Keywords: Robotics, Optimization algorithms
Abstract: Industrial grippers are generally either electric or pneumatic, with the latter being preferred as their air- based functioning guarantees many advantages such as cost effectiveness and reduced encumbrance. Despite the very large employment, pneumatic grippers do not yet offer performance beyond the open/closed behavior in the majority of cases. Pneumatic grippers mounted on industrial robotic arms are commonly rigid as high forces might be required during the grasping operations. The poorness of the control strategies for the grasping force, as well as for the fingers position, does not match the great advancement that robotics obtained in the last years. Therefore, this letter intends to deliver a new control algorithm for the control of pneumatic grippers. The proposed algorithm permits to finely control the position of the gripper fingers, exploiting a quadratic-programming function to minimize the controller output. Different experiments are shown to demonstrate the algorithm effectiveness.

Keywords: Robotics
Abstract: A main challenge in swarm robotics is the unknown mapping between simple agent-level behavior rules and emergent global behaviors. Currently, there is no known swarm control algorithm that maps global behaviors to local control policies. This paper proposes a novel method to circumvent this problem by learning the agent-level controllers of an observed swarm to imitate its emergent behavior. Agent-level controllers are treated as a set of policies that are combined to dictate the agent’s change in velocity. The trajectory data of known swarms is used with linear regression and nonlinear optimization methods to learn the relative weight of each policy. To show our approach’s ability for imitating swarm behavior, we apply this methodology to both simulated and physical swarms (i.e., a school of fish) exhibiting a multitude of distinct emergent behaviors. We found that our pipeline was effective at imitating the simulated behaviors using both accurate and inaccurate assumptions, being able to closely identify not only the policy gains, but also the agent’s radius of communication and their maximum velocity constraint.

Keywords: Robotics, Optimization, Stochastic optimal control
Abstract: This paper presents a chance-constrained formulation for robust trajectory optimization during manipulation. In particular, we present a chance-constrained optimization for Stochastic Discrete-time Linear Complementarity Systems (SDLCS). To solve the optimization problem, we formulate Mixed-Integer Quadratic Programming with Chance Constraints (MIQPCC). In our formulation, we explicitly consider joint chance constraints for complementarity as well as states to capture the stochastic evolution of dynamics. We evaluate robustness of our optimized trajectories in simulation on several systems. The proposed approach outperforms some recent approaches for robust trajectory optimization for SDLCS.

Keywords: Robotics, Human-in-the-loop control, Cooperative control
Abstract: We study a human-robot collaborative transportation task in presence of obstacles. The task for each agent is to carry a rigid object to a common target position, while safely avoiding obstacles and satisfying the compliance and actuation constraints of the other agent. Human and robot do not share the local view of the environment. The human either assists the robot when they deem the robot actions safe based on their perception of the environment, or actively leads the task.

Using estimated human inputs, the robot plans a trajectory for the transported object by solving a constrained finite time optimal control problem. Sensors on the robot measure the inputs applied by the human. The robot then appropriately applies a weighted combination of the human's applied and its own planned inputs, where the weights are chosen based on the robot's trust value on its estimates of the human's inputs. This allows for a dynamic leader-follower role adaptation of the robot throughout the task. Furthermore, under a low value of trust, if the robot approaches any obstacle potentially unknown to the human, it triggers a safe stopping policy, maintaining safety of the system and signaling a required change in the human's intent. The robot also uses the sensor feedback to infer obstacles known only by the human and updates its planner to better align with the human's movements. With experimental results, we demonstrate that our proposed approach increases the success rate of collision-free trials while decreasing the effort required by the human to intervene.

Keywords: Robotics, Autonomous robots, Control applications
Abstract: In this paper, we propose a novel online approach for reactive local navigation of a robotic agent, based on a fast approximation of the Generalized Voronoi Diagram in a neighborhood of the robot’s position. We consider the context of an unknown environment characterized by some narrow passages and a dynamic configuration. Given the uncertainty and unpredictability that affect the scenario, we aim at computing trajectories that are farthest away from every obstacle: this is obtained by following the Voronoi diagram. To ensure full autonomy, the navigation task is performed relying only upon on-board sensor measurement without any a-priori knowledge of the environment. The proposed technique builds upon a smooth free space representation that is spatially continuous and based on some raw measurements. In this way, we ensure an efficient computation of a trajectory that is continuously re-planned according to incoming sensor data. A theoretical proof shows that in ideal conditions the outlined solution exactly computes the local Generalized Voronoi Diagram. Finally, we assess the reactiveness and precision of the proposed method with realistic real-time simulations and with real-world experiments.

Keywords: Robotics, Constrained control, Mechatronics
Abstract: This paper adapts the invariant-set motion planner (ISMP) for robot motion planning. We derive control invariant subsets of configuration-space bubbles lifted into the state-space. The resulting sets guarantee collision avoidance since they are both constraint admissible and control invariant. We present a command governor that enforces the positive invariance of the constraints in closed-loop. This governor can be used to transform any nominal tracking controller into a constraint enforcing controller. We use these control invariant sets to quantify a relationship between velocity and control authority that enables collision avoidance. We demonstrate our invariant-sets through an illustrative numerical example.

Keywords: Robotics, Fault diagnosis, Identification
Abstract: In this paper, we investigate the fault isolation (FI) problem of a soft trunk robot and propose a dynamics learning-based FI approach which is generic and applicable to general types of faults. Specifically, an adaptive radial basis function neural network (RBF NN) based dynamics learning scheme is first developed to achieve accurate identification of the robot’s dominant dynamics under different faulty modes, and the learned knowledge is stored and represented by constant RBF NN models. The learned results are then merged by using a novel merging mechanism to construct a bank of global RBF NN models, for capturing the characteristics of the robot’s dynamics under each specific faulty mode. Based on these models, a bank of FI observers are designed to develop an important capability of accurately reconstructing the robot’s dynamics under various faulty modes. The FI scheme is developed using these FI observers, which monitors the robot’s operation status online to provide accurate isolation of faults occurring in the robot. Physical experiments are performed on the soft trunk robot to validate the effectiveness of our proposed approaches.

Keywords: Robotics, Switched systems, Hybrid systems
Abstract: With the goal of enabling the exploitation of impacts in robotic manipulation, a new framework is presented for control of robotic manipulators that are tasked to execute nominally simultaneous impacts. In this framework, we employ tracking of time-invariant reference vector fields corresponding to the ante- and post-impact motion, increasing its applicability over similar conventional tracking control approaches. The ante- and post-impact references are coupled through a rigid impact map, and are extended to overlap around the area where the impact is expected to take place, such that the reference corresponding to the actual contact state of the robot can always be followed. As a sequence of impacts at the different contact points will typically occur, resulting in uncertainty of the contact mode and unreliable velocity measurements, a new interim control mode catered towards time-invariant references is formulated. In this mode, a position feedback signal is derived from the ante-impact velocity reference, which is used to enforce sustained contact in all contact points without using velocity feedback. With an eye towards real implementation, the approach is formulated using a QP control framework, and is validated using numerical simulations both on a rigid robot with a hard inelastic contact model and on a realistic robot model with flexible joints and compliant partially elastic contact model.

Keywords: Robotics, Robust control, Predictive control for nonlinear systems
Abstract: Many lower-limb hybrid neuroprostheses lack powered ankle assistance and thus cannot compensate for functional electrical stimulation-induced muscle fatigue at the ankle joint. The lack of a powered ankle joint poses a safety issue for users with foot drop who cannot volitionally clear the ground during walking. We propose zeroing control barrier functions (ZCBFs) that guarantee safe foot clearance and fatigue mitigation, provided that the trajectory begins within the prescribed safety region. We employ a backstepping-based model predictive controller (MPC) to account for activation dynamics, and we formulate a constraint to ensure the ZCBF is robust to modeling uncertainty and disturbance. Simulations show the superior performance of the proposed robust MPC-ZCBF scheme for achieving foot clearance compared to traditional ZCBFs and Euclidean safety constraints.

Keywords: Stability of linear systems, Computer-aided control design, Decentralized control
Abstract: This paper integrates concepts from the frequency domain control methods, state space control and robot motion planning to produce a flexible control synthesis approach that is applicable to a wide class of dynamical systems. The method views a system's frequency response as a trajectory in the complex plane that is evolving under the influence of an artificial force to satisfy a geometric stability-performance criterion. A nonlinear subspace approach is used to translate these forces into an equivalent state space dynamical system that governs the dynamics of the parameters of the compensator used to generate the control signal. The design method places no restrictions on the order of the compensator or geometry of the frequency domain criterion. The approach is developed and a proof of its ability to converge, if a solution exists, to the tuning parameters set that satisfies the desired conditions is provided. The paper provides a set of design examples to demonstrate its applicability to different types of linear, nonlinear, SISO and MIMO systems.

Keywords: Machine learning, Feedback linearization, Uncertain systems
Abstract: A methodology is developed to learn a feedback linearization (i.e., nonlinear change of coordinates and input transformation) using a data-driven approach for a single input control-affine nonlinear system with unknown dynamics. We employ deep neural networks to learn the feedback law (input transformation) in conjunction with an extension of invertible neural networks to learn the nonlinear change of coordinates (state transformation). We also learn the matrices A and B of the transformed linear system and define loss terms to ensure controllability of the pair (A, B). The efficacy of our approach is demonstrated by simulations on a nonlinear system. Furthermore, we show that state feedback controllers designed using the feedback linearized system yield expected closed-loop behavior when applied to the original nonlinear system, further demonstrating validity of the learned feedback linearization.

Keywords: Machine learning, Game theory, Markov processes
Abstract: Stochastic games are a popular framework for studying multi-agent reinforcement learning (MARL). Recent advances in MARL have focused primarily on games with finitely many states. In this work, we study multi-agent learning in stochastic games with general state spaces and an information structure in which agents do not observe each other's actions. In this context, we propose a decentralized MARL algorithm and we establish the near-optimality of its policy updates. Furthermore, we study the global policy-updating dynamics for a general class of best-reply based algorithms and derive a closed-form characterization of convergence probabilities over the joint policy space.

Keywords: Machine learning, Networked control systems, Robotics
Abstract: This paper considers the problem of learning a control policy that generalize well to novel environments given a set of sample environments. We develop a federated learning framework that enables collaborative learning of multiple learners and a centralized server without sharing their raw data. In each iteration, each learner uploads its local control policy and the corresponding estimated normalized arrival time to the server, which then computes the global optimum among the learners and broadcasts the optimal policy to the learners. Each learner then selects between its local control policy and that from the server for next iteration. By leveraging generalization error, our analysis shows that the proposed framework is able to provide generalization guarantees on arrival time and safety as well as consensus at global optimal value in the limiting case. Monte Carlo simulation is conducted to evaluate the proposed framework.

Keywords: Machine learning, Direct adaptive control, Uncertain systems
Abstract: There has recently been an increased interest in reinforcement learning for nonlinear control problems. However standard reinforcement learning algorithms can often struggle even on seemingly simple set-point control problems. This paper argues that three ideas can improve reinforcement learning methods even for highly nonlinear set-point control problems: 1) Make use of a prior feedback controller to aid amplitude exploration. 2) Use integrated errors. 3) Train on model ensembles. Together these ideas lead to more efficient training, and a trained set-point controller that is more robust to modelling errors and thus can be directly deployed to real-world nonlinear systems. The claim is supported by experiments with a real-world nonlinear cascaded tank process and a simulated strongly nonlinear pH-control system.

Keywords: Machine learning, Predictive control for nonlinear systems, Chemical process control
Abstract: This work presents a model predictive control (MPC) scheme using online learning of recurrent neural network (RNN) models to approximate the dynamics of switched nonlinear systems subject to unknown but bounded disturbances, for which the mode transitions follow a prescribed switching schedule. A generalization error bound for online learning RNNs using non-independent and identically distributed (non-i.i.d.) data samples from real-time operation of switched nonlinear systems is first derived. Subsequently, a Lyapunov-based MPC scheme using online learning RNNs is developed to stabilize the switched nonlinear system for each mode and guarantee satisfaction of the scheduled mode transitions, followed by closed-loop stability analysis that accounts for the RNN generalization error. Finally, the effectiveness of the proposed MPC scheme is demonstrated using a chemical process example switched between two modes.

Keywords: Machine learning, Iterative learning control, Predictive control for nonlinear systems
Abstract: Deep learning models are frequently used to capture relations between inputs and outputs and to predict operation costs in dynamical systems. Computing optimal control policies based on the resulting regression models, however, is a challenging task because of the nonlinearity and nonconvexity of deep learning architectures. To address this issue, we propose in this paper a linearizable approach to design optimal control policies based on deep learning models for handling both continuous and discrete action spaces. When using piecewise linear activation functions, one can construct an equivalent representation of recurrent neural networks in terms of a set of mixed-integer linear constraints. That in turn means that the optimal control problem reduces to a mixed-integer linear program (MILP), which can then be solved using off-the-shelf MILP optimization solvers. Numerical experiments on standard reinforcement learning benchmarks attest to the good performance of the proposed approach.

Keywords: Machine learning, Neural networks, Predictive control for nonlinear systems
Abstract: This work develops a transfer learning (TL) framework for modeling nonlinear dynamic systems using recurrent neural networks (RNNs). The TL-based RNN models are then incorporated into the design of model predictive control (MPC) systems. Specifically, transfer learning uses a pre-trained model developed based on a source domain as the starting point, and adapts the model to a target domain with similar data distribution. The generalization error for TL-based RNNs (TL-RNNs) that depends on model capacity and discrepancy between source and target domains is first derived to demonstrate the generalization capability on target process. Subsequently, the TL-RNN model is utilized as the prediction model in MPC for the target process. Finally, a chemical process example is used to demonstrate the benefits of transfer learning.

Keywords: Machine learning, Optimization algorithms, Adaptive control
Abstract: In this paper, we address the design of personalized control systems, which pursue an individual and private objective defined for each user. To this end, a problem of policy update is formulated where an individual objective function is estimated and the corresponding optimal control law is updated. The novelty of the problem setting is in the presence of a system-user and the policy update driven by his/her rating. The system-user rates on the control system to be updated and the rating is used for estimating his/her objective function. It is assumed that the rating depends not only on his/her private objective but also on his/her trust on the control system. Then, we address the problem of the policy update improving the rating while not impairing the trust. Algorithms of the policy update, which is essentially the objective function estimation, are developed and their convergence analysis is presented. Finally, thorough a numerical experiment, the effectiveness of the algorithms is shown.

Keywords: Machine learning, Robotics, Autonomous systems
Abstract: Learning-based controllers, such as neural network (NN) controllers, can show high empirical performance but lack formal safety guarantees. To address this issue, control barrier functions (CBFs) have been applied as a safety filter to monitor and modify the outputs of learning-based controllers in order to guarantee the safety of the closed-loop system. However, such modification can be myopic with unpredictable long-term effects. In this work, we propose a safe-by-construction NN controller which employs differentiable CBF-based safety layers and relies on a set-theoretic parameterization. We compare the performance and computational complexity of the proposed controller and an alternative projection-based safe NN controller in learning-based control. Both methods demonstrate improved closed-loop performance over using CBF as a separate safety filter in numerical experiments.

Keywords: Machine learning, Stochastic systems, Numerical algorithms
Abstract: We consider the problem of forecasting dynamic covariance with uncertain inputs. Various Bayesian approaches, including the variational Wishart process (VWP), were previously used to forecast such covariance with deterministic inputs. However, the VWP framework is insufficient to perform reliable predictions when the input is uncertain. To address this issue, we propose two novel VWP approaches that can model and predict covariance with uncertain inputs. Simulation results show that when the input is uncertain, the proposed novel VWP approaches outperform the original VWP and produce more reliable performance. A comparative discussion between all the approaches is presented based on the simulation results.

Keywords: Flexible structures, Model Validation, Modeling
Abstract: Venous system disorders such as Orthostatic hypotension, deep vein thrombosis (DVT), and edema affect the lower limbs and are common causes of decreased work performance and quality of life. Solutions such as compression devices, rotation of staff, and regular breaks help improve these problems. Some active compression devices require air compression which needs a pump thus making them bulky. A cuff muscle device that uses a dielectric elastomer as a soft actuator and sensor is proposed to supplement the existing means of reducing the effects of these disorders. A physics-based model of the device is developed by combining the physics of a thin-walled dielectric elastomer vessel with the force interactions between the active vessel and the cylindrical passive elastomer within. The couplings between the two nonlinear elastic models are solved to capture the pressure change experienced by the device under an applied voltage. The model is then validated in the normal frequency range of the device. This model may be used to predict the influence of different model parameters on the performance of the device before the fabrication process reducing the need for multiple prototyping.

Keywords: Robotics, Modeling, Manufacturing systems
Abstract: Soft robotic actuators have repeatedly demon- strated their utility for underwater manipulation, particularly in the deep sea with delicate biological creatures and fragile artifacts. Up to this point, soft robotic actuators and gripping modules have been limited to relatively small prototypes that are on the same scale as a human hand. Scaling soft robotic grippers to larger sizes is a non-trivial task due to two major challenges: design and manufacturing. In this work, we present a complete and streamlined workflow of modeling, manufacturing, and testing scalable soft actuators that are directly produced using additive manufacturing methods and finite element modeling (FEA). The presented workflow is an iterative approach that uses information gathered from the FEA’s simulation to further improve the simplified known initial model. To demonstrate this new workflow, a series of soft actuator designs were modeled, created and tested. Additionally, a more complex theoretical actuator design that has a non-uniform bending geometry is created and modeled. Once the actuator design matches what is desired, additive manufacturing is used to physically create it. Using this full process, an actuator design is easily scaled to almost three times its original length and is manufactured in under 36 hours. The scaled up actuators are arranged in a custom full gripping array to grasp a cylinder underwater in a predictive manner.

Keywords: Robotics, Control applications, Modeling
Abstract: A soft continuum manipulator with tunable stiffness can not only take advantage of high compliance for safe adaptation in unknown environments, but also circumvent the drawbacks of instability and low loading capability. The high nonlinearity of soft manipulators and the strong coupling between actuation and stiffness-tuning make their simultaneous control challenging. In this work, a novel approach to simultaneous control of actuation and stiffness-tuning is proposed for soft pneumatic manipulators. With piecewise-constant curvature assumption, a Lagrangian-based dynamic model with realistic approximation is used for control design, where the dynamics of stiffness-tunable mechanism is incorporated. An extended Kalman filter (EKF) is proposed to estimate unmeasurable states including the stiffness and the velocity. An Nonlinear Model Predictive Control (NMPC) framework is developed first in the configuration space, and then extended to the task space, for simultaneous motion and stiffness control under inflation and vacuum pressure constraints. Simulation results are presented to support the efficacy of the proposed approach.

Keywords: Robotics, Mechatronics
Abstract: Abstract— In nature, animals with soft body parts demonstrate remarkable control over their shape, such as an elephant trunk wrapping around a tree branch to pick it up. However, most research on robotic manipulators focuses on controlling the end effector, partly because the manipulator’s arm is rigidly articulated. With recent advances in soft robotics research, controlling a soft manipulator into many different shapes will significantly improve the robot’s functionality, such as medical robots morphing their shape to navigate the digestive system and deliver drugs to specific locations. However, controlling the shape of soft robots is challenging due to their highly nonlinear dynamics that are computationally intensive. In this paper, we leverage a physics-informed, data-driven approach using the Koopman operator to realize the shape control of soft robots. We simulate the dynamics of a soft manipulator using a physics-based simulator (PyElastica) to generate the input-output data, which is then used to identify an approximated linear model based on the Koopman operator. We then formulate the shapecontrol problem as a convex optimization problem that is computationally efficient. Our linear model is over 12 times faster than the physics-based model in simulating the manipulator’s motion. Further, we can control a soft manipulator into different shapes using model predictive control. We envision that the proposed method can be effectively used to control the shapes of soft robots to interact with uncertain environments or enable shape-morphing robots to fulfill diverse tasks. This paper is complemented with a video.

Keywords: Robotics, Mechanical systems/robotics
Abstract: We present a method for feedback controlling a soft finger actuator and detecting “touch”, i.e., contact with an object in the environment. While this work uses our pneumatic elastomeric actuator with a soft bending sensitive resistive sensor along its dorsal surface, the method is suited for many soft actuator designs with a bending sensor. We use a closed- loop reference tracking controller and detect contact from the magnitude of the reference tracking error. This method uses a single bending sensitive sensor and does not require a force sensor collocated with the point of contact. We demonstrate the method’s ability to track a reference, sense and maintain contact with an external object, switch from a state of unimpeded motion to either a state of light touch or to a state of firm touch, and remain robust against orientation and saturation.

Keywords: Learning, Modeling, Fault tolerant systems
Abstract: Wake steering yaws upstream wind turbines to deflect their wakes from downstream turbines, increasing the total power produced by the wind farm. Most wake steering methods generate lookup tables offline which map a set of wind farm conditions, such as wind speed, to yaw offset angles for each turbine in a farm. These tables assume all turbines are operational and can be significantly non-optimal when one or more turbines shutdown--as they often do because of low wind speed, routine maintenance, or emergency maintenance. We present a new wake steering method that adapts to turbine shutdown. Using a hybrid model- and learning-based method, differentiable control, we train a neural network to determine yaw offset angles from conditions including turbine status (active/inactive). Unlike the lookup table approach, differentiable control does not solve an optimization problem for each combination of turbine shutdown in a farm; including learning in the method allows it to generalize. We present results for both standard wake steering (all turbines active) and adaptive wake steering (some turbines active). We find that differentiable control has comparable accuracy as and an order of magnitude faster offline compute time than the lookup table approach. Differentiable control enables adaptive wake steering through computationally efficient training and rapid online evaluation.

Keywords: Delay systems, Distributed parameter systems
Abstract: We present a method to estimate the time-varying free-flow wind speed on a wind farm based on local wind speed measurements taken by a wind turbine inside the wake zone of a turbine array. Our approach relies on a simple modeling of the speed deficit as a 1-D transport equation [1]. We propose to estimate the free-flow wind speed by integrating the error between the local wind measurement and an estimation of it computed with the free-flow estimate. We provide a bound on the estimation error which we formally prove. Finally, we provide numerical simulations to illustrate the interest and the performance of the proposed method.

Keywords: Control applications, Machine learning, Smart grid
Abstract: The power output of a wind farm is influenced by wake effects, a phenomenon in which upstream turbines facing the wind create sub-optimal conditions for turbines located downstream. Yaw misaligning strategies have been shown to increase total production. Yet designing efficient methods of cooperative control to find optimal yaw angles is a challenging task. Classical optimization methods become intractable as the size of the farm grows, do not recover from model inaccuracies and ignore the dynamic propagation of the wind inflow in real conditions. Reinforcement learning methods can provide a model-free alternative, but raise issues of scalability when the control is centralized. Existing decentralized RL methods have been shown to significantly increase power production under dynamic conditions, but relied on tabular methods with state and action space discretization. To accelerate convergence, we employ an actor-critic algorithm with linear function approximation for decentralized cooperative yaw control. We validate our method in dynamic simulators for wind farms with up to 32 turbines, and show empirically that, compared to previous tabular algorithms, our method is faster and scales to larger wind farms.

Keywords: Energy systems, Predictive control for nonlinear systems
Abstract: This paper presents a wind farm control strategy to use wake steering (yaw control) to augment pitch control for tracking a power reference signal. The outer loop controller employs a recently proposed dynamic yaw model with a time-varying graph structure that accounts for changes in the farm power output due to the propagation of wakes and wake interactions from yawing turbines. The inner pitch control loop uses a PI controller combined with a novel power-sharing arrangement that reduces the needed derate at each turbine. A compensation scheme accounts for the slow timescale effects of the yaw control actions within the faster timescale pitch control. The controller is applied to track two power trajectories (typical of secondary frequency regulation signals) using a large-eddy simulation wind farm plant. The results demonstrate that the additional control authority from yaw provides some added benefit in reducing the required turbine derates needed for wind farms to track transient power increases in the proposed setting. However, the benefit decreases and pitch control alone is sufficient when the turbines are derated beyond a certain level. These findings suggest that augmenting pitch control with yaw may provide financial incentives in terms of allowing wind farms to maximize power supply to the bulk power market while still providing regulation services. Further work is needed to analyze the costs and benefits of the additional control complexity versus bandwidth in augmenting pitch control with wake steering in these applications.

Keywords: Optimal control, Aerospace, PID control
Abstract: This paper presents a new active power control algorithm designed to maximize the power reserve of the individual turbines in a farm, in order to improve the tracking accuracy of a power reference signal. The control architecture is based on an open-loop optimal set-point scheduler combined with a feedback corrector, which actively regulate power by both wake steering and induction control. The control architecture is compared with a state-of-the-art PI-based controller by means of high-fidelity LES simulations. The new wind farm controller reduces the occurrence of local saturation events, thereby improving the overall tracking accuracy, and limits fatigue loading in conditions of relatively high-power demand.

Keywords: Optimization, Optimization algorithms, Distributed control
Abstract: We consider an in-network optimal resource allocation problem in which a group of agents interacting over a connected graph want to meet a demand while minimizing their collective cost. The contribution of this paper is to design a distributed continuous-time algorithm for this problem inspired by a recently developed first-order transformed primal-dual method. The solution applies to cluster-based setting where each agent may have a set of subagents, and its local cost is the sum of the cost of these subagents. The proposed algorithm guarantees an exponential convergence for strongly convex costs and asymptotic convergence for convex costs. Exponential convergence when the local cost functions are strongly convex is achieved even when the local gradients are only locally Lipschitz. For convex local cost functions, our algorithm guarantees asymptotic convergence to a point in the minimizer set. Through numerical examples, we show that our proposed algorithm delivers a faster convergence compared to existing distributed resource allocation algorithms.

Keywords: Optimization algorithms, Machine learning, Stochastic systems
Abstract: Stochastic nonconvex-concave min-max saddle point problems appear in many machine learning and control problems including distributionally robust optimization, generative adversarial networks, and adversarial learning. In this paper, we consider a class of nonconvex saddle point problems where the objective function satisfies the Polyak-Łojasiewicz condition with respect to the minimization variable and it is concave with respect to the maximization variable. The existing methods for solving nonconvex-concave saddle point problems often suffer from slow convergence and/or contain multiple loops. Our main contribution lies in proposing a novel single-loop accelerated primal-dual algorithm with new convergence rate results appearing for the first time in the literature, to the best of our knowledge.

Keywords: Optimization algorithms, Stability of nonlinear systems, Lyapunov methods
Abstract: We examine global exponential stability of the primal-dual gradient flow dynamics for differentiable convex problems with linear equality constraints. We show that if the set of equilibrium points is affine, then, regardless of the initial conditions, trajectories of the gradient flow move in the direction that is perpendicular to equilibrium set. When the objective function is strongly convex, we utilize this structure to show that the primal-dual dynamics are globally exponentially stable even if the constraint matrix is not full-row rank. We also provide an explicit characterization of the exponential convergence rate in terms of the smallest nonzero singular value of the constraint matrix.

Keywords: Optimization, Adaptive control, Optimization algorithms
Abstract: Convex optimization with equality and inequality constraints is a ubiquitous problem in several optimization and control problems in large-scale systems. Recently there has been a lot of interest in establishing accelerated convergence of the loss function. A class of high-order tuners was recently proposed in an effort to lead to accelerated convergence for the case when no constraints are present. In this paper, we propose a new high-order tuner that can accommodate the presence of equality constraints. In order to accommodate the underlying box constraints, time-varying gains are introduced in the high-order tuner which leverage convexity and ensure anytime feasibility of the constraints. Numerical examples are provided to support the theoretical derivations.

Keywords: Optimization algorithms, Distributed control, Adaptive control
Abstract: This brief aims to solve the distributed resource allocation problem for second-order multi-agent systems over an undirected network, where the global objective function is strongly convex but not necessarily Lipschitz continuous for its subgradient. The resource state is subject to a global equality constraint and several local inequality constraints with a convex function. Unlike existing tracking deviation control strategies, a dynamic event-triggered and initialization-free distributed resource allocation algorithm is proposed to reduce the communication burden among agents. The local constraints are solved by an adaptive control approach based on the Karush-Kuhn-Tucker condition. It is shown that the proposed algorithm asymptotically converges to the optimal solution by using the set-valued LaSalle’s invariance principle. Moreover, it is guaranteed that Zeno behavior is ruled out for any agent. Finally, a simulation example shows the effectiveness of the proposed algorithm.

Keywords: Agents-based systems, Distributed control
Abstract: Based on zero-gradient-sum (ZGS) algorithm, this paper studies the finite-time distributed optimization problem for multi-agent systems (MASs) over signed networks. First, a finite-time distributed control protocol is designed to ensure all agent states to realize bipartite consensus in a finite time under undirected signed graphs. Meanwhile, the optimized solutions of minimizing global convex objective functions under undirected signed graphs also converge to the bipartite consensus values. Moreover, the finite-time upper bound is given, which depends on the initial states and also the choice of the parameters in the proposed protocols. Then, extend the results to the case of signed digraphs. Finally, simulation results show the validity of the proposed methods.

Keywords: Nonlinear output feedback, Observers for nonlinear systems, Learning
Abstract: This paper considers the tracking control problem of a class of uncertain nonlinear systems with partial noisy measurements. To cope with the uncertainties including the unknown nonlinear dynamics and unmeasured state variables, simultaneous estimation of all the hidden states and unknown dynamics are required for the controller design. In this paper, a high-gain observer delivers a good property of disturbance rejection and provides state estimates which serves as the training data for learning the unknown dynamics. Because the measurements are corrupted by noise, this leads to estimation error in the state estimates. Since the Gaussian process (GP) has high flexibility to capture the complex unknown functions by using very few parameters and it inherently handles measurement noise, GP model is employed to learn the unknown dynamics from the state estimates. This provides critical information for the control design such that the unknown dynamics is compensated and a good tracking performance is delivered. In short, the high-gain observer provides state estimates for the GP model to learn the unknown dynamics from noisy measurements, which enables the development of the controller. Comparisons against L1 adaptive control and high-gain output feedback controller without GP learning are carried out.

Keywords: Control of networks, Distributed control, Stability of nonlinear systems
Abstract: We consider the problem of designing control pro- tocols for nonlinear network systems affected by heterogeneous, time-varying delays and disturbances. For these networks, the goal is to reject polynomial disturbances affecting the agents and to guarantee the fulfilment of some desired network behaviour. To satisfy these requirements, we propose an integral control design implemented via a multiplex architecture. We give sufficient conditions for the desired disturbance rejection and stability properties by leveraging tools from contraction theory. We illustrate the effectiveness of the results via a numerical example that involves the control of a multi-terminal high-voltage DC grid.

Keywords: Neural networks, Stability of nonlinear systems, Electrical machine control
Abstract: This paper tackles the problem of control for a class of nonlinear systems with state-dependent nonlinearities. A new control algorithm combining Time Delay Control and Neural Networks is proposed for such systems. Assuming all state variables are available, the proposed control algorithm is shown to learn the nonlinearity online, provide closed loop stability and achieve tracking performance better than that of time delay control. The performance of the proposed control algorithm is evaluated and compared to that of Time Delay Control and traditional PI control through simulation studies of an Interior type Permanent Magnet Synchronous Motor (IPMSM).

Keywords: Nonlinear output feedback, Optimization, LMIs
Abstract: The paper is about L2-gain computation and the small-gain theorem for nonlinear input-output systems. We show that the Koopman operator's spectrum can provide conditions for L2-gain guarantees and small-gain theorem-based stability of interconnection over a large region of the state space. The large region in the state space can be characterized in terms of the region where Koopman eigenfunctions and the solution of the Hamilton Jacobi equation are well defined. The connection of system L2-gain to the spectral properties of the Koopman operator has led to a novel approach, based on the approximation of the Koopman spectrum, for the computation of the L2-gain and stability verification of the interconnected system. We present simulation results including application of the developed framework to a power system example.

Keywords: Feedback linearization, Algebraic/geometric methods, Stability of nonlinear systems
Abstract: Applications of transverse feedback linearization (TFL) vary from path following mobile robots to vehicle formation control. These applications were, however, restricted to systems adequately modelled in continuous-time. Recent work demonstrated that the established technique fails when applied to a discrete-time system using a zero-order hold. An additional change of coordinates dependent on the sampling period that preserves the required properties was proposed as an alternative. This technique, however, only applies to sampled-data systems. This article instead proposes a direct design approach that starts with a discrete-time system and designs a discrete-time transverse feedback linearizing controller. The discrete-time transverse feedback linearization problem is posed, and resolved for a single-input nonlinear discrete-time system. An example of path following for a forward-Euler discretized, kinematic unicycle model is presented to demonstrate its effectiveness.

Keywords: Chemical process control, Randomized algorithms, Predictive control for nonlinear systems
Abstract: A chance-constrained full-state feedback control law is designed to regulate nonlinear systems under uncertainties. The proposed scheme utilizes Monte Carlo sampling to generate multiple scenarios, formulates the optimal control problem as a scenario-based nonlinear optimization, and develops a sequential algorithm to obtain probabilistic feasible solutions. The resulting controller offers three advantages: First, the optimization-based design minimizes the tracking error across considered scenarios. Second, the sampling complexity is determined adaptively and the chance of constraint violation is bounded with a guaranteed confidence interval. Third, the sequential algorithm can reach a probabilistic feasible solution faster than directly using a state-of-the-art solver for the full-scenario optimization problem. Two case studies, including a CSTR and fermentor, are presented to demonstrate the effectiveness of the proposed method.

Keywords: Identification, Computational methods, Subspace methods
Abstract: Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to approximate the action of the Koopman operator on a linear function space spanned by a dictionary of functions. The accuracy of EDMD model critically depends on the quality of the particular dictionary span, specifically on how close it is to being invariant under the Koopman operator. Motivated by the observation that the residual error of EDMD, typically used for dictionary learning, does not encode the quality of the function space and is sensitive to the choice of basis, we introduce the novel concept of consistency index. We show that this measure, based on using EDMD forward and backward in time, enjoys a number of desirable qualities that make it suitable for data-driven modeling of dynamical systems: it measures the quality of the function space, it is invariant under the choice of basis, can be computed in closed form from the data, and provides a tight upper-bound for the relative root mean square error of all function predictions on the entire span of the dictionary.

Keywords: Identification, Control education
Abstract: The T26.4 Method is a new approach to identifying the parameters of overdamped or slightly underdamped 2^nd order LTI systems either graphically or by table look-up. The method computes the ratio of the time at which the step response reaches 26.4% of its final value to the time at which it reaches a specific fraction of its final value (such as 60%, 75%, or 90%). This ratio is the input to a table or graph to determine the values of the poles normalized by the 26.4% time. Unlike the Beta T-star Method, the T26.4 method does not require differentiation of the step response, and thus it is well-suited to system identification from noisy or sparse step response data. This paper explains the significance of the 26.4% value for 2^nd order LTI systems, derives the method, and then shows its application to identifying models of a DC motor from experimental data and a slightly underdamped 2^nd order system from simulated data.

Keywords: Identification, Emerging control applications, Optimization
Abstract: This paper presents the use of discrete simultaneous perturbation stochastic approximation (DSPSA) as a routine method to efficiently determine features and parameters of idiographic (i.e. single subject) dynamic models for personalized behavioral interventions using various partitions of estimation and validation data. DSPSA is demonstrated as a valuable method to search over model features and regressor orders of AutoRegressive with eXogenous input estimated models using participant data from Just Walk (a behavioral intervention to promote physical activity in sedentary adults); results of DSPSA are compared to those of exhaustive search. In Just Walk, DSPSA efficiently and quickly estimates models of walking behavior, which can then be used to develop control systems to optimize the impacts of behavioral interventions. The use of DSPSA to evaluate models using various partitions of individual data into estimation and validation data sets also highlights data partitioning as an important feature of idiographic modeling that should be carefully considered.

Keywords: Identification, Estimation, Filtering
Abstract: We present two extensions of recursive least squares (RLS) with exponential forgetting (EF), namely, exponential resetting (ER) RLS and cyclic resetting (CR) RLS. Both methods guarantee that the covariance matrix is bounded above and below in the absence of persistent excitation. Under zero excitation, ER-RLS guarantees convergence of the covariance matrix P_k to a user-designed positive-definite matrix P_infty. However, ER-RLS is more computationally complex than EF-RLS. In contrast, CR-RLS has the same computational complexity as EF-RLS while guaranteeing that, under zero excitation, the difference between the covariance matrix P_k and P_infty is asymptotically bounded. A numerical example shows that ER-RLS and CR-RLS both perform nearly identically to EF-RLS under persistent excitation while protecting against covariance windup when persistent excitation is lost.

Keywords: Identification, Identification for control, Linear systems
Abstract: This paper proposes a novel identification approach for linear time-invariant descriptor systems based on input-state-output data. Under the assumption of regularity, the equivalent inverse form of the descriptor system is firstly introduced. Then two groups of data experiments are designed, and corresponding input, state and output data are collected. Furthermore, the parameters of the inverse form are uniquely identified based on those data sets. Since the inverse form possesses the same state, input, output signals and input-output transfer function as the original descriptor system, the identification is completed. Finally, an electrical circuit system is provided to illustrate the effectiveness of our method.

Keywords: Identification, Identification for control, Time-varying systems
Abstract: This paper considers the problem of system identification for linear systems. We propose a new system realization approach that uses an ``information-state" as the state vector, where the ``information-state" is composed of a finite number of past inputs and outputs. The system identification algorithm uses input-output data to fit an autoregressive moving average model (ARMA) to represent the current output in terms of finite past inputs and outputs. This information-state-based approach allows us to directly realize a state-space model using the estimated ARMA or time-varying ARMA parameters for linear time-invariant (LTI) or linear time-varying (LTV) systems, respectively. The paper develops the theoretical foundation for using ARMA parameters-based system representation using only the concept of linear observability, details the reasoning for exact output modeling using only the finite history, and shows that there is no need to separate the free and the forced response for identification. The proposed approach is tested on various different systems, and the performance is compared with state-of-the-art system identification techniques.

Keywords: Optimal control, Optimization, Computational methods
Abstract: International focus on the COVID-19 pandemic has caused a wealth of new mathematical models for capturing the impact of a virus. As COVID-19 seems to be approaching an endemic status, it is becoming increasingly clear that a new variant has a strong probability of becoming dominant in a short period of time from the first appearance. A model with the goal of representing past data and forecasting will need the flexibility to incorporate a time-evolution of variants. In this paper we explore a method for encompassing mutating viruses: coupling Ordinary Differential Equations (ODE) and Markov chains. In this approach, ODEs are used to represent classical compartmental models and Markov chains to govern the mutation of the virus between predetermined variants. This method considers a discrete variant space allowing for more simple parameter tuning to previously recorded data. A cost function is designed in order to study optimal decision making with respect to non-pharmaceutical interventions such as social distancing. This model will serve to highlight the importance of considering variants in the long-term decision making process.

Keywords: Uncertain systems, Estimation, Distributed parameter systems
Abstract: A population model for the transdermal transport of ethanol from the blood to an alcohol biosensor on the surface of the skin in the form of a random abstract parabolic hybrid system of coupled ordinary and partial differential equations is developed. Linear semigroup theory in a Gelfand triple of Bochner spaces is used to first formulate the model as an equivalent deterministic system in state space form and to then develop a finite dimensional approximation and convergence theory. Both parametric and non-parametric techniques, the method of moments and kernel density estimation, and clinically collected drinking data are used to estimate the distributions of the model’s random parameters. Numerical results demonstrate the efficacy of using our model to 1) deconvolve an estimate of blood alcohol concentration from biosensor measured transdermal alcohol level and 2) quantify the uncertainty in the estimate.

Keywords: Distributed parameter systems
Abstract: This paper presents an alternative control design for the macroscopic model of Kuramoto oscillators. The resulting partial differential equation describing the density of the collective dynamics is a nonlinear version of the continuity equation in which the control signals are coupled to the state. An optimal control for the bilinear system provides optimality of the controllers but it also results in an open-loop policy due to the backward in time integration of adjoint states. To tackle this, an adaptive alternative is considered and which views the control signals corresponding to a target density, as unknown spatiotemporally varying parameters. An adaptive observer is proposed along with the Lyapunov-redesign of the parameter adaptive laws. The stability of the closed-loop density equation using adaptive estimates of the controllers along with tracking convergence are examined.

Keywords: Distributed parameter systems, H-infinity control
Abstract: Our long term goal is to extend the H-Infinity paradigm to nonlinear, infinite dimensional systems under point actuation and point sensing. This paper is the first step in this direction. We find the minimum L2 gain from the noisy heat flux at one end of a rod to the temperature at an arbitrary point of the rod that can be achieved by state feedback on the heat flux at the other end of the rod. We do this by completing the square to obtain a Riccati partial differential equation whose solution yields a state feedback control law that achieves a given L2 gain. We solve the Riccati PDE by Fourier series. We iterate this process to find the minimum L2 gain.

Keywords: Output regulation, Nonlinear output feedback, Distributed parameter systems
Abstract: This paper presents an error feedback controller for approximate tracking and disturbance rejection for nonlinear distributed parameter systems. The controller is error feedback because the only information available to the controller is the error given as the difference between the reference signal to be tracked and the measured output of the plant. In particular, the controller cannot directly access the output data. Also, the unknown disturbance corrupting the plant is unavailable to the controller. The controller is ``approximate'' in the sense it only guarantees a small tracking error rather than an asymptotic zero tracking error. However, the asymptotic tracking error can be reduced by solving a sequence of controllers, similar to cascade controllers, where the error at one level becomes the target to track at the next level. At each step, the error is reduced geometrically, so achieving the desired tracking level seldom requires more than one or two iterations. We present a numerical example to demonstrate the utility of the method.

Keywords: Distributed parameter systems, Reduced order modeling
Abstract: Balanced truncation is a popular model reduction method that uses balanced realizations for finite dimensional systems. The latter are state space realizations where the controllability and observability gramians are equal to the same diagonal positive matrix. In this paper, a generalization of balanced realization for a class of infinite dimensional LTI systems is employed to perform balanced truncation. It is shown that balanced truncation is optimal in the Hilbert-Schmidt sense if a particular time-varying balanced realization is used for the original LTI system. It appears that the use of time-varying balanced realizations to study the optimality and perform balanced model reduction for LTI systems is novel.

Keywords: Estimation, Optimization, Sensor networks
Abstract: We present a distributed algorithm for multi-agent target tracking, posed as a maximum a-posteriori (MAP) optimization problem. MAP estimation is, in general, a non-convex optimization that depends on each agent's local observation of the target, necessitating a distributed algorithm. In our algorithm, each agent solves a series of local optimization problems to estimate the target's trajectory, while communicating with its one-hop neighbors over a communication network. The agents do not communicate their raw observations, which may be high dimensional (e.g., images), and they do not rely on a central coordinating node or leader, minimizing the communication bandwidth requirements of our approach. We utilize the sequential quadratic programming (SQP) paradigm, with distributed computation of the ensuing sub-problems achieved via the consensus alternating direction method of multipliers (C-ADMM). We empirically demonstrate faster convergence of our algorithm to a locally optimal solution compared to other distributed methods. In addition, our algorithm achieves about the same communication overhead as the best competing distributed algorithm.

Keywords: Estimation, Pattern recognition and classification, Biological systems
Abstract: In recent years, observing neuronal activity by inferring action potentials (APs) in mammals has attracted much attention. A common way to observe thousands of neurons simultaneously is by using calcium imaging techniques. However, estimating the APs based on the fluorescence signal obtained by the calcium imaging technique is a challenging task due to noise, slow imaging rates and especially the nonlinearity of the calcium binding kinetics. Though the electrical recording technique can measure the APs very precisely, it is rather time consuming in practice. In this paper, an approach is proposed that reconstruct the APs based on the noisy fluorescence signal. For this purpose, at first the forward-backward filtering is applied on the fluorescence signal to reduce the level of noise and to avoid the nonlinear shift in time with respect to the true fluorescence signal. Then, for each local maximum in the filtered fluorescence signal, three characteristic values, namely, the integral, the amplitude and the gradient are extracted to localize the neuronal activity. By exploiting the fuzzy c-means clustering method, the time instants and the number of APs can be estimated. The proposed approach is validated by using the well-established spikefinder challenger data. The comparison shows that the proposed approach outperforms other existing AP estimation approaches.

Keywords: Filtering, Kalman filtering, Estimation
Abstract: Different objectives and paradigms exist for tracking multiple targets when measurements do not contain information about the target identities (IDs). The Symmetric Measurement Equation (SME) filter can be used when one is agnostic to the labels and does not attempt to assign different IDs to the different targets. We present an extension of the Kernel-SME filter that, unlike the original variant, uses adaptive kernel widths that depend on the respective uncertainty. In our evaluation, it outperformed existing SME-based approaches, while it is only second to a more complex global nearest neighbor tracker.

Keywords: Quantum information and control, Optimization, Estimation
Abstract: Designing an observer of an unknown quantum density operator is difficult because the operator must be Hermitian positive semidefinite with unit trace. In this paper, we derive a closed-form solution for projecting an arbitrary matrix onto the set of valid density operators. This allows us to design linear quantum state observers and retract the observer's state back to this set while retaining the exponential convergence rate of the linear observer. The derived closed-form projection can be used alongside any quantum state estimation technique to produce a valid state estimate without increasing the state estimation error.

Keywords: Biomolecular systems, Estimation
Abstract: Real-time feedback-driven single particle tracking is an emerging method of measuring the state and dynamics of individual molecules and particles at the nanometer scale as they move inside living cells. Two problems limit current performance: the photon budget of fluorescent labels, and the control temporal budget. REACTMIN overcomes these challenges by reactively scanning a minimum of light to track diffusing particles and molecules. It is comprised of a non-holonomic based extremum seeking controller and structured illumination using a laser with a central minimum. The controller allows for estimationless tracking, addressing the control temporal budget, and the structured illumination enables information rich measurements, addressing the photon budget. We use two metrics of performance, Fisher information and tracking duration, to characterize the system and find optimal settings for one of the dominant controller parameters, the steady state orbital radius. We demonstrate a trade-off between tracking duration and localization precision and discuss how to select this parameter in the context of specific experimental aims.

Keywords: Cellular dynamics, Estimation, Process Control
Abstract: Human Mesenchymal Stromal Cells (hMSC) have shown promising pre-clinical results by eliciting immunomodulatory effects to alleviate inflammation. In order to further study these effects, consistent and automated expansion platforms are required. Recent theoretical innovations have shown that model-based automated controls can more effectively regulate key nutrient concentrations. However, this previous work did not account for time-varying cell growth and death which resulted in inconsistent modeling and controller performance. To mitigate these effects, we propose a new model with time-varying parameters to track viable, proliferating, and dead cells and their respective growth rates with algorithms to estimate these parameters as functions of our limited measured states. We then propose an updated control architecture (referred to as smooth-controller) to leverage the additional parameters for improved estimation and control. The control objective is to regulate glucose and lactate to fixed setpoints while minimizing total media usage and large flowrate disturbances. Finally, we demonstrate the new control architecture in hMSC expansion with improved lactate setpoint MSE (58% reduction), improved observer MSE (36% for glucose and 20% for lactate), and reduced process disturbance (1 to 0 lactate spikes). Although the smooth-controller did not improve cell yield (4.91*10^7 compared to 5.08*10^7), it did reduce media usage to match the reduced growth rate thereby increasing cell yield per mL of fed media (6.3*10^4 to 8.6*10^4).

Keywords: Agents-based systems, Autonomous systems, Cooperative control
Abstract: In this work, a multi-agent system with emergent hypocycloidal and epicycloidal behaviors is analyzed. Agents are assumed to be modeled as double integrators with an acceleration law designed so that the swarm exhibits cycloidal like trajectories. The resulting control protocol benefits from speeds and positions coupling among neighbors agents to let each agent perform hypocycloidal or epicycloidal curves according to the choice of the controller parameters and the agents initial conditions. As a first step, the model properties are obtained assuming that the communication topology of the multi-agent system is defined by a complete graph. As a further step, the model main features are extended by relaxing the complete connection assumption and replacing it with a more realistic one in which a connected graph is considered. This latter step is achieved by means of a consensus-based estimation of the swarm centroid, so that to virtualize the complete graph starting from a connected one. Simulations have been performed to show the properties of the obtained agents evolution.

Keywords: Agents-based systems, Autonomous systems, Cooperative control
Abstract: This paper introduces the concept of formation switching in time-varying formation tracking (TVFT) control for linear time-invariant (LTI) multi-agent systems (MASs) under the collision avoidance constraints. One of the main challenges in designing a novel formation controller is that the leader agent does not prespecify the desired formation to the follower agents. Also, the former may change the desired formation to any other at the run time according to task requirements and environmental spatial constraints. Based on estimation of the so-called generator matrix and the formation vector, follower agents maintain the time-varying formation while tracking the leader. The exponential stability of the overall proposed distributed control scheme is proved using the Lyapunov stability theory. Finally, the effectiveness of the formation switching in TVFT is demonstrated using a numerical example.

Keywords: Agents-based systems, Autonomous systems, Networked control systems
Abstract: In recent years, the security and resilience of distributed algorithms have become a feature of the utmost importance, especially for applications dealing with sensitive data or critical infrastructures. In this paper, we develop a robust weighted distributed consensus algorithm based on agents’ reputations. By resorting to Evidence Theory, our algorithm is able to evaluate the reputation of each communication link in the graph and to update it over time, following the evolution of each node’s behavior. Moreover, our approach is able to detect the presence of malicious or faulty nodes that vary their propensity to adhere to the correct consensus strategy over time. Finally, the reputation evaluation process is reinforced at each step by a novel weight correction algorithm, which improves the efficacy of recognizing corrupted nodes and is able to reduce their influence on past history. A simulation campaign completes the paper and demonstrates its effectiveness experimentally

Keywords: Agents-based systems, Biologically-inspired methods, Decentralized control
Abstract: In this article, we present a constraint-driven optimal control framework that achieves emergent cluster flocking within a constrained 2D environment. We formulate a decentralized optimal control problem that includes safety, flocking, and predator avoidance constraints. We explicitly derive conditions for constraint compatibility and propose an event-driven constraint relaxation scheme. We map this to an equivalent switching system that intuitively describes the behavior of each agent in the system. Instead of minimizing control effort, as it is common in the ecologically-inspired robotics literature, in our approach, we minimize each agent's deviation from their most efficient locomotion speed. Finally, we demonstrate our approach in simulation both with and without the presence of a predator.

Keywords: Agents-based systems, Control applications, Mechatronics
Abstract: In this article, the problem of designing an active disturbance rejection control (ADRC) strategy for omnidirectional mobile robots in leader-follower formation is addressed. The proposed solution utilizes the partially available robot dynamical model and only uses robot position as measurable information. A special extended state observer in error-based form is constructed allowing the controller to be designed without an explicit use of signal time-derivatives, which increases the practical appeal of the introduced control scheme. Experimental results show the effectiveness of the approach in terms of trajectory tracking and disturbance rejection.

Keywords: Agents-based systems, Cooperative control, Autonomous systems
Abstract: Consensus among double integrators, over a directed network in presence of a cycle, is not guaranteed even if the graph has a spanning tree. Necessary and sufficient condition for consensus in such a set-up shows that a positive lower bound exists on the `velocity coupling factor' when a cycle is present, as opposed to an acyclic graph where any positive coupling factor suffices. This positive lower bound, on account of a reverse edge addition, may require every agent in the network, to increase the coupling factor. Motivated by this, the present paper proposes several approaches to guarantee consensus for chain networks with a single reverse edge (resulting in a directed cycle). Moreover, the proposed strategies can be implemented locally since only the nodes or edge-weights involved in the cycle or adjacent to it need to effect changes to guarantee consensus while the rest of the agents remain unaffected.

Keywords: Game theory, Aerospace, Robust control
Abstract: The target defense game is an abstraction of the counter-UAV mission, where a defender intends to intercept an invading drone before it enters a target area. While most studies on target defense games assume the defender travels faster, defending a target area with a slower defender is a less studied yet challenging problem because capture cannot be guaranteed. This paper identifies two special cases where the defender has a chance to win, where the game region is bounded and where the target area is small. In the former case, the defender traps the invader at the corner. In the latter case, the defender delays the entering permanently by rotating around the target area at a sufficiently large angular speed. In both games, the optimal trajectory has a two-stage structure. Exploiting this feature, a novel method is proposed to solve for the barrier, which gives guidelines on how to deploy the defenders to ensure the target area been protected.

Keywords: Game theory, Agents-based systems, Distributed control
Abstract: We investigate a multi-agent decision problem in population games where each agent in a population makes a decision on strategy selection and revision to engage in repeated games with others. The strategy revision is subject to time delays which represent the time it takes for an agent revising its strategy needs to spend before it can adopt a new strategy and return back to the game. We discuss the effect of the time delays on long-term behavior of the agents’ strategy revision. In particular, when the time delays are large, the strategy revision would exhibit oscillation and the agents spend substantial time in “transitioning” between different strategies, which prevents the agents from attaining the Nash equilibrium of the game. As a main contribution of the paper, we propose an algorithm that tunes the rate of the agents’ strategy revision and show such tuning approach ensures convergence to the Nash equilibrium. We validate our analytical results using simulations.

Keywords: Game theory, Agents-based systems, Networked control systems
Abstract: In this paper, we study network games where players are involved in information aggregation processes subject to the differential privacy requirement for players’ payoff functions. We propose a Laplace linear-quadratic functional perturbation (LLQFP) mechanism, which perturbs players' payoff functions with linear-quadratic functions whose coefficients are produced from truncated Laplace distributions. For monotone games, we show that the LLQFP mechanism maintains the concavity property of the perturbed payoff functions, and produces a perturbed NE whose distance from the original NE is bounded and adjustable by Laplace parameter tuning. We focus on linear-quadratic games, which is a fundamental type of network games with players' payoffs being linear-quadratic functions, and derive explicit conditions on how the LLQFP mechanism ensures differential privacy with a given privacy budget. Lastly, numerical examples are provided for the verification of the advantages of the LLQFP mechanism.

Keywords: Game theory, Agents-based systems, Optimization
Abstract: In this work, we extend the convex body chasing problem to an adversarial setting, where an agent (the Player) is tasked to chase a sequence of convex bodies generated adversarially by an opponent. The Player aims to minimize the cost associated with its total movements, while the Opponent tries to maximize. The set of feasible convex bodies is finite and known to both agents, which allows us to provide performance guarantees with max-min optimality rather than via the competitive ratio. Under some mild assumptions, we show the continuity of the optimal value function and provide an algorithm to numerically generate the optimal policies with performance guarantees. Finally, the theoretical results are verified through numerical examples.

Keywords: Game theory, Agents-based systems
Abstract: A salient feature of many optimal decision-making policies in adversarial environments is a level of unpredictability, or randomness, which keeps opponents uncertain about the system's strategies. These considerations, along with feedback from adversarial behaviors, are crucial in ensuring the security of modern infrastructures and complex systems. This paper considers policies that do just the opposite, namely ones that reveal strategic intentions to an opponent before engaging in competition. We consider such scenarios in the context of General Lotto games, which models the competitive allocation of resources between opposing players. Here, we consider a dynamic extension where one of the players has the option to publicly pre-commit assets to a battlefield in the first stage. In response, the opponent decides whether to secure the battlefield by matching the pre-commitment with its own resources, or to withdraw from it entirely. They then engage over the remaining set of battlefields in the second stage. We show that the weaker-resource player can have incentives to pre-commit when the battlefield values are asymmetric across players. Previous work asserts this never holds when the values are symmetric across players. Our analysis demonstrates the viability of alternate strategic mechanisms that a competitor may be able to employ.

Keywords: Game theory, Autonomous robots
Abstract: We consider a path guarding problem in dynamic Defender-Attacker Blotto games (dDAB), where a team of robots must defend a path in a graph against adversarial agents. Multi-robot systems are particularly well suited to this application, as recent work has shown the effectiveness of these systems in related areas such as perimeter defense and surveillance. When designing a defender policy that guarantees the defense of a path, information about the adversary and the environment can be helpful and may reduce the number of resources required by the defender to achieve a sufficient level of security. In this work, we characterize the necessary and sufficient number of assets needed to guarantee the defense of a shortest path between two nodes in dDAB games when the defender can only detect assets within k-hops of a shortest path. By characterizing the relationship between sensing horizon and required resources, we show that increasing the sensing capability of the defender greatly reduces the number of defender assets needed to defend the path.

Keywords: Autonomous vehicles, Agents-based systems, Automotive control
Abstract: Flocking control of multi-agent ground vehicles recently attracted rising attention because of its strength in extending 1D platooning to coordinated 2D movements. However, the uniform interaction ranges and the non-defined orientation of the flocking lattice make flocking control of ground vehicles face some key issues. To achieve cooperative motions of connected and automated vehicles (CAVs), this letter proposed a novel and elliptical lattice to extend the existing flocking theory with a uniform hexagon lattice. The proposed elliptical lattice is designed based on the characteristics of the vehicle heading direction, velocity, minimum safety distance, and lane width to analytically adapt to vehicle driving environments. Moreover, a new flocking control law considering road boundaries’ (permanent) repulsive forces is developed to ensure the desired formation at a steady state. Simulation results show that the proposed elliptical lattice of flocking control can be applied to realize cooperative driving of multi-agent CAVs with the desired formation on the road.

Keywords: Automotive control, Control applications
Abstract: Recently, motor speed reference generators have been designed for the cruise control of electric vehicles with either centralized electric motors (straight manoeuvres) or in-wheel motors (bend manoeuvres with sufficiently small constant steering angles). Steady-state operation at a safe (though conservative) tire longitudinal slip can be achieved, with no a priori knowledge regarding the occurrence of a specific external condition. Here, an innovative solution is presented. It is based on an ingenious use of Pacejka-like curves - representing the torque current-slip characteristics of the vehicle - to design a new contraction-mapping-based automatic tuning procedure for the longitudinal velocity of the vehicle. Such an innovative procedure overcomes the highly conservative nature of the previous approach in terms of unduly small longitudinal velocities (and yaw rates) under relatively favourable external conditions while guaranteeing a safe operating condition close to the maximum of the torque-slip characteristics with no knowledge of the tire-road adhesion coefficient. Comparative CarSim simulations illustrate the effectiveness of the proposed approach, in the presence of uncertain parameters and complex vehicle dynamics that are neglected at the control design stage.

Keywords: Identification for control, Control applications, Automotive control
Abstract: Physics-informed deep learning is a popular trend in the modeling and control of dynamical systems. This paper presents a novel method for rapid online identification of vehicle cornering stiffness coefficient, a crucial parameter in vehicle stability control models and control algorithms. The new method enables designers to rapidly identify the vehicle front and rear cornering stiffness parameters so that the controller reference gains can be re-adjusted under varying road and vehicle conditions to improve the reference tracking performance of the control system during operation. The proposed method based on vehicle model-based deep learning is compared to other alternatives such as traditional neural network training and identification, and Pacejka model estimation with regression. Our initial findings show that, in comparison to these classical methods, high fidelity estimations can be done with much smaller data sets simple enough to be obtained from a lane-changing or vehicle overtake maneuver. In order to conduct experiments, and collect sensor data, a custom-built 1:8 scaled test vehicle platform is used real-time wireless networking capabilities. The proposed method is applicable to predict derived vehicle parameters such as the understeering coefficient so it can be used in parallel with conventional MIMO controllers. Our H∞ yaw rate regulation controller test results show that the reference gains updated with the proposed online estimation method improve the tracking performance in both simulations and vehicle experiments.

Keywords: Autonomous vehicles, Machine learning, Game theory
Abstract: In this paper, we set up a two-player-zero-sum Markov game (TZMG) framework to train a safe driving policy network so that the worst intentions of the neighbor vehicles can be considered. Compared to the conventional policy learning frameworks, the TZMG framework can embed the adversary from the neighbor vehicle throughout its training process. Furthermore, a novel TZMG Q-learning algorithm based on the Wolpertinger policy is proposed to be scalable to multiple adversarial neighbor vehicles. Finally, simulations and humans-in-the-loop experiments are conducted to verify the effectiveness of the TZMG framework and novel algorithm. Compared to the benchmarking safety controllers in the literature, our proposed novel TZMG algorithm can achieve a much lower collision rate when dealing with adversarial neighbor vehicles.

Keywords: Autonomous vehicles, Delay systems, Automotive control
Abstract: A lane-keeping controller for automobiles is analyzed in this paper, with the consideration of time delay in the feedback loop. Using numerical continuation, unstable periodic orbits are identified inside the linearly stable domain of control gains. Based on the amplitude of these unstable solutions, safe parameter zones can be identified, where the closed loop system is robust against perturbations, i.e., where the basin of attraction of the stable equilibrium is larger. The sensitivity to initial conditions in different regions of linearly stable control gains is demonstrated by a series of real vehicle experiments. Finally, modifications of the control law are proposed that lead to significant improvements in terms of the robustness against perturbations of the controlled vehicle, achieving global stability in the practical sense.

Keywords: Autonomous vehicles, Automotive control, Optimal control
Abstract: Vehicle-to-infrastructure (V2I) communication connects vehicles and enables collision-free and energy-efficient driving, such as eco-approaches and departures at signalized intersections. An increased connectivity range can connect multiple signalized intersections and lead to long-term energy-efficient driving using richer information. However, no published studies to date provide insights into the energy-saving potential of increasing the connectivity range. In this paper, we present a V2I-enabled eco-driving control that can perform multiple traffic signal eco-approaches, and we systematically design a large-scale simulation study to quantify the energy impact of the increased V2I range for various scenarios. Simulation results show that the V2I-enabled eco-driving control can reduce energy use by up to 40%, on average, compared to the baseline, depending on road attributes and vehicle powertrain type. We validate these findings by evaluating the controller through a vehicle-in-the-loop (VIL) testing platform.

Keywords: Distributed control, Agents-based systems, Autonomous robots
Abstract: UAV swarm needs careful task and time arrangement to complete complex tasks with spatiotemporal constraints such as search and rescue, which requires distributed scheduling methods. Market-based approach is the optimal choice to satisfy the centerless and self-organized characteristics of the swarm. However, the consensus methods adopted by most market-based algorithms require synchronous communication, which takes time to wait, so scholars resort to asynchronous consensus methods. The existing asynchronous method's communication traffic increases with the number of tasks, and the total number of messages sent can be further reduced. Therefore, this paper proposes a new asynchronous method to further reduce the communication traffic and the number of messages sent required by the market-based approach. Firstly, the timestamp of when a UAV updates its information is used cleverly, which reduces the communication traffic of the original timestamp of when a task's information is updated. And the new timestamp contains more information about the non-winner that is absent in the original timestamp, which facilitates new asynchronous consensus rules to resolve task conflicts faster. Secondly, agent-related asynchronous consensus rules with new timestamps are designed to resolve task conflicts, which effectively solves the problem of information arriving out of order and potentially reduces the number of messages sent. Finally, through a self-developed ad-hoc network simulation system, the swarm scheduling under real networking conditions is simulated. A large number of Monte Carlo simulation experiments show that compared with the most representative asynchronous method Asynchronous Consensus-Based Bundle Algorithm (ACBBA), the number of messages sent and communication traffic can be reduced by 61% and 70% at most, and the scheduling time can be reduced by up to 60%.

Keywords: Distributed control, Agents-based systems, Time-varying systems
Abstract: This letter proposes an observer-based formation tracking control approach for multi-agent velocity-controlled vehicles under the assumption that either relative or global position measurements are unavailable for all the vehicles. It is assumed that only some vehicles (at least one) have access to their own global position, and all vehicles are equipped with sensors capable of sensing the bearings relative to neighboring vehicles. Each vehicle estimates its global position using relative bearing measurements and estimates of neighboring vehicles received over a communications network. Then, a distributed output-feedback observer-based controller is designed relying on bearing measurements and the estimated global positions. In contrast with the literature on bearing-based localization and control, we relax the common assumption of so-called bearing rigidity, and, in addition, we do not assume that the interconnections are constant. To the best of our knowledge, the bearing-based localization-and-tracking control problem under such assumptions remains open. In support of our theoretical findings, some simulation results are presented to illustrate the performance of the proposed observer-based tracking controllers.

Keywords: Distributed control, Autonomous systems, Networked control systems
Abstract: Coverage control algorithms seek to spatially distribute agents in a domain of coverage, e.g., to minimize proximity to all points. Leader-follower consensus network algorithms use local coordination rules to influence the behavior of a multi-agent system (MAS) as a whole through explicit control of a subset of agents (called leaders) and neighbor interactions. In this paper, the equivalence of these two classes of distributed algorithms for swarm robotics, that were once considered inherently different, is established. We present a swarm robotics application, where the real agents (i.e., the robots) in the domain of coverage are followers; and virtual agents (i.e., the leaders) are introduced based on the domain of coverage. The dynamics of followers are shown to be in the form of a weighted, state-dependent consensus protocol and the dynamics of the leaders (dependent on the evolution of the domain) are provided. Formulating a standard coverage algorithm (i.e., Lloyd's algorithm) over 2D polygonal domains as a leader-follower consensus protocol makes the structure of the ensemble-level dynamics for the MAS explicit with respect to neighbor interaction. The resultant weighted graph Laplacian may contribute to the future investigation on the performance guarantees of a MAS tracking a time-varying domain. The equivalence of the two classes of algorithms is validated in simulation.

Keywords: Distributed control, Control of networks, Lyapunov methods
Abstract: This paper addresses the distributed bipartite containment tracking-control problem for autonomous vehicles steered by multiple leaders. Some leaders are cooperative and others are competitive, so the vehicles form a so-called coopetition network; in which the interaction links may be negative or positive. The presence of cooperative and antagonistic leaders does not enable the system to achieve consensus. Instead, the followers’ states converge to a residual compact set, not predefined, but depending only by the leaders’ states. We establish global exponential stability for this so-called bipartite containment set, and we compute the exact equilibria to which all agents converge inside of it. Our proofs are constructive, that is, we provide strict Lyapunov functions, which also allow us to establish robustness with respect to external disturbances. Numerical simulations illustrate our theoretical findings.

Keywords: Distributed control, Cooperative control, Adaptive control
Abstract: In this paper, we study the problem of Nash equilibrium seeking of N-player games for single integrator dynamics subject to bounded disturbances with unknown bounds. Compared with the existing results, two new features are worth mentioning. First, the communication network among players is jointly strongly connected, which can be disconnected at every time instant. Second, the class of the disturbances contains any bounded time function with the bounds unknown. To achieve our objective, we have proposed a novel approach by integrating the distributed estimator, some nonlinear control technique, and adaptive control technique. Our design is illustrated by the example of a group of velocity-actuated robots in sensor networks.

Keywords: Distributed control, Cooperative control, Adaptive control
Abstract: In this paper, a distributed adaptive control algorithm is designed for an uncertain multiagent system in the presence of unmeasurable coupled dynamics that adopts user-assigned Laplacian matrix nullspaces. Specifically, we use observer dynamics that help us to guarantee the overall system stability, low-frequency learning methods to deal with high-frequency learning, and a modified Laplacian matrix to coordinate the multiagent system. Our algorithm proposes the coordination of multiagent systems and an asymptotic decoupling approach. An illustrative numerical example is given to demonstrate our theoretical contributions.

Keywords: Robotics, Autonomous robots, Estimation
Abstract: The process-aware source seeking (PASS) problem in flow fields aims to find an informative trajectory to reach an unknown source location while taking the energy consumption in the flow fields into consideration. Taking advantage of the existing methods on flow field partition, this paper formulates this problem as a task and motion planning (TAMP) problem and proposes a bi-level hierarchical planning framework to decouple the planning of inter-region transition and inner-region trajectory by introducing inter-region junctions. An integrated strategy is utilized to enable efficient upper-level planning by investigating the optimal solution of the lower-level planner. The proposed algorithm provides guaranteed convergence of the trajectory, and achieves automatic trade-off between exploration and exploitation, which has been validated by the simulation results.

Keywords: Predictive control for nonlinear systems, Optimal control, Energy systems
Abstract: Designing control inputs for a system that involves dynamical responses in multiple timescales is nontrivial. This paper proposes a parameterized time-warping function to enable a non-uniformly sampling along a prediction horizon given some parameters. The horizon should capture the responses under faster dynamics in the near future and preview the impact from slower dynamics in the distant future. Then a variable sampling MPC (VS-MPC) strategy is proposed to jointly determine optimal control and sampling parameters at each timestamp. VS-MPC adapts how it samples along the horizon and determines optimal control accordingly at each timestamp without offline tuning or trial and error. A numerical example of a wind farm battery energy storage system is also provided to demonstrate that VS-MPC outperforms the uniform sampling MPC.

Keywords: Robotics, Autonomous robots, Predictive control for nonlinear systems
Abstract: We propose an interleaved method for robotic task and motion planning (TAMP) problems, which involves optimizing both continuous and discrete dynamic behaviors. The coupling between the task planning and motion planning results in a large search space, causing challenge for computing the optimal solution. To address this challenge, we develop a novel bi-level algorithm leveraging the Depth First Search (DFS) algorithm and the Monte Carlo Tree Search (MCTS) algorithm to solve the TAMP. Incorporating task completion cost estimation from the motion planning level, we solve the task planning problem in a computationally efficient manner. We prove that our proposed TAMP algorithm is complete, i.e., it always finds the optimal solution if there exists one. Finally, we present simulation results to demonstrate that the proposed algorithm can find the optimal solution of the TAMP problem with lower computation cost than existing algorithms.

Keywords: Predictive control for nonlinear systems, Optimization, Machine learning
Abstract: Data-driven predictive control (DPC) is a feedback control method for systems with unknown dynamics. It repeatedly optimizes a system's future trajectories based on past input-output data. We develop a numerical method that computes poisoning attacks that inject additive perturbations to the online output data to change the trajectories optimized by DPC. This method is based on implicitly differentiating the solution map of the trajectory optimization in DPC. We demonstrate that the resulting attacks can cause an output tracking error one order of magnitude higher than random perturbations in numerical experiments.

Keywords: Biologically-inspired methods, Identification, Robotics
Abstract: Water flow plays an important role in the operation of marine robotic vehicles (MRVs). In confined survey areas, accurate perception of the flow field can greatly assist MRVs in path planning and improve energy efficiency. Traditional flow observations rely on data from buoys and satellites, which is expensive and time-consuming. Therefore, predicting the flow field using the vehicle's position and velocity information can significantly enhance work efficiency. Motion tomography (MT) is a time-efficient and convenient technique that estimates the flow field by separating the movement caused by the flow field from the trajectory of the MRV. Additionally, robotic fish are ideal for this flow field sensing task due to their maneuverability and versatility. Using robotic fish to sense the flow field can greatly benefit transportation and environment studies. However, MT ignores the rigid-body dynamics, which can significantly undermine the estimation accuracy. To address this challenge, we add an active heading control (AHC) to moderate the passive heading change caused by the flow field. With AHC's help, the position and direction data collected from a robotic fish can provide a promising estimation of the flow field in both simulations and experiments.

Keywords: Autonomous robots, Robotics, Uncertain systems
Abstract: We present UrbanFly: an uncertainty-aware real-time planning framework for quadrotor navigation in urban high-rise environments. A core aspect of UrbanFly is its ability to robustly plan directly on the sparse point clouds generated by a Monocular Visual Inertial SLAM (VI-SLAM) backend. It achieves this by using the sparse point clouds to build an uncertainty-integrated cuboid representation of the environment through a data-driven monocular plane segmentation network. Our chosen world model provides faster distance queries than the more common voxel-grid representation. UrbanFly leverages this capability in two different ways leading to two trajectory optimizers. The first optimizer uses the gradient-free cross-entropy method to compute trajectories that minimize collision probability and smoothness cost. Our second optimizer is a a simplified version of the first and uses a sequential convex programming optimizer initialized based on probabilistic safety estimates on a set of randomly drawn trajectories. Both our trajectory optimizers are made computationally tractable and independent of the nature of underlying uncertainty by embedding the distribution of collision violations in Reproducing Kernel Hilbert Space. Empowered by the algorithmic innovation, UrbanFly outperforms competing baselines in metrics such as collision rate, trajectory length, etc., on a high-fidelity AirSim simulator augmented with synthetic and real-world dataset scenes.

Keywords: Building and facility automation, Optimization algorithms, Decentralized control
Abstract: Supervisory control strategies in heating, ventilating, and air-conditioning (HVAC) systems hold the potential for significant energy savings but they are difficult to set up and often depend on unreliable sensor measurements. In this paper, we propose a sensor-free approach to minimizing the energy penalties due to simultaneous heating and cooling in variable-air-volume (VAV) systems with reheat. A general-purpose real-time optimizer is described that is easy to set-up and integrate with existing control logic. A cost function is derived that quantifies the simultaneous heating and cooling penalty that does not require any sensor measurements. The optimizer then minimizes this cost function by automatically adjusting the supply temperature setpoint in the air-handling unit. The paper describes the approach and shows results from application from field trials on a 27-zone building.

Keywords: Smart cities/houses, Decentralized control, Smart grid
Abstract: The flexible, efficient, and reliable operation of grid-interactive efficient buildings (GEBs) is increasingly impacted by the growing penetration of distributed energy resources (DERs). Besides, the optimization and control of DERs, buildings, and distribution networks are further complicated by their interconnections. In this paper, we exploit the load-side flexibility and clean energy resources to develop a novel two-level hybrid decentralized-centralized (HDC) algorithm for the coordination and control of DER-connected GEBs. The proposed HDC 1) achieves scalability w.r.t. to a large number of grid-connected buildings and devices, 2) incorporates a two-level design where an aggregator centrally controls at the building level and the system operator coordinates at the distribution network level in a decentralized way, and 3) improves the computing efficiency and communicating resilience with heterogeneous temporal scales. Simulations are conducted based on the prototype of a campus building at the Oak Ridge National Laboratory to show the efficiency and efficacy of the proposed approach.

Keywords: Machine learning, Control applications, Optimization algorithms
Abstract: Bayesian optimization (BO) has recently been demonstrated as a powerful tool for efficient derivative-free optimization of expensive black-box functions, such as those prevalent in performance optimization of complex energy systems. Classical BO algorithms ignore the relationship between consecutive optimizer candidates, resulting in jumps in the admissible search space which can lead to fail-safe mechanisms being triggered, or undesired transient dynamics that violate operational constraints. In this paper, we propose LSR-BO, a novel global optimization methodology that enforces local search region (LSR) constraints by design, which restricts how much the optimizer candidate can be changed at every iteration. We demonstrate that naively incorporating LSR constraints into BO causes the algorithm to get stuck in local sub-optimal solutions, and overcome this challenge through the development a novel exploration strategy that can gracefully navigate the tradeoff between short-term local, and long-term global, performance improvement. Furthermore, we provide theoretical guarantees on the convergence of LSR-BO. Finally, we verify the effectiveness of our proposed LSR-BO method on an illustrative benchmark and a real-world energy minimization problem for a commercial vapor compression system.

Keywords: Identification for control, Stochastic systems, Smart grid
Abstract: Buildings are a promising source of flexibility for the application of demand response. In this work, we introduce a novel battery model formulation to capture the state evolution of a single building. Being fully data-driven, the battery model identification requires one dataset from a period of nominal controller operation, and one from a period with relative flexibility requests, without making any assumptions on the underlying, but fixed, controller structure. We consider parameter uncertainty in the model formulation and show how to use risk measures to encode risk preferences of the user in robust uncertainty sets. Finally, we demonstrate the uncertainty-aware prediction of flexibility envelopes for a building simulation model from the Python library Energym.

Keywords: Process Control, Modeling, Machine learning
Abstract: While implementing renewable energy systems and model predictive control (MPC) could reduce non-renewable energy consumption, one challenge to building climate control using MPC is the weather forecast uncertainty. In this work, we propose a data-driven robust model predictive control (DDRMPC) framework to address climate control of a sustainable building with renewable hybrid energy systems under weather forecast uncertainty. The control and energy system configurations include heating, ventilation, and air conditioning, geothermal heat pump, photovoltaic panel, and electricity storage battery. Historical weather forecast and measurement data are gathered from the weather station to identify the forecast errors and for the use of uncertainty set construction. The data-driven uncertainty sets are constructed with multiple machine learning techniques, including principal component analysis with kernel density estimation, K-means clustering coupled with PCA and KDE, density-based spatial clustering of applications with noise, and the Dirichlet process mixture model. Lastly, a data-driven robust optimization problem is developed to obtain the optimal control inputs for a building with renewable energy systems. A case study on controlling a building with renewable energy systems located on the Cornell University campus is used to demonstrate the advantages of the proposed DDRMPC framework.

Keywords: Predictive control for nonlinear systems, Energy systems, Control applications
Abstract: We present a methodology based on mixed-integer nonlinear model predictive control for a real-time building energy management system in application to a single-family house with a combined heat and power (CHP) unit. The developed strategy successfully deals with the switching behavior of the system components as well as minimum admissible operating time constraints by use of a special switch-cost-aware rounding procedure. The quality of the presented solution is evaluated in comparison to the globally optimal dynamic programming method and conventional rule-based control strategy. Based on a real-world scenario, we show that our approach is more than real-time capable while maintaining high correspondence with the globally optimal solution. We achieve an average optimality gap of 2.5% compared to 20% for a conventional control approach, and are faster and more scalable than a dynamic programming approach.

Keywords: Process Control, Predictive control for nonlinear systems, Chemical process control
Abstract: Integrating measurements and historical data can enhance control systems through learning-based techniques, but ensuring performance and safety is challenging. Robust model predictive control strategies, like stochastic model predictive control, can address this by accounting for uncertainty. Gaussian processes are often used but have limitations with larger models and data sets. We explore Bayesian neural networks for stochastic learning-assisted control, comparing their performance to Gaussian processes on a wastewater treatment plant model. Results show Bayesian neural networks achieve similar performance, highlighting their potential as an alternative for control designs, particularly when handling extensive data sets.

Keywords: Stochastic optimal control, Uncertain systems, Machine learning
Abstract: We propose formulating the finite-horizon stochastic optimal control problem for colloidal self-assembly in the space of probability density functions (PDFs) of the underlying state variables (namely, order parameters). The control objective is formulated in terms of steering the state PDFs from a prescribed initial probability measure towards a prescribed terminal probability measure with minimum control effort. For specificity, we use a univariate stochastic state model from the literature. Both the analysis and the computational steps for control synthesis as developed in this paper generalize for multivariate stochastic state dynamics given by generic nonlinear in state and non-affine in control models. We derive the conditions of optimality for the associated optimal control problem. This derivation yields a system of three coupled partial differential equations together with the boundary conditions at the initial and terminal times. The resulting system is a generalized instance of the so-called Schr"{o}dinger bridge problem. We then determine the optimal control policy by training a physics-informed deep neural network, where the "physics" are the derived conditions of optimality. The performance of the proposed solution is demonstrated via numerical simulations on a benchmark colloidal self-assembly problem.

Keywords: Optimal control, Stochastic optimal control, Control applications
Abstract: Anisotropy of temperature fields, chemical potentials and ion concentration gradients provide the fuel that feeds dynamical processes that sustain life. Dynamical flows in respective environments incur losses manifested as entropy production. In this work we consider a rudimentary model of an overdamped stochastic thermodynamic system in an anisotropic temperature heat bath, and analyze the problem to minimize entropy production while driving the system between thermodynamic states in finite time. It is noted that entropy production in a fully isotropic temperature field, can be expressed as the Wasserstein-2 length of the path traversed by the thermodynamic state of the system. In the presence of an anisotropic temperature field, the mechanism of entropy production is substantially more complicated as, besides dissipation, it entails seepage of energy between the ambient heat sources by way of the system dynamics. We show that, in this case, the entropy production can be expressed as the solution of a suitably constrained and generalized Optimal Mass Transport (OMT) problem. In contrast to the situation in standard OMT, entropy production may not be identically zero, even when the thermodynamic state remains unchanged. Physically, this is due to the fact that maintaining a Non-Equilibrium Steady State (NESS), incurs an intrinsic entropic cost. As already noted, NESSs are the hallmark of life and living systems by necessity operate away from equilibrium. Thus our problem of minimizing entropy production appears of central importance in understanding biological processes, such as molecular motors and motor proteins, and on how such processes may have evolved to optimize for available usage of resources.

Keywords: Machine learning, Estimation, Iterative learning control
Abstract: Duality of control and estimation allows mapping recent advances in data-guided control to the estimation setup. This paper formalizes and utilizes such a mapping to consider learning the optimal (steady-state) Kalman gain when process and measurement noise statistics are unknown. Specifically, building on the duality between synthesizing optimal control and estimation gains, the filter design problem is formalized as direct policy learning. In this direction, the duality is used to extend existing theoretical guarantees of direct policy updates for Linear Quadratic Regulator (LQR) to establish global convergence of the Gradient Descent (GD) algorithm for the estimation problem–while addressing subtle differences between the two synthesis problems. Subsequently, a Stochastic Gradient Descent (SGD) approach is adopted to learn the optimal Kalman gain without the knowledge of noise covariances. The results are illustrated via several numerical examples.

Keywords: Filtering, Stochastic optimal control
Abstract: We study the filtering problem over a Lie group that plays an important role in robotics and aerospace applications. We present a new particle filtering algorithm based on stochastic control. In particular, our algorithm is based on a duality between smoothing and optimal control. Leveraging this duality, we reformulate the smoothing problem into an optimal control problem, and by approximately solving it (using, e.g., iLQR) we establish a superior proposal for particle smoothing. Combining it with a suitable designed sliding window mechanism, we obtain a particle filtering algorithm that suffers less from sample degeneracy compared with existing methods. Finally, we exemplify our algorithm in a filtering problem over SO(3) for satellite attitude estimation.

Keywords: Stochastic optimal control, Optimization algorithms, Learning
Abstract: This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic optimal control problem as a policy optimization problem over the augmented state space. Then, the infinite-dimensional policy optimization problem is approximated as a finite-dimensional nonlinear program by applying function approximation, deterministic sampling, and temporal truncation. The approximated problem is solved by using automatic differentiation and condensed-space interior-point methods. We formulate several conceptual and practical open questions regarding the asymptotic exactness of the approximation and the solution strategies for the approximated problem. As proof of concept, we present numerical examples demonstrating the performance of the proposed method.

Keywords: Modeling, Energy systems, Machine learning
Abstract: Lithium-ion batteries are playing a key role in the sustainable energy transition. To fully exploit the potential of this technology, a variety of modeling, estimation, and prediction problems need to be addressed to enhance its design and optimize its utilization. Batteries are complex electrochemical systems whose behavior drastically changes as a function of aging, temperature, C-rate, and state of charge, posing unique modeling and control research questions. In this tutorial paper, we provide insights into three battery modeling methodologies, namely first principle, machine learning, and hybrid modeling. Each approach has its own strengths and weaknesses, and by means of three case studies we describe main characteristics and challenges of each of the three methods.

Keywords: Automotive control
Abstract: This talk is motivated by the potential of both solid-state and liquid electrolyte lithium-sulfur batteries to provide significant performance advantages over state-of-the-art lithium-ion batteries, especially in terms of specific energy. The talk provides a brief introduction to the lithium-sulfur chemistry, focusing on the modeling, estimation, and control challenges associated with this chemistry. The talk then surveys some of the key challenges and opportunities associated with the application of machine learning methods, especially the deep learning of battery dynamics, to this chemistry. Areas of overlap and potential synergy between machine learning and physics-based modeling approaches are particularly emphasized in this discussion.

Keywords: Mechatronics
Abstract: The quadrotor hierarchical control design (position-attitude) based on the state-space modeling has been widely applied in the past. Although the state-space representation, based on a group of first-order differential equations, is effective in modeling many dynamic systems, inherent high-order dynamics and control of quadrotor systems may not be properly handled by the state-space modeling. This letter proposes a modified high-order fully actuated (HOFA) theory for a group of high-order dynamic systems, including the quadrotor system, without relying on pseudo strict-feedback forms required by the original HOFA approach. Hence, the quadrotor model can be essentially converted into two HOFA subsystems. A nonlinear 3-DOF quadrotor modeling and control is applied as an example to demonstrate the effectiveness of the proposed approach, which can achieve arbitrarily assignable eigenstructure like a stabilized linear system.

Keywords: Modeling, Flight control, Linear systems
Abstract: Traditional cascade controller design based on state-space modeling has been widely applied for quadrotor systems. The state-space representation can effectively model many dynamic systems. Yet, a group of first-order differential equations may not be the most suitable way to model and control inherent high-order dynamic systems, such as quadrotors. This paper proposes a modified high-order fully actuated (HOFA) approach with recursive actions based on a mixed-order quadrotor model. Unlike the existing HOFA approach developed for generalized strict-feedback systems, the modified HOFA method does not require the system in a strict-feedback form. Hence, the 6-DOF quadrotor model can be essentially converted into three HOFA subsystems. Based on the obtained HOFA systems, the control design of 6-DOF nonlinear quadrotor systems can be readily achieved like linear systems with arbitrarily assignable eigenstructure. Simulation and experimental results are shown to verify the effectiveness of the proposed HOFA modeling and control approach.

Keywords: Mechatronics, Control applications, Mechanical systems/robotics
Abstract: In this brief, a new input shaping-based control law is proposed for an overhead crane with time-varying cable length. The proposed approach can accommodate a generalized input shaper and general hoisting motions. It will be shown that a non-robust input shaper can be used within the established scheme to completely suppress residual vibration at the completion of a maneuver, outperforming the standard (robust) input shaping controllers. Simulation results are provided.

Keywords: Mechatronics, Identification, Machine learning
Abstract: During the past few year, recurrent neural network (RNN) has been proposed to model the nonlinear dynamics of various dynamic systems, such as nano positioning systems (e.g, piezo electric actuators (PEAs)). Although high modeling accuracy has been demonstrated using RNNs, it has been found that the conventional RNNs (such as vanilla RNN) are susceptible to gradient vanishing or exploding issue and hence difficult to train. Deep RNNs, such as Long short-term memory (LSTM), have been proposed to address these issues. However, due to the conventional training data construction, the training is susceptible to overfitting and the computation is extensive. In this paper, we propose a new type of LSTM in the application of PEA system identification: a sequence-to- sequence learning approach (namely, LSTMseq2seq). The structure of LSTMseq2seq and its training data construction are presented in detail. The efficacy of LSTMseq2seq in terms of modeling accuracy and computation speed is demonstrated by applying it for PEA system identification and comparing its performance with that of vanilla RNN.

Keywords: Mechatronics, Mechanical systems/robotics, Closed-loop identification
Abstract: This paper proposes a feedforward compensation approach of scan-induced disturbances to improve the uncertainty of an active-sample tracking 3D measurement module. The measurement module acts as a robotic endeffector and is designed for precise robotic measurement applications directly in the vibration-prone environment of an industrial production line. By means of a feedback control-induced stiff link, a constant position of the electromagnetically levitated measurement platform (MP) is maintained with respect to the sample surface under test. Precise 3D imaging is enabled by scanning the measuring light spot of a 1D confocal chromatic sensor with a 2D fast steering mirror (FSM). Disturbances are caused due to scanning-induced reaction forces on the MP, impairing the system’s sample-tracking and 3D measurement performance. Based on the identified disturbance dynamics, a tailored feedforward control is designed to compensate the causing reaction forces. To experimentally evaluate the system performance, 3D measurements at the maximum frame of 1 fps are performed with disabled and enabled feedforward control. Evaluating the experimental results, the sample-tracking error in the MP’s translational degree of freedom z is significantly reduced by a factor of 7 down to 42 nm rms, being close to the MP’s static positioning noise. The reduced sample-tracking error further enables a higher 3D measurement performance, reducing the structural height uncertainty by 36% down to 180 nm rms.

Keywords: Mechatronics, Modeling, Switched systems
Abstract: Digital-to-analog conversion is essential in digital signal processing applications, including closed-loop control schemes. Noise and distortion in digital-to-analog converters result in reduced performance for high-precision mechatronics such as nano-positioning. Glitches are common in practical switched systems such as digital-to-analog converters; observed as an output disturbance. Due to the wide-bandwidth, impulse-like behavior, control law bandwidth is generally too low to provide adequate attenuation; deteriorating open and closed-loop performance. This article demonstrates how large-amplitude high-frequency periodic dither mitigates the effect of glitches in a nano-positioning system under closed-loop control. Simulations are performed using a model that includes significant non-linearities with a response fitted to an off-the-shelf commercial device, as well as using standard linear time-invariant models for other system components fitted to the responses of common, commercially available devices. The results highlight the significance of reconstruction filter design when applying dithering in this setting.

Keywords: Mechatronics, Robust control, Control applications
Abstract: In this paper, we propose a novel transform-based imaging mode for Atomic Force Microscopy (AFM), where the cantilever oscillations are made to track the output of a mock-model system. The states of the resulting tracking error dynamics is appended by another set of suitably designed states, which enable a specific time-varying coordinate transformation, which in turn results in dynamic models that are very conducive to linear control synthesis design methods. The proposed imaging mode enables higher throughput in AFM imaging without the need for significantly high resonant frequency AFM cantilever probes. This method overcomes the fundamental limitation of nonlinear input-output relationship in Amplitude Modulation AFM (AM-AFM) imaging mode by applying an appropriately chosen real-time transform on the output signal. In combination with model-based reference generation, the proposed real-time transform yields linear dynamical input-output characteristics. Simulations on detailed AFM models with H_∞-optimal control designs show the efficacy of the proposed imaging mode for feature bandwidths higher than 5% of the cantilever resonant frequency.

Keywords: Mechatronics
Abstract: We present a point-to-point trajectory generation framework that helps in enhancing the positioning of systems having uncertain lightly-damped vibration modes. To avoid exciting these modes, their uncertainties are matched with frequency bands and then used to specify the rejected frequencies under a k-cascaded second-order notch filter. To facilitate trajectory generation, the impulse response of this filter is altered by composing it off-line with a certain polynomial function of even degree in the time domain followed by a transformation. This will result in a unit-pulse acceleration signal with attenuated frequency contents in the rejected frequency bands, and therefore a reduced excitation of the lightly-damped modes is achieved. The resulting off-line generated unit-pulse acceleration signal is used as a template to ease real-time trajectory extrapolation using simple calculations due to the closed-form solutions provided. Therefore, real-time computational overhead is significantly reduced. Comparisons between the proposed method and frequency-shaped polynomials, finite-impulse response and input shaping are provided. The effectiveness of the proposed framework is illustrated through a numeric simulation.

Keywords: MEMs and Nano systems, Mechatronics, Manufacturing systems
Abstract: A system to suspend a silicon disk between two sets of stator electrodes is reported. Electrode pairs are used for both control and sensing by exerting electrostatic forces on the disk and measuring differential capacitances related to the disk's position. The disk is a six degree-of-freedom system, however, lateral and yaw motion are not measurable by the electrode arrangement so only the disk's vertical position, roll, and pitch are regulated. Two separate control strategies are pursued --decentralized feedback around the electrode-disk gaps and feedback around a decoupled coordinate frame related to the disk's controllable degrees-of-freedom. Experimental frequency responses obtained from closed-loop results of the suspended disk are reported and compared to analytical models.

Keywords: Stochastic optimal control, Mechatronics, Robotics
Abstract: For more than half a century, vibratory bowl feeders have een the standard in automated assembly for singulation, orientation, and manipulation of small parts. Unfortunately, these feeders are expensive, noisy, and highly specialized on single part design bases. We consider an alternative device and learning control method for singulation, orientation, and manipulation by means of seven fixed-position variable-energy solenoid impulse actuators located beneath a semi-rigid part supporting surface. Using computer vision to provide part pose information, we tested various machine learning (ML) algorithms to generate a control policy that selects the optimal actuator and actuation energy. Our manipulation test object is a 6-sided craps-style die. Using the most suitable ML algorithm, we were able to flip the die to any desired face 30.4% of the time with a single impulse, and 51.3% with two chosen impulses, versus a random policy succeeding 5.1%% of the time (that is, a randomly chosen impulse delivered by a randomly chosen solenoid).

Keywords: Optimization algorithms, Autonomous robots, Robotics
Abstract: Trajectory optimizations encountered in mobile robot navigation are non-convex, and thus the solution process is prone to get stuck at poor local optima, resulting in collisions with the environment. A conceptually simple workaround is to simply run the optimizer from several initializations in parallel and choose the best solution. But realizing this simple trick with off-the-shelf optimizers is challenging since they are not customized for parallel/batch operation. We fill this gap by proposing a novel batchable and GPU accelerated trajectory optimizer for autonomous navigation. Our batch optimizer can run several hundred instances of the problem in parallel in real time. We improve the state-of-the-art in the following respects. First, we show that parallel initialization naturally discovers a distribution of locally optimal trajectories residing in different homotopies. Second, we improve the navigation quality (success rate, tracking) compared to the baseline approach that relies on computing a single locally optimal trajectory at each control loop. Finally, we show that when initialized with trajectory samples from a Gaussian distribution, our batch optimizer outperforms the state-of-the-art cross-entropy method in solution quality. textbf{Codes:} url{https://tinyurl.com/a3b99m8}, Video: url{https://www.youtube.com/watch?v=ZlWJk-w03d8}

Keywords: Optimization, Autonomous systems
Abstract: Control barrier function-based quadratic programs (CBF-based QP) provide an avenue for agile and numerically efficient obstacle avoidance algorithms. However, the CBF-based QP methods may lead to lengthy detours and undesirable transient tracking performance without proper trajectory planning. This paper expands the CBF-based QP concept to create a modified safe reference trajectory with a prescribed avoidance radius and direction, where the modified reference shadows the actual reference during the avoidance maneuver. We use a control Lyapunov function (CLF) to match the modified reference with the actual reference and three CBFs to formulate safety and performance objectives to maintain distance, adjust velocity, and determine the direction of the avoidance maneuver. These formulations produce constraints that are synthesized by means of a quadratic program. The QP generates a desirable velocity profile for the safe reference trajectory. Numerical simulations verify the effectiveness of the proposed trajectory planning method.

Keywords: Optimization, Constrained control, Robotics
Abstract: Control systems often need to satisfy strict safety requirements. Safety index provides a handy way to evaluate the safety level of the system and derive the resulting safe control policies. However, designing safety index functions under control limits is difficult and requires a great amount of expert knowledge. This paper proposes a framework for synthesizing the safety index for general control systems using sum-of-squares programming. Our approach is to show that ensuring the non-emptiness of safe control on the safe set boundary is equivalent to a local manifold positiveness problem. We then prove that this problem is equivalent to sum-of-squares programming via the Positivstellensatz of algebraic geometry. We validate the proposed method on robot arms with different degrees of freedom and ground vehicles. The results show that the synthesized safety index guarantees safety and our method is effective even in high-dimensional robot systems.

Keywords: Optimization, Control applications, Power electronics
Abstract: Lifetime of the photovoltaic (PV) inverters is influenced by its power profile. The reliability of such PV inverters is affected by the thermal fatigue cycles witnessed by the underlying components. However, there is a trade-off between the inverter efficiency and the fatigue witnessed by its components. With a systematic formulation of this trade-off, a real-time nonlinear optimization problem is formulated to generate the appropriate reactive power set-points to the PV inverter controller. The proposed approach improves the lifetime of the inverters while keeping its efficiency above desired threshold value. The time domain loss and damage models that uses PV power profile as an input are critical to the proposed optimization framework. The proposed framework provides an option to the customer to operate the PV inverter with an objective of lifetime improvement under the acceptable losses by flattening the component thermal fatigue cycles. The framework is evaluated using the PV power profile of a 10 kVA PV inverter with various simulated case studies.

Keywords: Optimization, Estimation, Computational methods
Abstract: Stochastic approximation (SA) algorithms can be used in system optimization problems when only noisy measurements of a system are available. This paper formally compares the performance of two popular SA algorithms in a multivariate Kiefer-Wolfowitz setting of simultaneous-perturbation SA (SPSA) and the random-directions SA (RDSA). This paper provides sufficient conditions to demonstrate which algorithm has the smaller asymptotic mean squared error (MSE) and numerically presents comparison of SPSA and RDSA in a test function and a model-free control system. The theory and supporting numerics indicate that SPSA has better efficiency (lower MSE) across a broad range of problem settings.

Keywords: Optimization, Optimal control, Learning
Abstract: We propose a fundamental-model-based optimization framework for open-loop and real-time batch recipe optimization using mathematical programing (MP) and reinforcement learning (RL). The dynamic fundamental model gives rise to a complex nonlinear differential algebraic equations (DAE) system. We introduce a decomposition-based initialization algorithm for solving the large-scale nonlinear program (NLP) resulting from the discretization of the DAE system. The proposed MP and RL-based approaches are implemented to optimize the recipe of a semi-batch process in the Dow Chemical Company. For open-loop optimization, we find the optimal profiles of two input variables and the batch length that maximize average profit. For real time optimization, we train the RL agent using the fundamental model with uncertainties. The trained agent can interact with the actual process and provide control actions in real time.

Keywords: Optimization algorithms, Variational methods, Lyapunov methods
Abstract: Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local linearizations leading to tractable, convex sum-of-squares problems. We prove local convergence under the assumption of strong regularity, a common condition in variational analysis. The new approach is applied to estimate the region of attraction of a polynomial aircraft model, where it greatly outperforms previous methods for nonconvex sum-of-squares problems.

Keywords: Optimization, Optimization algorithms
Abstract: In this paper, we introduce a new notion of guaranteed privacy for distributed nonconvex optimization algorithms. In particular, leveraging mixed-monotone inclusion functions, we propose a privacy-preserving mechanism which is based on deterministic, but unknown affine perturbations of the local objective functions. The design requires a robust optimization method to characterize the best accuracy that can be achieved by an optimal perturbation. This is used to guide the refinement of a guaranteed-private perturbation mechanism that can achieve a quantifiable accuracy via a theoretical upper bound that is independent of the chosen optimization algorithm. Finally, simulation results illustrate that our approach outperforms a benchmark differentially private distributed optimization algorithm in the literature.

Keywords: Optimization, Uncertain systems, Computational methods
Abstract: Control co-design (CCD) has received much attention since it can achieve superior system performance by optimizing physical and control systems simultaneously. Despite many successful examples from diverse engineering fields using CCD, a lack of attention toward accounting for uncertainty hinders application to real-world systems. This paper aims to solve CCD problems under uncertainty by proposing a robust CCD formulation and algorithm. A robust feedback controller using tube-based model predictive control (tube-based MPC) approach is incorporated into a bi-level optimization architecture. The use of the set invariance theory and an approximation algorithm helps identify the set of all possible states due to disturbances, this set is known as a tube, and quantify system robustness by calculating the tube size. It enables designers to make performance-robustness tradeoffs with the approximate Pareto fronts. A numerical example and a simplified model of the satellite attitude control system are used to demonstrate the proposed method. Results show that the CCD solutions dominate most of the solutions from the traditional sequential design and control design only. This study will be extended into nonlinear applications in our future work.

Keywords: Optimization algorithms, Optimal control
Abstract: This work presents an optimal sampling-based method to solve the real-time motion planning problem in static and dynamic environments, exploiting the Rapid-exploring Random Trees (RRT) algorithm and the Model Predictive Path Integral (MPPI) algorithm. The RRT algorithm provides a nominal mean value of the random control distribution in the MPPI algorithm, resulting in satisfactory control performance in static and dynamic environments without a need for fine parameter tuning. We also discuss the importance of choosing the right mean of the MPPI algorithm, which balances exploration and optimality gap, given a fixed sample size. In particular, a sufficiently large mean is required to explore the state space enough, and a sufficiently small mean is required to guarantee that the samples reconstruct the optimal controls. The proposed methodology automates the procedure of choosing the right mean by incorporating the RRT algorithm. The simulations demonstrate that the proposed algorithm can solve the motion planning problem in real time for static or dynamic environments.

Keywords: Mechanical systems/robotics, Control applications, Vision-based control
Abstract: Ball-batting is a challenging task because it requires excellent eye-hand coordination and instantaneous decision making. Moreover, as a winning strategy, the task of ball-batting concerns not only about “hitting a flying ball with a bat”, but about “sending the rebounding ball to a prespecified location”. Therefore, the decisions on when and where to hit the ball and what the velocity of the bat is at the impact time are crucial for a successful ball-batting. Making such decisions should consider the flying and rebounding behavior of the ball and is very complicated. In this paper, we apply the deep reinforcement learning (DRL) method to train the ball-batting robot developed by the authors for making timely and appropriate batting decisions. A simulated environment consisting of a physical flying model and a neural network rebounding model is constructed for efficient training. Then experiments in the real world are conducted and the results show that after being trained by DRL, the robot can hit the incoming ball in all tests and send the rebounding ball to the target location with a successful rate of 58.8%.

Keywords: Mechanical systems/robotics, Learning, Optimal control
Abstract: Controlling oscillation is vital for applications in which flexible systems are employed. Many existing control methods rely on knowledge of the system dynamics to mitigate unwanted vibration. However, model-free methods can also be employed to control vibration. One method for model-free control is reinforcement learning (RL). Although the RL agent does not require information about the system to learn a control policy, domain knowledge of dynamics and control can be used to augment the agent and aid in generating an effective control policy. This work analyzes the effectiveness of training RL controllers that operate in combination with conventional controllers. Agents were trained in simulation using a model of a small-scale double-pendulum crane. The effect of the conventional control component on training as well as sensitivity to modeling error are analyzed. Agent transferability is investigated by implementing the simulation-trained controllers on a physical small-scale double-pendulum crane.

Keywords: Mechanical systems/robotics, Modeling, Simulation
Abstract: In order to calculate the necessary joint torques and end-effector forces in accordance with a desired dynamic behavior for assembly and manipulation tasks in the field of robotics, robotic impedance control has been extensively employed. Current complete congruent mapping equations have not been validated through actual robotic manipulators in impedance control tasks. In this paper, we show and validate from fundamental principles, with the use of a 6 DoF robotic manipulator, the transformation equations of the stiffness and damping matrices from Cartesian to joint space without losing generality. Our findings highlight the significance of the Cartesian damping coupling term, which is typically absent from the existent robotics literature, in the stiffness matrices after mapping them to the joint space.

Keywords: Robotics, Flexible structures, Emerging control applications
Abstract: Recent quadrotors have transcended conventional designs, emphasizing more on foldable and reconfigurable bodies. The state of the art still focuses on the mechanical feasibility of such designs with limited discussions on the tracking performance of the vehicle during configuration switching. In this article, we first present a common framework to analyse the attitude errors of a folding quadrotor via the theory of switched systems. We then employ this framework to investigate the attitude tracking performance for two case scenarios - one with a conventional geometric controller for precisely known system dynamics; and second, with our proposed morphology-aware adaptive controller that accounts for any modeling uncertainties. Finally, we cater to the desired switching requirements from our stability analysis by exploiting the trajectory planner to obtain superior tracking performance while switching. Simulation results are presented that validate the proposed control and planning framework for a foldable quadrotor's flight through a passageway.

Keywords: Robust adaptive control, Robotics, Neural networks
Abstract: This paper develops accelerated model-free robust adaptive control algorithms for unknown static maps which correspond to forward kinematics in robotics. The technique is based on the estimation of unknown Jacobian matrix by using a neural-network based approximation and use of monotonically increasing gain functions in the controller and update law. The introduced algorithms provide robustness against the unknown environmental disturbances and achieve asymptotic, exponential and prescribed-time reference trajectory tracking. The fixed-time stabilization in prescribed time is the strongest notion among them that allows user to predefine a terminal time irrespective of initial condition and system parameters. A formal stability analysis for each algorithm is presented and theoretical results are validated through numerical simulations conducted on a single-section three-actuator continuum robot.

Keywords: Robotics, Autonomous robots, Autonomous systems
Abstract: In this paper, a novel strategy for practical inspection planning in dry docks using unmanned aerial vehicles (UAVs) is presented. Planning is a fundamental prerequisite for accurate navigation and control of the UAV. The proposed method utilises the random sample consensus (RANSAC) algorithm to extract plane models from a voxel grid representation of the environment. For high-level planning, semantic knowledge of the environment is leveraged in a novel manner to exploit of structured obstacles, such as straight walls and orthogonal corners. In order to deal with lower-level navigation, the approach incorporates a simple graph-based local replanner to generate paths that avoid obstacles in the environment. The proposed method is compared with state-of-the-art graph-based planner in simulation and subsequently evaluated in a real environment. The paper maintains the use case of UAV vessel inspection and presents exhaustive simulation and field testing, which demonstrate the viability of the proposed approach in a fully working large-scale industrial environment.

Keywords: Distributed parameter systems, Linear systems, Energy systems
Abstract: We develop stochastic dynamical reduced-order models of wind farm turbulence that capture the effects of yaw misalignment due to control or atmospheric variability on turbine wakes and their interactions. Our models are based on the stochastically forced linearized Navier-Stokes equations around analytical descriptions of the wake velocity provided by low-fidelity engineering wake models. The power-spectral density of the source of additive stochastic excitation is identified via convex optimization to ensure statistical consistency with high-fidelity models while preserving model parsimony. We demonstrate the utility of our approach in capturing turbulence intensity variations in accordance with large-eddy simulations of the flow over a cascade of wind turbines. While our models are developed to match velocity correlations from sensors that are placed directly behind perfectly aligned wind turbine rotors, their predictions maintain a desirable level of accuracy even when the turbines are yawed.

Keywords: Emerging control applications, Simulation, Electrical machine control
Abstract: In most current offshore wind farms, the turbines are controlled greedily, neglecting any coupling by wake effects with other turbines. By neglecting these effects of aerodynamic interactions, the power production performance is substantially reduced.

Besides the well-known wake steering and dynamic induction control wake control strategies, a novel wind farm flow control strategy called the Helix approach has been recently proposed to mitigate the impacts of wake effects and optimize wind farm performance. The Helix approach adopts the individual pitch control (IPC) technique to dynamically deform the wake into the helical shape, which induces wake instability and thereby stimulates wake recovery. The first results employing a single-harmonic signal have demonstrated promising enhancement in wake recovery effects. However, more complex signals to potentially improve the effectiveness of the Helix approach have never been studied.

This paper explores the potential of using higher-harmonic signals in the Helix approach to further enhance wake mixing. The aeroelastic simulator, OpenFAST, with its recently developed free vortex wake codes is adopted to simulate the dynamic wake evolution. A Fourier stability analysis is used to quantitatively identify the wake breakdown position. Results show that the wake breaks down at 1.75 rotor diameter (D) from the rotor using optimized multi-sine signals, which is a significant improvement over the breakdown distance at 2.50 D resulting from the conventional single-sine Helix. The earlier wake breakdown indicates faster wake recovery and is to be validated by future higher-fidelity simulation studies.

Keywords: Energy systems, Simulation, Control applications
Abstract: The Helix approach is a control technology that reduces the wake effect in wind farms by accelerating wake mixing through individual pitch control, resulting in significant AEP gain. However, this study found that the controller may increase pitch bearing damage and loads on some turbine components, depending on its settings. Using a modified version of NREL's Reference OpenSource Controller in OpenFAST, this study analysed the sensitivity of loads and pitch bearing damage to different Helix controller settings on the IEA-15MW reference offshore wind turbine. Results showed that loads increased with the amplitude of the excitation signal but were less affected by its frequency. Additionally, more pitch bearing damage was observed in the counterclockwise Helix direction, while slightly higher loads were observed in the clockwise direction when using the same excitation signal amplitude and frequency for both directions.

Keywords: Estimation, Energy systems, Kalman filtering
Abstract: Wind farm control can be enhanced by feedback information about the current flow situation in the farm. Especially for closed-loop wake-steering control, the position of a wind turbine's wake with respect to the next turbine is valuable. Depending on the context, e.g. installed sensory or required time- and wake position resolution, different methods for wake tracking exist. With increasing fidelity, not only time-averaged wakes but also instantaneous wake conditions, arising from the meandering nature of a wind turbine wake, are considered for control. In this work, two methods for the dynamic estimation of the wake centre position are experimentally tested. One of them is based on wind turbine blade loads, the other on a fixed-beam staring lidar. Both methods use an Extended Kalman Filter with a dynamic model that takes the meandering nature of a wind turbine wake into account. In the atmospheric boundary layer, turbulence patterns of multiple rotor diameters are driving the downstream meandering of the wake. In wind tunnel setups with large model turbines, these spatial scale ratios are hardly reachable, thus meandering conditions were difficult to reproduce up to now. In this work, the inflow conditions are generated in a wind tunnel with an active grid, which imprints both a wind speed deficit and additional turbulence in a meandering frame of reference. The paper describes the creation and characterization of such inflow, while not claiming for an exact representation of a meandering wake in an atmospheric boundary layer. Inflow conditions of different meandering dynamics are created and their impact on the tracking methods is analyzed. The experiments show that the generated inflow conditions both resemble a wake and induce an expected response of the model turbine. The results from the wake tracking methods are comparable with the available literature, thus further indicate the potential of the setup for control-oriented experiments in the context of meandering wakes, turbine-turbine interaction and load alleviation.

Keywords: Control applications, Energy systems, Sensor networks
Abstract: Wake controls in wind farms has evolved significantly in the last twenty years, motivated mainly by its potential to increase annual energy production (AEP) through reduction of wake losses. Engineering models that characterize the wakes in the farm have enhanced fidelity and computational efficiency. Computational environments have been developed to adjust turbine control settings based on these models to reduce the impact of wakes. Several experimental campaigns have been carried out to validate the computational predictions. Yet, experimental results have typically shown lower AEP gains than expected. The variability in wake characteristics and the inability to calculate them online are key factors limiting the practical value of existing wake control solutions.

This work presents a wake control approach that proposes new sensors to measure the wakes online and uses accurate wake characteristics to enable further energy capture in offshore wind farms. A network of low-cost radar sensors is specifically designed to detect wakes in wind farms. A model-based estimation approach is developed to reduce the online wake uncertainty. Then, a model-based optimization framework is used to calculate AEP gains achieved by steering wakes via yaw actuation. The feasibility of the proposed approach is assessed by quantifying the changes in the levelized cost of energy (LCOE) resulting from the additional AEP gains and the extra cost of the new sensors.

Keywords: Optimization algorithms, Optimization, Stability of linear systems
Abstract: We study momentum-based first-order optimization algorithms in which the iterations utilize information from the two previous steps and are subject to additive white noise. For strongly convex quadratic problems, we utilize Jury stability criterion to provide a novel geometric characterization of linear convergence and exploit this insight to derive alternative proofs of standard convergence results and identify fundamental performance tradeoffs. We use the steady-state variance of the error in the optimization variable to quantify noise amplification and establish analytical lower bounds on the product between the settling time and the smallest/largest achievable noise amplification that scale quadratically with the condition number. This extends the prior work [1], where only the special cases of Polyak's heavy-ball and Nesterov's accelerated algorithms were studied. We also use this geometric characterization to introduce a parameterized family of algorithms that strikes a balance between noise amplification and settling time while preserving order-wise Pareto optimality.

Keywords: Optimization algorithms, Optimization
Abstract: In this paper, we study the almost sure convergence analysis of zeroth-order mirror descent algorithm. The algorithm admits non-smooth convex function with an estimate of gradient using Nesterov's Gausssian Approximation technique. We establish that under suitable condition of step-size iterates of the algorithm converge to a neighborhood of optimal function value almost surely. We extend the analysis in distributed optimization. We validate the almost sure convergence on a non-smooth optimization problem.

Keywords: Learning, Machine learning, Optimization algorithms
Abstract: This paper proposes an algorithm for Federated Learning (FL) with a two-layer structure that achieves both variance reduction and a faster convergence rate to an optimal solution in the setting where each agent has an arbitrary probability of selection in each iteration. The first layer of our algorithm corresponds to the model parameter propagation across agents done by the server. In the second layer, each agent does its local update with a stochastic and variance-reduced technique called Stochastic Variance Reduced Gradient (SVRG). We leverage the concept of variance reduction from stochastic optimization when the agents want to do their local update step to reduce the variance caused by stochastic gradient descent (SGD). The special attention in this paper is on FL operation where the agents' participation in the update process in each round is probabilistic and non-uniform. We provide a convergence bound for our algorithm which improves the rate from O(1/K^(1/2))to O(1/K) by using a constant step-size when the cost is strongly convex. For non-convex costs, we establish a O(1/K^(2/3)) to a stationary point using a vanishing stepsize. We demonstrate the performance of our algorithm using numerical~simulations.

Keywords: Optimization algorithms, Optimization, Machine learning
Abstract: We consider the open federated learning (FL) systems, where clients may join and/or leave the system during the FL process. Given the variability of the number of present clients, convergence to a fixed model cannot be guaranteed in open systems. Instead, we resort to a new performance metric that we term the stability of open FL systems, which quantifies the magnitude of the learned model in open systems. Under the assumption that local clients' functions are strongly convex and smooth, we theoretically quantify the radius of stability for two FL algorithms, namely local SGD and local Adam. We observe that this radius relies on several key parameters, including the function condition number as well as the variance of the stochastic gradient. Our theoretical results are further verified by numerical simulations on synthetic data.

Keywords: Optimization algorithms, Stability of hybrid systems
Abstract: We present a totally asynchronous multiagent algorithm, based on the heavy ball method, that guarantees fast convergence to the minimizer of a twice continuously differentiable, convex objective function over a convex constraint set. The algorithm is parallelized in the sense that the decision variable is partitioned into blocks, each of which is updated by only a single agent. We consider two types of asynchrony: in agents’ computations and in communications between agents, both under arbitrarily long delays. We show that, for certain values of the step size and other parameters, the heavy ball algorithm exponentially converges to a minimizer, even under total asynchrony. Numerical results validate these findings and demonstrate significantly faster convergence than a comparable gradient descent algorithm.

Keywords: Optimization algorithms
Abstract: In this paper, we investigate the framework of Online Convex Optimization (OCO) for online learning. OCO offers a very powerful online learning framework for many applications. In this context, we study a specific framework of OCO called {it OCO with {long-term} constraints}. {Long-term} constraints are introduced typically as an alternative to reduce the complexity of projection at every update step in online optimization. While many algorithmic advances have been made towards online optimization with {long-term} constraints, these algorithms typically assume that the sequence of cost functions over a certain T finite steps that determine the cost to the online learner are adversarially generated. In many circumstances, the sequence of cost functions may not be unrelated, and thus predictable from those observed till a point of time. In this paper, we study the setting where the sequences are predictable. We present a novel algorithm for online optimization with {long-term} constraints that can leverage such predictability for linear cost functions. We show that, with a predictor that can supply the gradient information of the next function in the sequence, our algorithm can achieve an overall regret and constraint violation rate that is strictly less than the rate that is achievable without prediction.

Keywords: Nonholonomic systems, Adaptive control, Biologically-inspired methods
Abstract: We propose a novel 3D source seeking algorithm for rigid bodies with a non-collocated sensor inspired by the chemotactic navigation strategy of sea urchin sperm known as helical klinotaxis. We work directly with the rotation group text{SO}(3) without parameterization in representing the attitude of a rigid body. As a consequence, the proposed algorithm does not require attitude feedback for implementation as opposed to all previous work on 3D source seeking. The stability of the proposed algorithm is proven using a careful application of singular perturbation and second order averaging.

Keywords: Nonholonomic systems, Constrained control, Mechanical systems/robotics
Abstract: This paper presents a computationally efficient, heuristic-free, and nonlinear feedback control framework for the tracking control of the position and orientation of a differential drive wheeled mobile robot (WMR) subjected to high-speed maneuvers and external disturbances. We synthesize the control law by an extension of Gauss’s principle of least constraint with dynamic incorporation of holonomic and nonholonomic equality constraints and with coordinate transformation. The command control actions for the WMR’s constrained dynamics result from solving a linear matrix equation (a Karush-Kuhn-Tucker system) at each point in time. No dynamics linearization or iterative solution is involved in the framework. Numerical experiments of a high-speed, differential drive WMR under sinusoidal and Gaussian external disturbances are presented to showcase the effectiveness of the proposed method.

Keywords: Nonholonomic systems, Lyapunov methods, Robotics
Abstract: This paper uses time-reversal symmetry (T-symmetry), which is inherent in many mechanical systems, to establish global controllability results for a class of underactuated mechanical systems, i.e., the systems with fewer actuators than the number of degrees of freedom (DoF). The idea is to find a control law guaranteeing a globally asymptotically stabilizable equilibrium (GAS) state, at which small-time local controllability (STLC) is also granted. Then, such equilibrium state can be used as a connection to design a global controller by using the time-reversal symmetry, i.e., the system can be driven from any initial state to any target state within finite time via the connection. By using the same line of reasoning, an UMS with an almost GAS equilibrium state proves to be almost-globally controllable. It shows that underactuated pendula with one degree of unactuation are almost-globally controllable (except a set of Lebesgue measure zero), for which the connection state is when all the links are at the downmost positions.

Keywords: Nonholonomic systems, Optimal control
Abstract: Geometric optimal control utilizes tools from differential geometry to analyze the structure of a problem to determine the control and state trajectories to reach a desired outcome while minimizing some cost function. For a controlled mechanical system, the control usually manifests as an external force which, if conservative, can be added to the Hamiltonian. In this work, we focus on mechanical systems with controls added to the symplectic form rather than the Hamiltonian. In practice, this translates to controlling the magnetic field for an electrically charged system. We develop a basic theory deriving necessary conditions for optimality of such a system subjected to nonholonomic constraints. We consider the representative example of a magnetically charged Chaplygin Sleigh, whose resulting optimal control problem is completely integrable.

Keywords: Algebraic/geometric methods, Nonholonomic systems, Autonomous systems
Abstract: In this paper we address the problem of identifying contracting systems among dynamical systems appearing in mechanics. First, we introduce a sufficient condition to identify contracting systems in a general Riemannian manifold. Then, we apply this technique to establish that a particular type of dissipative forced mechanical system is contracting, while stating immediate consequences of this fact for its stability. Finally, we use the previous results to study the stability of particular types of Contact and Nonholonomic systems.

Keywords: Computational methods, Nonholonomic systems, Optimal control
Abstract: Optimal motion planning is an essential task within the field of control theory. Therein, the key task is to synthesize optimal system trajectories that pass through cluttered environments while respecting given homotopy class constraints, which is critical in many topology-restricted applications such as search and rescue. In this paper, we introduce a novel optimal motion planning technique with 2-dimensional homotopy class constraints for general dynamical systems. We first initialize an optimal system trajectory regardless of obstacles and homotopy class constraints, and design an auxiliary obstacle trajectory for each obstacle such that the system trajectory belongs to the desired homotopy class regarding these auxiliary obstacle trajectories. During the procedure of deforming the auxiliary obstacle trajectory to the original counterparts, we propose a homotopy method based on nonlinear programming (NLP) such that the synthesized optimal system trajectories fulfill the aforementioned homotopy class constraints. The proposed method is validated with numerical results on two classic nonlinear systems with planar static and moving obstacles.

Keywords: Nonlinear systems identification, Electrical machine control, Estimation
Abstract: A New solution to the identification problem of current and flux fed Short Pitched Winding Switched Reluctance Motors (SPW-SRM) in the presence of strong saturation is developed. This is done by expanding the rotational periodicity and magnetic saturation in a high dimensional feature space spanned by a user defined combined periodic and smooth functions. The importance of this identification scheme lies in the good generalization ability of the constructed models, their robustness with respect to output measurement noise, and the diversity of their use as an estimation, prediction or diagnosis tool. Furthermore, no particular attention is required while the identification experiment since that data can be collected in vehicle normal operating regimes. Identification results obtained for a 60 kW SRM in the presence of measurement noise within automotive applications involving Fourier series and rational polynomial functions are quite satisfactory.

Keywords: Nonlinear systems identification, Identification, Estimation
Abstract: This paper concerns identification of uncontrolled or closed loop nonlinear systems using a set of trajectories that are generated by the system in a domain of attraction. The objective is to ensure that the trajectories of the identified systems are close to the trajectories of the real system, as quantified by an error bound that is prescribed a priori. A majority of existing methods for nonlinear system identification rely on techniques such as neural networks, autoregressive moving averages, and spectral decomposition that do not provide systematic approaches to meet pre-defined error bounds. The developed method is based on Carleman linearization-based lifting of the nonlinear system to an infinite dimensional linear system. The linear system is then truncated to a suitable order, computed based on the prescribed error bound, and parameters of the truncated linear system are estimated from data. The effectiveness of the technique is demonstrated by identifying an approximation of the Van der Pol oscillator from data within a prescribed error bound.

Keywords: Nonlinear systems identification, Identification, Identification for control
Abstract: In this paper, a system identification algorithm is proposed for control-affine, discrete-time fractional-order nonlinear systems. The proposed algorithm is a data-integrated framework that provides a mechanism for data generation and then uses this data to obtain the drift-vector, control-vector fields, and the fractional order of the system. The proposed algorithm includes two steps. In the first step, experiments are designed to generate the required data for dynamic inference. The second step utilizes the generated data in the first step to obtain the system dynamics. The memory-dependent property of fractional-order Gr"{u}nwald-Letnikov difference operator is used to compute the fractional order of the system. Then, drift-vector and control-vector fields are reconstructed using orthonormal basis functions, and calculation of the coefficients is formulated as an optimization problem. Finally, simulation results are provided to illustrate the effectiveness of the proposed framework. Additionally, one of the methods for identifying integer-order systems is applied to the generated data by a fractional-order system, and the results are included to show the benefit of using a fractional-order model in long-range dependent processes.

Keywords: Nonlinear systems identification, Identification for control, Modeling
Abstract: A learning method is proposed for Koopman operator-based models with the goal of improving closed-loop control behavior. A neural network-based approach is used to discover a space of observables in which nonlinear dynamics is linearly embedded. While accurate state predictions can be expected with the use of such complex state-to-observable maps, undesirable side-effects may be introduced when the model is deployed in a closed-loop environment. This is because of modeling or residual error in the linear embedding process, which can manifest itself in a different manner compared to the state prediction. To this end, a technique is proposed to refine the originally trained model with the goal of improving the closed-loop behavior of the model while retaining the state-prediction accuracy obtained in the initial learning. Finally, a simple data sampling strategy is proposed to use inputs deterministically sampled from continuous functions, leading to additional improvements in the controller performance for nonlinear dynamical systems. Several numerical examples are provided to show the efficacy of the proposed method.

Keywords: Nonlinear systems identification, Kalman filtering, Robotics
Abstract: This paper deals with the online model identification of robots suffering from backlash in their transmission, such as is the case for cable-driven endoscopic robots. Although online backlash identification is advantageous due to potential textit{in-situ} evolution of the backlash behavior, most existing methods focus on offline identification. Existing online approaches are either designed for DOF-by-DOF identification or limited by the simplicity of the underlying backlash models. We propose a new identification method based on Discontinuous EKF (DEKF) filtering to learn, online, the correct parameters of a multi-DOF backlash model. This allows to account for measurement noise and to include more complex backlash behaviors. A proof of concept on a simulated 3 DOF flexible endoscopic robot is presented to demonstrate the potential of such an approach.

Keywords: Nonlinear output feedback, Nonlinear systems identification, Identification for control
Abstract: Data-driven controls using Gaussian process regression have recently gained much attention. In such approaches, system identification by Gaussian process regression is mainly followed by model-based controller designs. However, the outcomes of Gaussian process regression are often too complicated to apply conventional control designs, which makes the numerical design such as model predictive control employed in many cases. To overcome the restriction, our idea is to perform Gaussian process regression to the inverse of the plant with the same input/output data for the conventional regression. With the inverse, one can design a model reference controller without resorting to numerical control methods. This paper considers single-input single-output (SISO) discrete-time nonlinear systems of minimum phase with relative degree one. It is highlighted that the model reference Gaussian process regression (MR-GPR) controller is designed directly from pre-collected input/output data without identification of the system itself.

Keywords: Distributed parameter systems, Identification, Machine learning
Abstract: This paper is concerned with the problem of machine failure rate identification of a 3-state reparable system and its implementation via deep learning. The mathematical model is governed by a distributed parameter system involving coupled partial and integro-differential equations. The objective of this work is to identify the failure rates using the sampled system output measurements. Deep learning based failure rate identification methods are proposed. Numerical examples are provided to illustrate the designs and results.

Keywords: Distributed parameter systems, Robotics
Abstract: The control problem of soft robots has been considered a challenging subject because they are of infinite degrees of freedom and highly under-actuated. Existing studies have mainly relied on approximated finite-dimensional models. In this work, we exploit infinite-dimensional feedback control for soft robots. We adopt the Cosserat-rod theory and employ nonlinear partial differential equations (PDEs) to model the kinematics and dynamics of soft manipulators, including their translational motions (for shear and elongation) and rotational motions (for bending and torsion). The objective is to achieve position tracking of the entire manipulator in a planar task space by controlling the moments (generated by actuators). The design is inspired by the energy decay property of damped wave equations and has an inner-outer loop structure. In the outer loop, we design desired rotational motions that rotate the translational component into a direction that asymptotically dissipates the energy associated with position tracking errors. In the inner loop, we design inputs for the rotational components to track their desired motions, again by dissipating the rotational energy. We prove that the closed-loop system is exponentially stable and evaluate its performance through simulations.

Keywords: Distributed parameter systems
Abstract: This paper considers the synchronization of identical structurally perturbed infinite dimensional systems. Due to the structured perturbations, represented by nonlinear functions of output signals, a standard synchronization via standard consensus protocols cannot provide any form of agreement unless one removes the presence of structured perturbations. When the structured perturbations are estimated adaptively, via an adaptive functional estimation scheme, the inclusion of their adaptive estimates facilitates and enhances the synchronization of the networked systems. Adaptive consensus protocols are applied to both the synchronization controllers ensuring that all networked systems agree with each other, and to the functional estimates ensuring that all functional estimates are synchronized.

Keywords: Adaptive control, Distributed parameter systems
Abstract: This paper derives rates of convergence of ap- proximations of observers and controllers arising in the native space embedding method for adaptive estimation and control of a class of nonlinear ordinary differential equations (ODEs) that feature functional uncertainty. The native space embedding method views the nonlinear ODE as a type of distributed parameter system (DPS), and ideal controllers are derived from the DPS representation. Implementable estimators or controllers for the ODE are obtained by approximation of the DPS using history-dependent, scattered bases in the native space. The basis functions are defined in terms of their centers of approximation. This paper shows that for a large collection of choices of the native space, it is possible to derive convergence rates for implementable schemes that are expressed in terms of the fill distance of the centers of approximation in a subset that supports the observation or measurement process. The error bounds are derived in terms of the power function of the reproducing kernel and resemble those derived recently in machine learning theory and Bayesian estimation as applied to discrete stochastic systems.

Keywords: Distributed parameter systems, Observers for Linear systems, Predictive control for linear systems
Abstract: We present an observer-based model predictive control scheme for a wave equation with non-collocated boundary control and observation. The design comprises a Luenberger-type state estimator combined with a model predictive controller which we show to stabilize the considered wave equation in the sense that the energy of the system decays asymptotically to zero. Moreover, if the initial state estimation error is sufficiently small, the controller is guaranteed to robustly satisfy given input constraints. The performance of the proposed design is demonstrated on a numerical simulation.

Keywords: Distributed parameter systems, Observers for Linear systems, Fluid flow systems
Abstract: Explicit solutions are given for a set of n + m linear hyperbolic observer backstepping kernel equations used for leak detection in branched pipe flows. It is identified that the kernel equations can be separated into N+1 distinct Goursat problems for 2(j+1) coupled PDEs each, j in {0,1,...,N} and N+1 being the number of pipes connected via the branching point. Expressing the solutions as infinite matrix power series, the solution to each set of equations is shown to depend on a simplified, scalar Goursat problem, the solution of which is given in terms of derivatives of a modified Bessel function of the first kind. Furthermore, it is shown that the infinite matrix power series expressing the solution writes in terms of modified Bessel functions of the first kind and Marcum Q-functions, as is the case for the previously solved 2×2 constant coefficient case. A numerical example showing adaptive observer gains for leak detection computed via the explicit solutions for multiple operating points of a branched pipe flow is given to illustrate the results.

Keywords: Estimation, Automotive systems, Automotive control
Abstract: A novel approach based on a mounted monocular camera and an IMU to estimate the lateral dynamics (sideslip angle and lateral velocity) of Powered Two-Wheeled Vehicles (P2WV) is proposed in this paper. This approach is divided into two parts, the estimation of the derivative of the lateral offset and the relative heading. For the first, a method based on inverse perspective mapping to detect the lane markers and fit them into a second-degree polynomial that gives the lateral offset, then the derivative is estimated from the latter. For the relative heading, a method based on detecting the vanishing point is used to estimate it. Finally, these two main parameters are used to estimate the sideslip angle and the lateral velocity. The proposed method is tested on a popular motorcycle simulator software (BikeSim) throughout several scenarios on straight and curved roads with high and low speeds while executing a Double Lane Change (DLC) maneuver. The proposed method shows promising results in terms of error and real-time execution.

Keywords: Estimation, Linear systems, Agents-based systems
Abstract: This paper addresses the problem of secure state estimation in multi-agent systems consisting of n agents. For the problem, the sparse observability index is a well-known measure of the system resilience. This index is defined as the largest integer δ for which the system observability is preserved even if any δ sensors are eliminated. The larger δ is, the more the system state can be reconstructed even if the system is subjected to more sensor attacks. In this paper, we analyze the relationship between the number of agents n and the sparse observability index δ especially when the network structure is path and cycle graphs. Intuitively, it is assumed that, as the number of agents n increases, the system resilience, i.e., δ, increases accordingly. However, as this study provides, δ does not monotonically increase with an increase in n. In path graphs, δ depends on whether n+1 is prime or composite, while in cycle graphs, δ depends on whether n is prime or composite. In path graphs, δ depends on whether n+1 is prime or composite, and the system resilience is enhanced when n+1 is prime. In cycle graphs, δ obeys whether n is prime or composite, and the system is more resilient when n is prime.

Keywords: Estimation, Machine learning, Observers for nonlinear systems
Abstract: In this paper, we present a novel (empirical) observability Gramian for nonlinear stochastic systems in the light of Bayesian inference. First, we define our observability Gramian, which we refer to as the estimability Gramian, based on the relation to the so-called Bayesian Fisher information matrix for initial state estimation. Then, we study the fundamental properties of an empirical version of the estimability Gramian. The practical usefulness of the proposed framework is examined through its application to a parameter and initial state estimation in a natural gas engine cylinder.

Keywords: Estimation, Observers for nonlinear systems, Automotive systems
Abstract: Brake-by-wire systems are prevailing more than ever for electric autonomous vehicles owing to several advantages, such as faster clamping force response, more accurate clamping force control, and more convenient to be integrated with other vehicle active safety functions. This paper mainly focuses on Electromechanical Brake (EMB) system. However, due to high sensor costs and limited sensor installation spaces, wide applications of EMB systems are prevented. One such example is the clamping force sensor. To replace the clamping force sensor, an innovative clamping force estimation method, i.e., the Braking Force Separation Strategy, is proposed in this paper. Different from existing estimation approaches that model the clamping force as a nonlinear polynomial function of motor position and brake gap distance, the proposed approach estimates the clamping force without brake gap distance. The decoupling is achieved by the application of an unknown input observer that enables simultaneous states and inputs estimation. To demonstrate the effectiveness of the proposed algorithm, simulations are performed under different input scenarios with or without fictitious measurement noise. The results show that the braking force can be accurately estimated by the proposed algorithm. It also demonstrates better performance by comparing with traditional method.

Keywords: Estimation, Observers for nonlinear systems, Control applications
Abstract: This paper considers the design of a multi-output high gain observer for a vehicle trajectory tracking application. The high gain observer approach offers the advantages of guaranteed feasibility and global stability with just one constant observer gain for this application. The challenges of transforming the vehicle dynamic model into the required companion form for applying the high gain observer technique are addressed. Transforming a traditional kinematic model to companion form is found to result in an increased number of states. Instead, a coordinate transformation that allows for varying velocity and varying slip angle is shown to be appropriate. The high gain observer methodology for a dynamic system with multiple outputs is presented and the calculation of the Lipschitz constant for the vehicle tracking application is discussed.

Keywords: Estimation, Observers for nonlinear systems, Mechatronics
Abstract: This paper analyzes state estimation for nonlinear systems in the presence of sensor noise and process disturbances. A class of systems involving nonlinear functions of vector arguments in the output equations is considered. A nonlinear observer that satisfies a H_∞ disturbance rejection constraint in addition to providing asymptotic stability in the absence of disturbances is developed using Lyapunov analysis. The observer is shown analytically to provide a guaranteed upper bound on the norm of the estimation error. The performance of the nonlinear observer is compared with the performance of two of the most popular and powerful methods for estimation in nonlinear systems - the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). A magnetic position estimation problem is utilized as the real-world application for the evaluation. In the case of the disturbances being gaussian noise, the UKF and the nonlinear observer provide approximately the same level of performance and they both surpass the performance of the EKF. However, in the case of 2-norm-bounded non gaussian noise such as spikes/ pulses, the nonlinear observer is shown to significantly outperform both the UKF and the EKF.

Keywords: Agents-based systems, Cooperative control, Nonholonomic systems
Abstract: We present a distance-based distributed formation-motion control law for unicycle agents that are required to move together at a constant reference speed. The distributed control law consists of the standard distance-based formation gradient control law, which is projected to the longitudinal and angular velocity inputs of the unicycle, and of a linear term that depends on the reference speed. The main contribution of this paper is to realize the consistency of unicycle agents' orientations without orientation measurement, thereby reducing the possibility of significant orientation measurement errors in real-world applications. We prove and show numerically the local exponential convergence of the unicycle agents to the desired formation, where they eventually move in unison at a constant reference speed.

Keywords: Optimization algorithms, Decentralized control
Abstract: We propose a decentralized optimization algorithm that preserves the privacy of agents' cost functions without sacrificing accuracy, termed EFPSN. The algorithm adopts Paillier cryptosystem to construct zero-sum functional perturbations. Then, based on the perturbed cost functions, any existing decentralized optimization algorithm can be utilized to obtain the accurate solution. We theoretically prove that EFPSN is (epsilon, delta)-differentially private and can achieve nearly perfect privacy under deliberate parameter settings. Numerical experiments further confirm the effectiveness of the algorithm.

Keywords: Agents-based systems, Estimation, Observers for nonlinear systems
Abstract: We consider the problem of distributed attitude estimation of multi-agent systems, evolving on SO(3), relying on individual angular velocity and relative attitude measurements. We propose a nonlinear distributed hybrid attitude estimation scheme guaranteeing global asymptotic convergence of the attitude estimation errors to a common constant orientation, under an undirected, connected and acyclic graph topology. Moreover, in the presence of a leader in the group (knowing its absolute orientation), one can guarantee global asymptotic convergence of the attitude estimation errors to zero. Numerical simulation results are presented to illustrate the performance of our proposed scheme.

Keywords: Agents-based systems, Game theory, Network analysis and control
Abstract: In this paper we propose a continuous-time non-linear model of opinion dynamics. One of the main novelties of our model is that it costs resources for an agent to express an opinion. Each agent receives a utility based on the complete opinion profile of all agents. Each agent seeks to maximize its own utility function by suitably revising its opinion and the proposed dynamics arises from all agents simultaneously doing this. For the proposed model, we show ultimate boundedness of opinions. We also show stability of equilibrium points and convergence to an equilibrium point when all agents are non-contrarian. We give conditions for the existence of a consensus equilibrium and analyze the role that resources play in determining the social power of the agents in terms of the deviation of the consensus value from the agents' internal preference. We also carry out a Nash equilibrium analysis of the underlying game and show that when all agents are non-contrarian, the set of equilibria of the opinion dynamics is the same as the set of Nash equilibria for the underlying game. We illustrate our results using simulations.

Keywords: Agents-based systems, Identification for control, Adaptive control
Abstract: In this paper, the consensus problem of the leader following system is addressed by considering the false data injection (FDI) attacks. An integral-based observer induced by nonlinear activation functions is proposed. By suitably choosing the activation function, the proposed observer is able to attenuate the effects of the fault data injection attack and achieve a no-error consensus. The consensus property and the attack rejection feature are analyzed considering both constant and time-varying attacks. It has been proven that the proposed method is able to mitigate the effects of different types of attacks. The effectiveness of the proposed observer is been verified by extensive numerical examples with comparisons to recent methods.

Keywords: Stability of linear systems, PID control, Agents-based systems
Abstract: This paper concerns robust consensus problems for continuous-time first-order multi-agent systems with respect to uncertain gain and phase of the agent's frequency response varying within certain ranges. We consider dynamic output feedback control protocol in the form of proportional-integral (PI) control. The agents can in general be nonminimum phase and unstable systems, which are interconnected by an undirected graph network. We seek to determine the largest ranges of gain and phase variations, referred to as the gain consensus margin (GCM) and the phase consensus margin (PCM), respectively, so that consensus can be achieved robustly within these ranges. Our main results consist of explicit analytical expressions of the GCM and PCM, which demonstrate how the agent's unstable pole and nonminimum phase zero, as well as the network connectivity may fundamentally confine the gain and phase variation ranges so that consensus can or cannot be maintained.

Keywords: Game theory, Communication networks
Abstract: In proposed path-aware designs for the Internet, end hosts can select which path their packets use. What criteria should the end hosts use to select paths? Recent work has proposed path-aware access control frameworks in which routing nodes publicly report their knowledge of the security postures of other nodes; end hosts can then base their routing choices on these reports. However, nothing is known regarding the nodes' incentives to report their knowledge truthfully. In this paper, we consider the case in which each network node is strategic, and seeks to craft its public reports to manipulate traffic patterns in its own favor. In the context of a simple selfish routing problem with two strategic nodes, we show that for a wide swath of the parameter space, each node has a dominant reporting strategy, meaning that its individually optimal strategy does not depend on the strategy of the other node. These dominant strategies are generally not truthful. At the resulting dominant-strategy Nash equilibrium, we show that the expected social cost is (often considerably) higher than that achieved when both nodes are completely truthful. Nonetheless, we prove that these equilibrium reporting strategies are never perverse, meaning that their resulting social cost is never worse than if traffic were uninformed as to network state.

Keywords: Game theory, Delay systems, Large-scale systems
Abstract: This paper investigates the equilibrium convergence properties of a proposed algorithm for potential games with continuous strategy spaces in the presence of feedback delays, a main challenge in multi-agent systems that compromises the performance of various optimization schemes. The proposed algorithm is built upon an improved version of the accelerated gradient descent method. We extend it to a decentralized multi-agent scenario and equip it with a delayed feedback utilization scheme. By appropriately tuning the step sizes and studying the interplay between delay functions and step sizes, we derive the convergence rates of the proposed algorithm to the optimal value of the potential function when the growth of the feedback delays in time is subject to sublinear, linear, and superlinear upper bounds. Finally, simulations of a routing game are performed to empirically verify our findings.

Keywords: Game theory, Hybrid systems, Networked control systems
Abstract: We introduce a class of decentralized high-order pricing dynamics (HOPD) for the solution of optimal incentive problems in affine congestion games with full resource utilization. The dynamics incorporate momentum and decentralized coordinated resets to achieve better transient performance compared to traditional first-order gradient-based pricing algorithms. The proposed dynamics are studied using tools from graph theory, game theory, and hybrid dynamical systems theory. Our main results establish suitable stability and convergence properties with respect to the set of incentives that generate Nash flows that also maximize the social welfare function of the game. The theoretical results are illustrated via numerical examples in two different types of communication graphs, highlighting the effect of the communication topology and the coordination between players on the transient performance of the HOPD.

Keywords: Game theory, Lyapunov methods, Optimization
Abstract: Evolutionary dynamics in the context of population games models the dynamic non-cooperative strategic interactions among many nondescript agents. Each agent follows one strategy at a time from a finite set. A game assigns a payoff to each strategy as a function of the so-called population state vector, whose entries are the proportions of the population adopting the available strategies. Each agent repeatedly revises its strategy according to a revision protocol. We focus on a well-known class of protocols that prioritizes strategies with higher excess payoffs relative to a population-weighted average. In contrast to existing work for these protocols, we allow each agent’s revision rate to depend explicitly on its current strategy. Motivated by applications and relevance to distributed optimization, we focus on potential games and investigate the population state’s convergence to the game’s Nash equilibria. Our contributions are twofold: (1) For the considered protocol class, prior work established conditions that ensure convergence under strategy-independent revision rates. We show that these conditions may be violated when the revision rates are strategy-dependent. (2) We prove that a minor, well-motivated modification of the considered protocol class satisfies these conditions for any strategy-dependent revision rates. We also illustrate our results using a distributed task allocation example.

Keywords: Game theory, Markov processes, Learning
Abstract: In this paper, we carry out finite-sample analysis of decentralized Q-learning algorithms in the tabular setting for a significant subclass of general-sum stochastic games (SGs) – weakly acyclic SGs, which includes potential games and Markov team problems as special cases. In the practical while challenging decentralized setting, neither the rewards nor the actions of other agents can be observed by each agent. In fact, each agent can be completely oblivious to the presence of other decision makers. In this work, the sample complexity of the decentralized tabular Q-learning algorithm to converge to a Markov perfect equilibrium is developed.

Keywords: Game theory, Mean field games, Decentralized control
Abstract: We study stochastic mean-field games among finite number of teams each with large finite as well as infinite numbers of decision makers (DMs). We establish the existence of a Nash equilibrium (NE) and show that a NE exhibits exchangeability in the finite DM regime and symmetry in the infinite one. We establish the existence of a randomized NE that is exchangeable (not necessarily symmetric) among DMs within each team for a general class of exchangeable stochastic games. As the number of DMs within each team drives to infinity (that is for the mean-field games among teams), using a de Finetti representation theorem, we establish the existence of a randomized NE that is symmetric (i.e., identical) among DMs within each team and also independently randomized. Finally, we establish that a NE for a class of mean-field games among teams (which is symmetric) constitutes an approximate NE for the corresponding pre-limit game among teams with mean-field interaction and large but finite number of DMs.

Keywords: Observers for nonlinear systems, Robust control, Autonomous vehicles
Abstract: This work provides formal safety guarantees for control systems with disturbance. A disturbance observer-based robust safety-critical controller is proposed, that estimates the effect of the disturbance on safety and utilizes this estimate with control barrier functions to attain provably safe dynamic behavior. The observer error bound – which consists of transient and steady-state parts – is quantified, and the system is endowed with robustness against this error via the proposed controller. An adaptive cruise control problem is used as illustrative example through simulations including real disturbance data.

Keywords: Constrained control, Feedback linearization, Autonomous robots
Abstract: This paper proposes a collision avoidance control strategy for constrained differential-drive robots moving in static but unknown obstacle scenarios. We assume that the robot is equipped with an on-board path planner providing a sequence of obstacle-free waypoints, and we design an ad-hoc constrained control strategy for ensuring absence of collisions and velocity constraints fulfillment. To this end, the nonlinear robot kinematics is redefined via a dynamic feedback linearization procedure, while a receding horizon control strategy is tailored to deal with time-varying state and input constraints. First, by considering the worst-case constraints realization, a conservative solution is offline determined to guarantee stability, recursive feasibility, and absence of collisions. Then, online, the tracking performance is significantly improved leveraging a non-conservative representation of the input constraints and set-theoretical containment conditions. Simulation results involving a differential-drive robot operating in a maze-like obstacle scenario are presented to show the effectiveness of the proposed solution.

Keywords: Automotive control, Constrained control, Predictive control for linear systems
Abstract: Automated vehicles may encounter non-nominal situations called failure scenarios, due for instance to errors in perception or environment prediction. In some failure scenarios, a risk area must suddenly be avoided, possibly at the price of no longer satisfying all the constraints enforced in nominal driving conditions. We propose a design for a failure-safe controller that operates the vehicle according to the specifications in nominal conditions, while ensuring that, should a known failure occur, an evasive maneuver can be performed that avoids the risk area and satisfies a, possibly relaxed, set of driving constraints. We design evasive maneuver controllers parametrized in their reference, and we leverage set based methods to determine the region where such controllers satisfy the constraints and avoid the risk area. Membership in such a region during nominal operation is achieved by imposing additional constraints on the controller for nominal driving. We demonstrate the approach in simulations in a few different scenarios.

Keywords: Automotive control, Automotive systems, Cooperative control
Abstract: Tire blowout strongly affects vehicle stability and road safety by introducing sudden and intensive tire force disturbances. In such an emergent event, vehicles equipped with an automatic controller for normal path following (i.e., SAE driving automation level 2/3) may have degraded performance, which requires cooperation with a human driver. Considering a panicked driver could perform improper or wrong operations, this paper proposes a novel trust-based shared steering control for vehicle stabilization after tire blowout. Based on specific and crucial factors in tire blowout events, the driver’s steering input and the resulting driver’s fault and performance are comprehensively evaluated in a designed controller-to-human (C2H) trust module. The real-time computational trust simultaneously adjusts the cooperative level in a dynamic control authority allocation function. Matlab/Simulink and CarSim® co-simulation results validate that the proposed shared control can effectively enhance vehicle stability and driving safety after tire blowout, even with the faulty and excessive steering inputs from a panicked driver.

Keywords: Traffic control
Abstract: Queue length estimation in urban intersections represents a crucial issue for real-time traffic flows optimization. In this paper, we discuss different approaches to estimate the queue length using only inductive loops over two possible sensor layouts. Firstly, a model describing the queue dynamics is derived and a methodology to estimate the queue length at the preceding traffic light cycle is formulated, under the assumption of a single inductive loop sensor. Then, two strategies relying on a double-sensor layout are investigated to improve the quality of the queue length estimate, showing the potential of the use of a second inductive loop. The effectiveness of the proposed techniques is validated both on real-world data and through a microscopic traffic simulator, where real-world traffic profiles are employed.

Keywords: Automotive control, Autonomous systems, Optimal control
Abstract: A new motion planning framework for automated highway merging is presented in this paper. To plan the merge and predict the motion of the neighboring vehicle, the ego automated vehicle solves a joint optimization of both vehicle costs over a receding horizon. The non-convex nature of feasible regions and lane discipline is handled by introducing integer decision variables resulting in a mixed integer quadratic programming (MIQP) formulation of the model predictive control (MPC) problem. Furthermore, the ego uses an inverse optimal control approach to impute the weights of neighboring vehicle cost by observing the neighbor’s recent motion and adapts its solution accordingly. We call this adaptive interactive mixed integer MPC (aiMPC). Simulation results show the effectiveness of the proposed framework.