of its observability gramian.

Keywords: Robust adaptive control, Vision-based control, Autonomous systems
Abstract: Autonomous systems increasingly rely on machine learning techniques to transform high-dimensional raw inputs into predictions that are then used for decision-making and control. However, it is often easy to maliciously manipulate such inputs and, as a result, predictions. While effective techniques have been proposed to certify the robustness of predictions to adversarial input perturbations, such techniques have been disembodied from control systems that make downstream use of the predictions. We propose the first approach for composing robustness certification of predictions with respect to raw input perturbations with robust control to obtain certified robustness of control to adversarial input perturbations. We use a case study of adaptive vehicle control to illustrate our approach and show the value of the resulting end-to-end certificates through extensive experiments.

Keywords: Formal verification/synthesis, Learning, Neural networks
Abstract: In this paper, we consider the problem of synthesizing a controller in the presence of uncertainty such that the resulting closed-loop system satisfies certain hard constraints while optimizing certain (soft) performance objectives. We assume that the hard constraints encoding safety or mission-critical specifications are expressed using Signal Temporal Logic (STL), while performance is quantified using standard cost functions on system trajectories. To ensure satisfaction of the STL constraints, we algorithmically obtain control barrier functions (CBFs) from the STL specifications. We model controllers as neural networks (NNs) and provide an algorithm to train the NN parameters to simultaneously optimize the performance objectives while satisfying the CBF conditions (with a user-specified robustness margin). We evaluate the risk incurred by the trade-off between the robustness margin of the system and its performance using the formalism of risk measures. We demonstrate our approach on challenging nonlinear control examples such as quadcopter motion planning and a unicycle.

Keywords: Learning, Iterative learning control, Optimal control
Abstract: Incorporating risk in the decision-making process has been shown to lead to significant performance improvement in optimal control and reinforcement learning algorithms. We construct a temporal-difference risk-sensitive reinforcement learning algorithm using the exponential criteria commonly used in risk-sensitive control. The proposed method resembles an actor-critic architecture with the ‘actor’ implementing a policy gradient algorithm based on the exponential of the reward-to-go, which is estimated by the ‘critic’. The novelty of the update rule of the ‘critic’ lies in the use of a modified objective function that corresponds to the underlying multiplicative Bellman's equation. Our results suggest that the use of the exponential criteria accelerates the learning process and reduces its variance, i.e., risk-sensitiveness can be utilized by actor-critic methods and can lead to improved performance.

Keywords: Networked control systems, Network analysis and control, Control of networks
Abstract: We develop a framework to assess the risk of cascading failures when a team of agents aims to rendezvous in time in the presence of exogenous noise and communication time-delay. The notion of value-at-risk (VaR) measure is used to evaluate the risk of cascading failures (i.e., waves of large fluctuations) when some agents have failed to rendezvous. Furthermore, an efficient explicit formula is obtained to calculate the risk of higher-order cascading failures recursively. Finally, from a risk-aware design perspective, we report an evaluation of the most vulnerable sequence of agents in various communication graphs.

Keywords: Lyapunov methods, Formal verification/synthesis, Optimization
Abstract: Control Lyapunov functions (CLFs) and control barrier functions (CBFs) are widely used tools for synthesizing controllers subject to stability and safety constraints. Paired with online optimization, they provide stabilizing control actions that satisfy input constraints and avoid unsafe regions of state-space. Designing CLFs and CBFs with rigorous perfor- mance guarantees is computationally challenging. To certify existence of control actions, current techniques not only design a CLF/CBF, but also a nominal controller. This can make the synthesis task more expensive, and performance estimation more conservative. In this work, we characterize polynomial CLFs/CBFs using sum-of-squares conditions, which can be directly certified using convex optimization. This yields a CLF and CBF synthesis technique that does not rely on a nominal controller. We then present algorithms for iteratively enlarging estimates of the stabilizable and safe regions. We demonstrate our algorithms on a 2D toy system, a pendulum and a quadrotor.

Keywords: Lyapunov methods, Robust control, Stability of nonlinear systems
Abstract: This paper introduces a new robust-safety notion for differential inclusions. That is, we say that the system is strongly robustly safe if it remains safe in the presence of a continuous and positive perturbation, named robustness margin, added to both the argument and the image of its right-hand side. While in existing literature, including the preceding Parts I and II, the perturbation term is added only to the image of the right-hand side, the notion proposed in this paper is shown to be relatively stronger, especially when the right-hand side is a general set-valued map. Furthermore, we show that some of the existing sufficient conditions for robust safety, in term of barrier functions, are strong enough to guarantee strong robust safety, provided that mild assumptions on the right-hand side hold. Following that, we establish the equivalence between strong robust safety and the existence of a smooth barrier certificate.

Keywords: Lyapunov methods, Stability of nonlinear systems
Abstract: This paper proposes a method for certifying the local asymptotic stability of a given nonlinear Ordinary Differential Equation (ODE) by using Sum-of Squares (SOS) programming to search for a partially quadratic Lyapunov Function (LF). The proposed method is particularly well suited to the stability analysis of ODEs with high dimensional state spaces. This is due to the fact that partially quadratic LFs are parametrized by fewer decision variables when compared with general SOS LFs. The main contribution of this paper is using the Center Manifold Theorem to show that partially quadratic LFs that certify the local asymptotic stability of a given ODE exist under certain conditions.

Keywords: Lyapunov methods, Stability of nonlinear systems
Abstract: The paper introduces novel families of cruise controllers for autonomous vehicles on lane-free ring-roads. The design of the cruise controllers is based on the appropriate selection of a Control Lyapunov Function expressed on measures of the energy of the system with the kinetic energy expressed in ways similar to Newtonian or relativistic mechanics. The derived feedback laws (cruise controllers) are decentralized (per vehicle), as each vehicle determines its control input based on: (i) its own state; (ii) either only the distance from adjacent vehicles (inviscid cruise controllers) or the state of adjacent vehicles (viscous cruise controllers); and (iii) its distance from the boundaries of the ring-road.

Keywords: Lyapunov methods, Uncertain systems, Optimization
Abstract: We use Lyapunov-like functions and convex optimization to propagate uncertainty in the initial condition of nonlinear systems governed by ordinary differential equations. We consider the full nonlinear dynamics without approximation, producing rigorous bounds on the expected future value of a quantity of interest even when only limited statistics of the initial condition (e.g., mean and variance) are known. For dynamical systems evolving in compact sets, the best upper (lower) bound coincides with the largest (smallest) expectation among all initial state distributions consistent with the known statistics. For systems governed by polynomial equations and polynomial quantities of interest, one-sided estimates on the optimal bounds can be computed using tools from polynomial optimization and semidefinite programming. Moreover, these numerical bounds provably converge to the optimal ones in the compact case. We illustrate the approach on a van der Pol oscillator and on the Lorenz system in the chaotic regime.

Keywords: Autonomous robots, Lyapunov methods
Abstract: We study the problem of providing safety guarantees for dynamic systems of high relative degree in the presence of state measurement errors. To this end, we propose High-Order Measurement Robust Control Barrier Functions (HO-MR-CBFs), an extension of the recently proposed Measurement Robust Control Barrier Functions. We begin by formally defining HO-MR-CBF, and identify conditions under which the proposed HO-MR-CBF can render the system’s safe set forward invariant. In addition, we provide bounds on the state measurement errors for which the optimization problem for identifying the corresponding safe controllers is feasible for all states within the safe set and given restricted control inputs. We demonstrate the proposed approach through numerical experiments on a collision avoidance scenario in presence of measurement noise using a nonlinear kinematic model of a wheeled robot. We show that using our proposed control method, the robot, who has access to only biased state estimates, will be successful in avoiding the obstacle.

Keywords: Linear systems, Adaptive control, Identification
Abstract: Willems' Fundamental Lemma provides a powerful data-driven parametrization of all trajectories of a controllable linear time-invariant system based on one trajectory with persistently exciting (PE) input. In this paper, we present a novel proof of this result which is inspired by the classical adaptive control literature and differs from existing proofs in multiple aspects. The proof involves a quantitative and directional PE notion, allowing to characterize robust PE properties via singular value bounds, as opposed to binary rank-based PE conditions. Further, the proof is constructive, i.e., we derive an explicit PE lower bound for the generated data. As a contribution of independent interest, we generalize existing PE results from the adaptive control literature and reveal a crucial role of the system's zeros.

Keywords: Linear systems, Control of networks, Network analysis and control
Abstract: In this paper, we consider the case of a particular class of linear time-invariant (LTI) dynamic systems that only require the actuation of a single state to yield controllability of the entire system, dually, only a single state need be observed to render the system observable. This work ties together elements of the state-space, graph, and transfer function representations of dynamic systems to evaluate the controllability and observability properties of a system. More specifically, necessary and sufficient conditions for Ubiquitous Single-Input Controllability (USIC) are introduced using traditional state-feedback perspectives, transfer functions, and a graph theoretical perspective is used to define an additional set of both necessary conditions and sufficient conditions. Ties are also made to structural controllability, and it is shown that any LTI system that meets the USIC condition also meets the structural controllability condition. Finally, brief practical examples are presented.

Keywords: Linear systems, Identification, Identification for control
Abstract: The fundamental lemma by Willems and coauthors enables a parameterization of all trajectories of a linear time-invariant system in terms of a single, measured one. This result plays a key role in data-driven simulation and control. The fundamental lemma relies on a persistently exciting input to the system to ensure that the Hankel matrix of resulting input/output data has the "right" rank, meaning that its columns span the entire subspace of trajectories. However, such binary rank conditions are known to be fragile in the sense that a small additive noise could already cause the Hankel matrix to have full rank. In this letter we present a robust version of the fundamental lemma. The idea behind the approach is to guarantee certain lower bounds on the singular values of the data Hankel matrix, rather than qualitative rank conditions. This is achieved by designing the inputs of the experiment such that the minimum singular value of an input Hankel matrix is sufficiently large, inspiring a quantitative notion of persistency of excitation. We highlight the relevance of the result in a data-driven control case study by comparing the predictive control performance for varying degrees of persistently exciting data.

Keywords: Linear systems, Optimal control, Learning
Abstract: In this article, an optimal sensor selection problem is considered under the framework of linear quadratic control. The objective is to find the best strategy of selecting one sensor among a set of sensors at each time step so that the expected system performance is minimized over multiple time steps. This problem is formulated as a multi-armed bandit problem. Uncertainties are captured through noisy sensor measurements, which account for the performance deterioration caused by unknown sensor noise covariance. In this context, several action-value based reinforcement learning methods are proposed to evaluate the performance of different sensor selection strategies. Moreover, a statistical method is developed to estimate the unknown sensor noise covariance as a byproduct. The almost sure convergence to the true sensor noise covariance is guaranteed as the number of times a sensor being selected goes to infinity. A linear quadratic control example is presented to illustrate the proposed approaches and to demonstrate their effectiveness.

Keywords: Linear systems, Optimization, Identification for control
Abstract: We study the identification of a linear time-invariant dynamical system affected by large-and-sparse disturbances modeling adversarial attacks or faults. Under the assumption that the states are measurable, we develop necessary and sufficient conditions for the recovery of the system matrices by solving a constrained lasso-type optimization problem. In addition, we provide an upper bound on the estimation error whenever the disturbance sequence is a combination of small noise values and large adversarial values. Our results depend on the null space property that has been widely used in the lasso literature, and we investigate under what conditions this property holds for linear time-invariant dynamical systems. Lastly, we further study the conditions for a specific probabilistic model and support the results with numerical experiments.

Keywords: Linear systems, Stochastic systems
Abstract: Application of low pass filters (LPFs) to remove noise components is a widely used methodology for processing signals acquired from diverse systems. LPFs are also intrinsic components of many natural and man-made systems, both intended and epiphenomenal, from electromechanical systems to traffic networks and the brain. Across all cases, the effects of LPFs are often studied in a pure filtering sense, such as temporal smoothing and removing high-pass noise components, causing delays and phase distortions, or limiting bandwidths. In this work, we instead show that low-pass filtering and the temporal averaging that underlies it can also have a major and fundamental impact on the linearity of the dynamics. We show using rigorous analysis that across a wide range of stochastic nonlinear systems, temporal averaging dampens nonlinearities and leads to more and more linear dynamics with stronger temporal averaging (lower LPF cutoff frequency), leading asymptotically to a completely linear system as the width of the window over which temporal averaging occurs tends to infinity (LPF cutoff frequency tends to zero). Our results have major implications in a wide range of application areas, including the study of the nervous system whereby LPFs are biologically and algorithmically abundant and a growing body of empirical evidence has found linear models as capable as nonlinear ones in describing neuronal time series.

Keywords: Networked control systems, Agents-based systems, H-infinity control
Abstract: This paper addresses the problem of robust consensus of an undirected network of homogeneous multi-agent systems with uncertain agent dynamics and system noise. We consider uncertain time-varying input matrices that are arbitrary up to a known bound for the singular values. We also assume that each agent's controller is able to access the neighbors' relative states. We focus on the design of a linear controller gain that is to be identical across all agents. We provide sufficient conditions for the control gains to achieve both consensus in the noiseless setting and a transfer function with a given bounded H_{infty} norm in the setting with noise. More specifically, we show that this is achieved if a set of linear matrix inequalities using the non-zero eigenvalues of the Laplacian are satisfied. In a numerical simulation, we illustrate these theoretical results and show that our method outperforms a consensus region-based approach.

Keywords: Networked control systems, Distributed control, Stochastic systems
Abstract: In practical networking scenarios, communication links can rarely be considered to be deterministic, yet the influence of stochastic interconnections on multi-agent systems is neglected most of the time. To bridge this gap, this paper develops synthesis conditions for distributed state- and output-feedback controllers that guarantee an upper bound on the closed-loop H₂-norm under the effect of Bernoulli distributed packet loss. Utilizing the frameworks of Markov jump linear system and decomposable systems, the synthesis problem is formulated as a linear matrix inequality problem with complexity that scales linearly with the number of agents. Finally, the closed-loop performance is assessed in simulation studies with a signal-to-interference-plus-noise ratio based packet loss model for communication between autonomous underwater vehicles.

Keywords: Networked control systems, Distributed control
Abstract: This paper proposes a distributed consensus controller for a class of heterogeneous nonlinear multi-agent systems. The control law enacted at each agent is based on predicted outputs of itself and its neighboring agents. It implements a fluid-flow version of the Newton-Raphson method for solving equations, and this, together with the way the predictions are used, guarantees asymptotic consensus for a general class of systems defined by ordinary differential equations. The scope of the analysis includes heterogeneous systems whose agent subsystems have different state-space models with different dimensions, but it requires that all the inputs and outputs of the agents' subsystems have the same dimension. Following a presentation of the consensus-control technique, we analyse its convergence and present simulation results for a heterogeneous nonlinear system.

Keywords: Networked control systems, Lyapunov methods
Abstract: In this paper, the problem of scheduling data transmissions in multiagent systems, which are composed of a team of nonholonomic mobile robots, is studied. To represent the equations of motion of each robot as double integrator dynamics, we first feedback linearize the robot dynamics that allows us to avoid nonholonomic control architecture synthesis. We then propose a decentralized, norm-free, and adaptive event-triggering rule for control of this multiagent system in a distributed manner with reduced robot-to-robot position and velocity data transmissions. Stability of the resulting event-triggered multiagent system is presented and an illustrative numerical example is also included to demonstrate its efficacy.

Keywords: Fault tolerant systems, Networked control systems, Multivehicle systems
Abstract: Typical cooperative multi-agent systems (MASs) exchange information to coordinate their motion in proximity-based control consensus schemes to complete a common objective. However, in the event of faults or cyber attacks to on-board positioning sensors of agents, global control performance may be compromised resulting in a hijacking of the entire MAS. For systems that operate in unknown or landmark-free environments (e.g., open terrain, sea, or air) and also beyond range/proximity sensing of nearby agents, compromised agents lose localization capabilities. To maintain resilience in these scenarios, we propose a method to recover compromised agents by utilizing Received Signal Strength Indication (RSSI) from nearby agents (i.e., mobile landmarks) to provide reliable position measurements for localization. To minimize estimation error: i) a multilateration scheme is proposed to leverage RSSI and position information received from neighboring agents as mobile landmarks and ii) a Kalman filtering method adaptively updates the unknown RSSI-based position measurement covariance matrix at runtime that is robust to unreliable state estimates. The proposed framework is demonstrated with simulations on MAS formations in the presence of faults and cyber attacks to on-board position sensors.

Keywords: Adaptive control, Uncertain systems
Abstract: Adaptive control for non-minimum phase systems is a challenging problem. This paper proposes a method of adaptive control for systems that may be both nonlinear and non-minimum phase. This is accomplished by exploiting time scale separation between the internal and external dynamics. The original non-minimum phase control problem is reduced to two minimum phase control problems through a time scale analysis. The resulting adaptive control signals are fused via multiple time scale control techniques. Singular perturbation theory is used to prove the stability and convergence of the fullorder system as an extension of the stability and convergence of the two reduced-order systems. The effectiveness of this method is validated on a nonlinear example system.

Keywords: Adaptive control, Uncertain systems, Constrained control
Abstract: This paper proposes a novel control architecture for state and input constrained Euler-Lagrange (E-L) systems with parametric uncertainties. A simple saturated controller is strategically coupled with a Barrier Lyapunov Function (BLF) based controller to ensure state and input constraint satisfaction. To the best of the authors' knowledge, this is the first result for E-L systems that guarantees asymptotic tracking with user-specified state and input constraints. The proposed controller also ensures that all the closed-loop signals remain bounded. The efficacy of the proposed controller in terms of constraint satisfaction and tracking performance is verified using simulation on a robot manipulator system.

Keywords: Adaptive control, Uncertain systems
Abstract: Balancing an inverted pendulum on an unmanned aerial vehicle has been a topic of interest in recent literature. For example, a recent study uses an LQR controller to balance the inverted pendulum on a quadrotor drone. However, these studies consider the length of the pendulum to be known a priori. Indeed, in certain applications this assumption might not hold true. For example, consider a quadrotor hoverboard being used by people of different heights. In such cases, an approach is required to estimate the length of the pendulum. This paper analyzes the linearized dynamics of the combined system of quadrotor and inverted pendulum. It is found that unknown length of pendulum causes the system to fall in the category of unmatched uncertain systems where the control input cannot be used to cancel the uncertainty. This paper formulates the problem in such a manner that the system is still controllable in presence of this unmatched uncertainty. A concurrent learning adaptive controller, which avoids the use of persistently exciting signals, is then utilized to estimate the unmatched uncertainty and hence the length of the pendulum. Simulation results validate the effectiveness of the adaptive controller for the proposed problem.

Keywords: Adaptive control, Uncertain systems
Abstract: Transient tracking error dynamics are inevitable in any practical closed-loop control system. While numerous works are devoted to improving these dynamics, in this paper, we focus on taking advantage of it first, in the context of adaptive control. We propose a memory architecture that can make use of stored significant data about the transients of previously experienced anomalies to aid in obtaining a resilient system against uncertainties. The proposed architecture consists of 1) a memory containing data about a variety of uncertainties, 2) a short-term memory that aids in handling new uncertainties, and 3) an attention-based reading mechanism that enables the controller to retrieve only relevant data from the memory. The effectiveness of the architecture is validated through numerical simulations, and a rigorous Lyapunov stability analysis is provided.

Keywords: Direct adaptive control, Adaptive control, Linear systems
Abstract: This paper presents a novel approach to model reference adaptive control inspired by the adaptive pole-placement technique of Elliot and based on retrospective cost optimization (RC-MRAC). RC-MRAC is applicable to nonminimum-phase (NMP) systems assuming that the NMP zeros are known. Under this assumption, the advantage of RC-MRAC is a reduced need for persistency.

Keywords: Robust adaptive control, Switched systems, Lyapunov methods
Abstract: For decades, nonlinear control methodologies have been developed to compensate for uncertain terms in the dynamical model that are upper bounded by constants. Classes of discontinuous and continuous controllers have been developed to compensate for these problematic terms; however, these controllers are prone to chatter or have been restricted to particular classes of uncertain and smooth nonlinear systems. Despite decades of research, an open question that remains is whether a chatter-mitigating control law can be developed to compensate for terms bounded by constants for a wider class of uncertain nonlinear systems, including switched or nonsmooth systems. To address this open question, this work considered a class of nonsmooth, uncertain, and control-affine nonlinear dynamic systems with an uncertain control effectiveness matrix. Furthermore, a novel filtered error, adaptive update law, and chatter-mitigating control law are developed to compensate for the uncertain control effectiveness matrix and the terms in the closed-loop error system that are bounded by constants. A nonsmooth Lyapunov-like stability analysis is performed to ensure semi-global exponential trajectory tracking to an ultimate bound.

Keywords: Spacecraft control, Predictive control for linear systems, Uncertain systems
Abstract: This paper proposes a model predictive control based on set-membership filtering for a time-varying discrete system with an unknown but bounded process and measurement noise. The estimated states are computed from set-membership filtering by solving a semi-definite program utilizing ellipsoidal bounds. The estimated sets are used for optimization in the model predictive control. Control input sequence is computed from model predictive control by minimizing the cost function. At each time step, a two-step prediction and measurement update process is used for ellipsoidal state estimation. Set-membership filtering guarantees that the true states lie within the ellipsoid. Finally, a rendezvous and proximity operation simulation is executed to guide the chaser to a target to illustrate the efficacy of the proposed approach.

Keywords: Autonomous systems, Control applications, Aerospace
Abstract: With the rise of increasingly complex autonomous systems powered by black box AI models, there is a growing need for Run Time Assurance (RTA) systems that provide online safety filtering to untrusted primary controller output. Currently, research in RTA tends to be ad hoc and inflexible, diminishing collaboration and the pace of innovation. The Safe Autonomy Run Time Assurance Framework presented in this paper provides a standardized interface for modular RTA building blocks and a set of universal implementations of constraint-based RTA modules. By leveraging JAX Automatic Differentiation, a technique popularized by deep learning, this framework provides unmatched flexibility in the RTA space by automatically populating advanced optimization based RTA methods from user defined constraints and dynamics. This eliminates tedious manual differentiation and minimizes user effort and error. To validate the feasibility of this framework, a simulation of a multi-agent spacecraft inspection problem is shown with differentiable safety constraints on position and velocity.

Keywords: Aerospace, Constrained control, Predictive control for nonlinear systems
Abstract: This paper adapts the rapidly-exploring variant of invariant-set motion planner (ISMP) for spacecraft attitude motion planning and control. The ISMP is a motion-planning algorithm that uses positive-invariant sets of the closed-loop dynamics to find a constraint admissible path to a desired target through an obstacle filled environment. We present four mathematical results that enable the sub-routines used to rapidly construct a search-tree for the ISMP. These mathematical results describe how to uniformly sample safe quaternions, how to find the nearest orientation in the search-tree, how to move the sampled orientation to form an edge, and how to scale the invariant set to guarantee constraint admissibility. We present simulation results that demonstrate the ISMP for spacecraft attitude motion planning.

Keywords: Optimization algorithms, Sensor networks, Spacecraft control
Abstract: As both the number and size of satellite constellations continue to increase, there likewise exists a growing need for incorporating methods for autonomous sensor selection into these networks. Particularly, constraints due to computation and communication can often prevent all available satellite sensors from actively making observations at a given time. We pose this constrained sensor selection problem in terms of a submodular optimization problem and explore the use of randomized greedy algorithms to obtain an approximately optimal sensor selection. To this end, we propose a novel pair of randomized greedy algorithms, namely, modified randomized greedy and dual randomized greedy to approximately solve budget and performance-constrained problems, respectively. For each of these algorithms, we derive theoretical high-probability guarantees bounding their suboptimality. We then demonstrate the efficacy of these algorithms in several pertinent applications for Earth-observing constellations, specifically, state estimation for atmospheric weather conditions and ground coverage.

Keywords: Spacecraft control, Autonomous systems, Formal verification/synthesis
Abstract: The safe operation of satellites is critical as the space domain becomes more cluttered with resident objects. Controller synthesis is a technique used to automatically generate correct-by-construction controllers that guarantee a system will satisfy some requirements, such as safety. In this work, we cast the safe satellite operation problem as a controller synthesis problem, and propose an algorithm that synthesizes full-state control of a satellite. This is done by decoupling the translational control from the attitude control. We deploy this algorithm in a close-proximity scenario and show that the synthesized controller satisfies our requirements and guarantees the safety of a chaser satellite.

Keywords: Robust control, Lyapunov methods, Uncertain systems
Abstract: Model mismatches prevail in real-world applications. Ensuring safety for systems with uncertain dynamic models is critical. However, existing robust safe controllers may not be realizable when control limits exist. And existing methods use loose over-approximation of uncertainties, leading to conservative safe controls. To address these challenges, we propose a control-limits aware robust safe control framework for bounded state-dependent uncertainties. We propose safety index synthesis to find a robust safe controller guaranteed to be realizable under control limits. And we solve for robust safe control via Convex Semi-Infinite Programming, which is the tightest formulation for convex bounded uncertainties and leads to the least conservative control. In addition, we analyze when and how safety can be preserved under unmodeled uncertainties. Experiment results show that our robust safe controller is always realizable under control limits and is much less conservative than strong baselines.