Keywords: Networked control systems, Distributed control, Switched systems
Abstract: In this paper, we first establish an output-based distributed observer for a general linear leader system over a periodic jointly connected switching communication network, which extends the applicability of the output-based distributed observer from a marginally stable linear leader system to any linear leader system and from an undirected switching graph to a directed switching graph. Then we further solve the cooperative output regulation problem of linear multi-agent systems utilizing the output-based distributed observer.

Keywords: Networked control systems, Identification, Robust control
Abstract: The article shows that it is possible to leverage relevant recent results developed in the area of identification of dynamic networks to

introduce a notion of robustness with respect to uncertainties in the graph structure of a distributed system. It is assumed that in an observational framework, only a subset of the variables of a networked system are measured and the topology of the interconnections between the variables is not fully known. When the objective is designing a controller for the overall system, the topological uncertainties impede the exact identification of the overall open-loop transfer function and consequently, the exact design of the controller. It is shown, however, that some of the transfer functions of the network could be consistently identified using some sufficient and necessary graphical conditions and, in some cases, the overall open loop transfer function can be modeled by a term that can be consistently estimated and an uncertain term which is proven to be bounded. Consequently, this allows one to borrow control design techniques from the area of robust control.

Keywords: Networked control systems, Identification, Stochastic systems
Abstract: The article presents a technique to identify a certain transfer function in a dynamic network when the input and the output of the transfer function are influenced by an unmeasured confounding variable.

It is assumed that in an observational framework, only a subset of the variables of the network are measured and the topology of the interconnections between the variables is partially known. The focus of the paper is the challenging scenario where it is not possible to measure any variables on the directed paths from the confounding variable to either the input or the output of the transfer function of interest. Sufficient conditions are derived to determine a set of instrumental variables and a set of auxiliary variables that guarantee consistent identification of the transfer function using an algorithm based on prediction error method for the class of acyclic networks. It is also shown that using similar ideas, the results could be extended to cyclic networks. In particular, we show how consistent estimates of some transfer functions in a network with feedback loops could be used to identify some other transfer functions whose inputs and outputs are influenced by unmeasured confounding variables.

Keywords: Networked control systems, Linear systems, Network analysis and control
Abstract: In this paper, problems of designing advanced stealthy false data injection (FDI) attack sequences are investigated. It is proved that, for systems with spectral radius larger than or equal to 1, abnormal increments of residual data are incurred for finite number of steps by improved stealthy FDI attack strategy proposed in this paper while diverging estimation error is achieved. For systems with spectral radius less than 1, infinite estimation error can never be achieved by stealthy FDI attacks. Therefore, an optimal FDI attack strategy is proposed to achieve largest possible steady state estimation error while remaining stealthy. Stealthiness of proposed attack sequences is proved in the presence of a summation (SUM) detector. Finally, simulation results are given to verify the effectiveness of attack strategies designed in this paper.

Keywords: Networked control systems, Markov processes, LMIs
Abstract: This paper focuses on the stability and controller design problem of networked control systems (NCSs) under multiple cyber-attacks, which are random and no priority has been pre-defined. A Markovian-based observer is designed to estimate the affected system states, with the desired gain changing with different attacks. Furthermore, a criterion is obtained in LMI to guarantee stochastically stable for closed-loop system and the corresponding controller design is addressed. Finally, the effectiveness of the proposed method is demonstrated by evaluating contrast simulation example.

Keywords: Networked control systems, Robotics
Abstract: In this paper, we investigate a coverage strategy for a multi-robot system across a domain of interest for applications involving pose-sensitive event services. The resulting problem is modeled as a coverage control problem on the special Euclidean groups. Based on the geometry inherent to the unimodular Lie groups, the geodesic-based Voronoi cell of a robot in charge of a subdomain and the locational cost function representing the coverage quality are defined. The controller for driving a team of planar robots to a critical point of the locational cost is derived and augmented by a control barrier certificate for the purpose of collision avoidance. The performance of the proposed controller is compared with the situation where the orientations of the robots are ignored during the coverage process using the standard Lloyd’s algorithm for both homogeneous and heterogeneous (in terms of robots' relative mobility and safe radii) multi-robot teams.

Keywords: Networked control systems, Stability of linear systems
Abstract: Many natural and man-made network systems need to maintain certain patterns, such as working at equilibria or limit cycles, to function properly. Thus, the ability to stabilize such patterns is crucial. Most of the existing studies on stabilization assume that network systems' states can be measured online so that feedback control strategies can be used. However, in many real-world scenarios, systems' states, e.g., neuronal activity in the brain, are often difficult to measure. In this paper, we take this situation into account and study the stabilization problem of linear network systems with an open-loop control strategy: vibrational control. We derive a graph-theoretic sufficient condition for structural vibrational stabilizability, under which network systems can always be stabilized. We further provide an approach to select the locations in the network for control placement and design corresponding vibrational inputs to stabilize systems that satisfy this condition. Finally, we provide some numerical results that demonstrate the validity of our theoretical findings.

Keywords: Networked control systems, Stochastic systems, Identification
Abstract: The paper presents systematic tests to determine if a particular transfer function in an interconnected system is strictly proper or has a feedthrough. Considering a strictly proper module between two nodes in a networked system, if only the data of the two nodes are used, there are situations where numerical tests to determine if the module is strictly proper will fail. It is shown, however, that marginalizing some of the nodes of a networked system under certain conditions preserves delays and feedthroughs in certain links. Therefore, using a set of auxiliary nodes that satisfies certain conditions, it is possible to design a systematic test to determine if a module in the networked system is strictly proper. The conditions are proven to be sufficient. Similar ideas are used to formulate a systematic test to determine if a module has a feedthrough.

Keywords: Networked control systems, Uncertain systems, Adaptive control
Abstract: We consider the asymptotic consensus problem for 2nd-order nonlinear multi-agent systems subject to predefined constraints for the system response, such as maximum over- shoot or minimum convergence rate. We design a distributed discontinuous adaptive control protocol that guarantees that the inter-agent consensus errors evolve in a prescribed funnel and converge to zero. The multi-agent dynamics contain parametric and structural uncertainties, without boundedness or approximation/parametric factorization assumptions. The response of the closed-loop system is solely determined by the predefined funnel and is independent from the control gain selection. Finally, simulation results verify the theoretical findings.

Keywords: Networked control systems, Optimal control, Kalman filtering
Abstract: This paper proposes an attack strategy for remote estimators in cyber-physical systems. In contrast with the common approaches by maximizing the state estimation difference and estimation error covariance of a remote estimator, we consider the scenario where attackers expect to regulate the estimation error to the value arbitrarily defined by attackers, which not only enables attackers to release attacks of different intensities according to their intentions, but also reduces the possibility detected by the amplitude detector and the human monitor. By taking advantage of the dynamic programming, an explicit expression of the optimal attack sequence is derived, and its convergence and feasibility are analyzed. Finally, simulation results are presented to validate the effectiveness of the proposed strategy.

Keywords: Predictive control for linear systems, Constrained control, Observers for Linear systems
Abstract: Model predictive control (MPC) for uncertain systems in the presence of hard constraints on state and input is a non-trivial problem, and the challenge is increased manyfold in the absence of state measurements. In this paper, we propose an adaptive output feedback MPC technique, based on a novel combination of an adaptive observer and robust MPC, for single-input single-output discrete-time linear time-invariant systems. At each time instant, the adaptive observer provides estimates of the states and the system parameters that are then leveraged in the MPC optimization routine while robustly accounting for the estimation errors. The solution to the optimization problem results in a homothetic tube where the state estimate trajectory lies. The true state evolves inside a larger outer tube obtained by augmenting a set, invariant to the state estimation error, around the homothetic tube sections. The proof for recursive feasibility for the proposed `homothetic and invariant' two-tube approach is provided, along with simulation results on an academic system.

Keywords: Predictive control for linear systems, Constrained control, Optimization algorithms
Abstract: In this paper, we propose an inexact-Uzawa solver for embedded linear model predictive control (MPC). The inexact-Uzawa algorithm falls into the general framework of first-order primal-dual methods but employs both proximal-point and matrix splitting schemes to derive a numerically robust algorithm with mathcal{O}(1/k) convergence rate in the primal-dual gap to some saddle-point solution where k is the iteration count. Numerical MPC example shows the efficiency and the ease of implementation of the algorithm as compared to other related methods in the literature.

Keywords: Predictive control for linear systems, Constrained control, Output regulation
Abstract: The regulation problem of a system with integer mixed constrained inputs is analyzed in this contribution. First, the stability analysis of the model is carried out, and the regulation problem is solved by considering a PID controller and a feed-forward gain in the continuous-time setting. Then, due to the poor performance of the controller, the discrete representation of the system is derived, and the model predictive controller is designed for the tracking problem. The simulation results show that the controller can oscillate around the desired reference, as it is not a reachable steady state of the system.

Keywords: Predictive control for linear systems, Constrained control, Stochastic systems
Abstract: This paper presents a distributionally robust data-driven model predictive control (MPC) framework for discrete-time linear systems with additive disturbances, while assuming the distribution is only partially known through samples. The corresponding optimal control problem considers a distributionally robust (DR) objective over an ambiguity set of estimated disturbance expectations. A statistical learning bound is provided to validate the ambiguity set. For this control problem, polytopic hard input constraints and state chance constraints are considered. State chance constraints are formulated into linear deterministic constraints through solving a DR optimization problem with Wasserstein ambiguity set. The resulting optimal control problem can be equivalently solved by a linear program. We prove recursive feasibility and provide an average asymptotic cost bound for the corresponding MPC framework. The method is compared and demonstrated and analysed on a mass spring control example.

Keywords: Predictive control for linear systems, Hierarchical control, Constrained control
Abstract: A tube-based robust Model Predictive Control (MPC) formulation is presented for systems with slow and fast timescale dynamics. The controller uses a reduced-order model that approximates the slow timescale dynamics and is implemented with a relatively large time step size. By analyzing the error between the full- and reduced-order models, the MPC optimization problem is proven to be recursively feasible and to produce closed-loop trajectories that satisfy state and input constraints. By relating bounds on all model errors to bounds on the change of the input in time, input change bounds are included as decision variables in the MPC problem to achieve a time-varying balance between fast transients with large model error and steady-state operation with zero model error. Zonotopes are used to make the approach practical and a numerical example demonstrates the benefits of optimizing time-varying input change bounds as part of the MPC formulation.

Keywords: Predictive control for linear systems, Linear systems, Stochastic systems
Abstract: We present an output feedback stochastic model predictive controller (SMPC) for constrained linear time-invariant systems. The system is perturbed by additive Gaussian disturbances on state and additive Gaussian measurement noise on output. A Kalman filter is used for state estimation and an SMPC is designed to satisfy chance constraints on states and hard constraints on actuator inputs. The proposed SMPC constructs bounded sets for the state evolution and uses a tube-based constraint tightening strategy where the tightened constraints are time-invariant. We prove that the proposed SMPC can guarantee an infeasibility rate below a user-specified tolerance. We numerically compare our method with a classical output feedback SMPC with simulation results which highlight the efficacy of the proposed algorithm.

Keywords: Predictive control for linear systems, Optimal control, Variational methods
Abstract: This paper develops a new approach to soft constrained model predictive control (MPC) for real-time trajectory tracking. The presented method does not rely on solving an iterative optimization algorithm at each sampling instance. In fact, the optimal control input is directly computed via an inner product of two vectors. This enables the computation of an optimal control input in real-time rather than having to use a suboptimal solution as is the case in most current real-time MPC approaches. The computational complexity of the presented method is linear w.r.t. the prediction horizon, state and input dimension, which makes it ideal for fast sampled, large systems. The functionality of the new approach is demonstrated in a laboratory setup of an underactuated, crane-like system. Furthermore, its performance is compared with a suboptimal MPC based on an active-set method with warm-start (ASM-MPC). It is shown that the new method is of the order of 10e5 times faster than the ASM-MPC, while achieving similar and in some cases even better tracking accuracy.

Keywords: Predictive control for linear systems, Optimization, Robotics
Abstract: This paper presents a novel Adaptive-frequency MPC framework for bipedal locomotion over terrain with uneven stepping stones. In detail, we intend to achieve adaptive gait periods with variable MPC frequency for bipedal periodic walking gait to traverse terrain with discontinuities without slowing down. We pair this adaptive-frequency MPC with kino-dynamics trajectory optimization to obtain MPC adaptive frequencies (in terms of sampling times), center of mass (CoM) trajectory, and foot placements. We use whole-body control (WBC) along with adaptive-frequency MPC to track the optimal trajectories from offline optimization. In numerical validations, our adaptive-frequency optimization and MPC framework have shown advantages over fixed-frequency MPC. The proposed framework can control the bipedal robot to traverse through uneven stepping stone terrains with perturbed stone heights, widths, and surface shapes while maintaining an average speed of 1.5 m/s.

Keywords: Predictive control for linear systems, Optimization algorithms, Constrained control
Abstract: Limited computation resources forcing early (sub-optimal) termination of the solvers used for model predictive controllers (MPCs) can compromise the feasibility and stability guarantees of the initial MPC design. In this work, we consider a primal-dual algorithm for solving linear MPC problems under a fixed number of optimization iterations. To address feasibility issues caused by sub-optimal solutions, we propose a novel sub-optimal MPC with a dynamical constraint tightening strategy. We characterize the interaction between the sub-optimally controlled system and the constraint tightening update process as two interconnected subsystems. By constructing a region of attraction estimate for the interconnected system and utilizing the small-gain theorem, we show sufficient conditions on the number of iterations of the optimization algorithm and the initial tightening parameter which guarantee recursive feasibility and asymptotic stability of the closed-loop system.

Keywords: Predictive control for linear systems, Robust control, Uncertain systems
Abstract: We propose a robust model predictive control (MPC) approach for open-loop unstable systems with initially measured input-state data. Compared with a behavioral approach used in the existing data-driven MPC, a data-based system representation which is better to describe the original system is constructed to replace the classic model to predict future behaviors, leading to the reduction of computational burden and the improvement of the model mismatch between the prediction model and the original plant. Accordingly, the terminal ingredients dependent on this data-based representation are designed. Simulation results are provided to show the effectiveness of the proposed approach.

Keywords: Robotics, Biomedical, Optimization
Abstract: Task-dependent controllers widely used in exoskeletons track predefined trajectories, which overly constrain the volitional motion of individuals with remnant voluntary mobility. Energy shaping, on the other hand, provides task- invariant assistance by altering the human body’s dynamic characteristics in the closed loop. While human-exoskeleton systems are often modeled using Euler-Lagrange equations, in our previous work we modeled the system as a port-controlled- Hamiltonian system, and a task-invariant controller was de- signed for a knee-ankle exoskeleton using interconnection- damping assignment passivity-based control. In this paper, we extend this framework to design a controller for a backdrivable hip exoskeleton to assist multiple tasks. A set of basis functions that contains information of kinematics is selected and corresponding coefficients are optimized, which allows the controller to provide torque that fits normative human torque for different activities of daily life. Human-subject experiments with two able-bodied subjects demonstrated the controller’s capability to reduce muscle effort across different tasks.

Keywords: Robotics, Mechanical systems/robotics
Abstract: Kinematic constraints can be used to describe the behavior of systems by specifying a set of admissible motions. When the systems interact with each other, a large number of constraints have to be enforced in order to completely specify the admissible motions. At the same time, because of the interaction, some kinematic constraints might be violated. This violation leads to energy dissipation. In this work, we consider swarms of robots physically interacting among each other and with the environment in which they are deployed in order to accomplish a given task. The constraints coming from the physical interaction may restrict or even impede the motion of the robots, leading to dissipation of energy. Leveraging insights from Lagrangian mechanics and optimization, we design controllers for swarm of brushbots with the objective of minimizing the power dissipated because of the physical interaction constraints. The devised controller is showcased in simulation on a swarm of brushbots.

Keywords: Energy systems, Robotics, Maritime control
Abstract: The Gulf Stream represents a major potential resource for renewable energy but is presently only sparsely characterized via radar, buoys, gliders, and intermittently operating human-operated research vessels. Dramatically greater resolution is possible through the use of persistently operating autonomous surface vessels (ASVs), which are powered by wind, wave, or solar resources. Optimizing the control of these ASVs, taking into account the devices' energetic performance and constraints, in addition to the renewable resource and flow profile, is crucial to obtaining good data. An ASV's path and velocity profile along that path both significantly influence the amount of a mission domain that can be covered and, ultimately, the scientific quality of the mission. While our previous work focused on optimizing the path of a solar-powered ASV with fixed speed, the present work represents the complement: optimizing the speed for a given path, accounting for the ASV dynamics, flow resource, and solar resource. We perform this optimization through a model predictive controller that maximizes the projected distance traversed by the ASV, with a terminal incentive that captures the estimated additional long-duration range that is achievable from a given terminal battery state of charge. We present simulation results based on the SeaTrac SP-48 ASV, Mid-Atlantic Bight/South-Atlantic Bight Regional Ocean Model, and European Centre for Medium-Range Weather Forecasts solar model. Our results show improved performance relative to simpler heuristic controllers that aim to maintain constant speed or constant state of charge. However, we also show that the design of the MPC terminal incentive and design of the heuristic comparison controller can significantly impact the achieved performance; by examining underlying simulation results for different designs, we are able to identify likely causes of performance discrepancies.

Keywords: Optimal control, Energy systems, Simulation
Abstract: This work presents a control methodology for maximizing the net power generated by an underwater kite capable of adjusting wingspan in real time. Underwater kite systems generate energy by performing cross-current figure-eight flight maneuvers while tethered to a winch system. These systems generate net positive power through cyclic spooling: spooling out under high-tension cross-current flight and spooling in radially under low tension. In the presence of structural constraints, simultaneous variation in the kite's angle of attack and span is superior to simply reducing the angle of attack in order to stay within permissible structural loading. Furthermore, the optimal combination of these variables depends on the amount of tether spooled out and the spatiotemporally-varying flow field. Leveraging a multi-degree-of-freedom model previously developed by the authors, the performance of three kites-- two with fixed span and one with variable span -- was compared. To maximize the performance of the modeled kites, an optimal control framework was developed. For the fixed-span case, spool-out speeds and mean elevation angles for the kite were optimized to maximize energy generation over a spool-out cycle. For the morphing span case, spool-out speeds, mean elevation angle, and wingspan were optimized to maximize energy generation over a spool-out cycle while considering the energetic cost of morphing. Simulation results show that the kite capable of span-morphing generated 38.7% more energy than a fixed-span kite of maximum allowable span and 13.2% more energy than a kite of the optimal fixed-span.

Keywords: Modeling, Stability of nonlinear systems, Algebraic/geometric methods
Abstract: We present and prove a theorem guaranteeing global stability in a non-linear system representing the iterative self-repair process where a 3D printer repairs its timing pulley. The process consists of gradually improving the broken part in the 3D printer until the printer reaches its repaired state. To prove global stability, we verify that the limit of the self-repair sequence does not depend on the initial condition, and always converges to the repaired state. Even though the convergence of this process has been analyzed under strong assumptions, in the present work, the convergence is proven for a more general case.

Keywords: Energy systems, Robotics, Mechatronics
Abstract: A control system is called emph{self-powered} if the only energy it requires for operation is that which it absorbs from the plant. For a linear feedback law to be feasible for a self-powered control system, its feedback signal must be colocated with the control inputs, and its input-output mapping must satisfy an associated passivity constraint. In this paper we consider the use of actively-controlled electronics to impose a self-powered linear feedback law. In this case, the feasibility of a linear feedback law must account for parasitic losses in the electronics and energy storage system. For the case in which the feedback law is linear and time-invariant, this paper derives necessary feasibility conditions which explicitly account for these losses. This feasibility condition is then illustrated in a simple example.

Keywords: Optimal control, Optimization, Control applications
Abstract: In this paper, a multi-input-multi-output (MIMO) optimal control for a six-degree-of-freedom UAV having four rotors powered by brushless DC motors is designed in many-objective settings. To this end, the mathematical model of the UAV is derived and then linearized around one of its operating points. Then, nested control algorithms with three loops are designed after dividing the UAV dynamics into small subsystems. The outermost loop includes two control algorithms that calculate the required roll and pitch to maneuver the vehicle to the desired X and Y position. At the same time, the innermost loop controls the angular velocities of each axis of the quadrotor. The control loop between the outer and inner loops is called the middle control loop, which regulates the attitude and altitude of the quadrotor. Finally, a many-objective optimization problem that involves 20 design parameters and ten objective functions is formulated and solved by SPEA2SDE (Strength Pareto Evolutionary Algorithm 2 with Shift-based Density Estimation (SDE)), which is one of the popular many-objective optimization approaches. Both stability and performance constraints are imposed on the optimization problem. Numerical simulations conducted on the nonlinear UAV model show that the proposed many-objective and optimal design method is quite effective.

Keywords: Optimal control, Autonomous systems
Abstract: In this paper, we seek to build connections between control Lyapunov functions (CLFs) and Hamilton-Jacobi (HJ) reachability analysis. CLFs have been used extensively in the control community for synthesizing stabilizing feedback controllers. However, there is no systematic way to construct CLFs for general nonlinear systems and the problem can become more complex with input constraints. HJ reachability is a formal

method that can be used to guarantee safety or reachability for general

nonlinear systems with input constraints. The main drawback is the well-known ``curse of dimensionality.'' In this paper we modify HJ reachability to construct what we call a control Lyapunov-Value Function (CLVF) which can be used to find and stabilize to the smallest

control invariant set around a point of interest. We prove that the CLVF is the viscosity solution to a modified HJ variational inequality (VI), and can be computed numerically, during which the input constraints and exponential decay rate are incorporated. This process identifies the region of exponential stability to the smallest control invariant set given the desired input bounds and decay rate. Finally, a

feasibility-guaranteed quadratic program (QP) is proposed for online implementation.

Keywords: Optimal control, Computational methods, Identification for control
Abstract: We propose a computational method for the finite-time nonlinear optimal control problem. We compute the solutions by first performing a coordinate transformation using the principle Koopman eigenfunctions. Then, we synthesize past and present techniques for obtaining a general explicit solution to the resulting differential Riccati equation. We demonstrate our method on a numerical example, for which the analytic Koopman eigenfunctions are known.

Keywords: Optimal control, Constrained control, Robotics
Abstract: We consider the problem of harvesting data from a set of targets in a wireless sensor network using a collection of mobile agents. The targets lie in a one dimensional mission space and broadcast their data while the agents move overhead. The agents are required to collect all the data and move to terminal locations to offload that data. We use a Hamiltonian analysis to show that the optimal control can be described using a parameterized policy and then develop a gradient descent scheme using infinitesimal perturbation analysis (IPA) to calculate the gradients of the cost function with respect to the control parameters. To avoid collisions between agents, we then apply a Control Lyapunov Function-Control Barrier Function (CLF-CBF) technique to ensure the agents closely track the desired optimal trajectory to complete their mission while avoiding any collisions. Additionally, we analyze the problem of symmetric deadline in the CLF-CBF controller and show that it can be avoided by adding a small perturbation to the initial and final heights of the agents over the mission space. The approach is demonstrated through simulation.

Keywords: Optimal control, Optimization, Uncertain systems
Abstract: We study the problem of designing a robust parameter-independent feedback control input that steers, with minimum energy, the average of a linear system submitted to parameter perturbations where the states are initialized and finalized according to a given initial and final distribution. We formulate this problem as an optimal transport problem, where the transport cost of an initial and final state is the minimum energy of the ensemble of linear systems that have started from the initial state and the average of the ensemble of states at the final time is the final state. The by-product of this formulation is that using tools from optimal transport, we are able to design a robust parameter-independent feedback control with minimum energy for the ensemble of uncertain linear systems. This relies on the existence of a transport map which we characterize as the gradient of a convex function.

Keywords: Optimal control, Control applications, Process Control
Abstract: An improved mathematical model describing the process of generating energy from household waste treatment is proposed and analyzed. It is a three-dimensional nonlinear system that illustrates the process of transforming household waste stored in a landfill into energy that flows to a user's network. More precisely, the state of the system describes at a broad scale a process of generating energy E by treating a quota of a waste stock x through K-valorization units that may also consume a part of the produced energy for their operation. Our main objective is to maximize the energy produced and transmitted to the user's network. In particular, we investigate the issue of determining an optimal investing strategy that monitors the deployment of treatment plants. Using Pontryagin's maximum principle (PMP), we characterize, over a fixed time-frame [0, T], the optimal investment that maximizes the produced energy while limiting the overall production costs. In addition, the efficiency of the suggested strategy is validated and illustrated throughout this work using a direct optimization method.

Keywords: Iterative learning control, Constrained control, Robust control
Abstract: This paper proposes a dynamic anti-windup scheme for a class of iterative learning control (ILC) systems. The anti-windup compensator has the same structure as a class of compensators for 1D systems and is able to guarantee similar properties: (i) that the constrained system with anti-windup compensation is exponentially stable if a certain linear matrix inequality is satisfied; and (ii) if the trajectory to be tracked by the nominal ILC controller is consistent with the control constraints, the anti-windup compensator will ensure that the behaviour of the nominal ILC controller is eventually recovered.

Keywords: Iterative learning control, Estimation, Uncertain systems
Abstract: Functional electrical stimulation (FES) is an effective upper limb stroke rehabilitation technology that helps patients recover lost movement by assisting functional task training. Unfortunately, current FES controllers cannot satisfy the competing demands of high accuracy, robustness to modelling error and limited set-up/identification time needed for clinical or home deployment. To address this, an estimation-based multiple model switched iterative learning control framework is proposed, combining the most successful adaptive learning features of existing FES controllers. A practical design procedure that guarantees robust performance is developed, and efficacy is established across realistic testing scenarios.

Keywords: Iterative learning control, Linear systems, Stability of linear systems
Abstract: Iterative learning control has been developed for application to systems that repetitively execute the same finite duration task, where the objective is to follow a supplied reference trajectory. In many current designs, the reference trajectory is specified at the outset, but others, such as materials processing, may require one or more changes, or switching, of this trajectory. This paper develops a new design for the previously unconsidered case of discrete linear dynamics with a switching reference trajectory and saturation of the input signal. The design is established using the stability theory for nonlinear repetitive processes, a class of 2D systems, and uses vector Lyapunov functions. A numerical case study demonstrates the applicability of the new design.

Keywords: Iterative learning control, Linear systems
Abstract: In this paper, a data-driven iterative learning control approach to multi-input-multi-output (MIMO) systems with strong cross-axis coupling is proposed. Iterative learning control (ILC) of MIMO systems with strong cross-axis coupling effect is challenging as model-based ILC to MIMO systems is complicated by the modeling process of MIMO systems being involved and time-consuming, the trade-off between the model accuracy and the performance, and the limitation to systems with weak-cross-coupling. Contrarily, constant gain ILC methods are mainly effective for tracking at low-speed, and suffer from slow convergence, particularly in the presence of the random disturbances. Thus, the aim of this paper is to develop a data-driven robust optimal ILC (DDRO-ILC) approach to MIMO systems of strong cross-axis coupling under random output disturbance. The iteration gain is constructed and updated by using past input and output data to capture the dynamics of the system via the singular value decomposition (SVD) technique. It is shown that monotonic convergence in the presence of random disturbance is guaranteed, and an optimal gain can be obtained to maximize the convergence rate and minimize the residual error. The proposed DDROILC technique is illustrated through a numerical simulation on a three-input three-output linear time invariant system model, and compared to the multi-axis inversion-based iterative control (MAIIC) technique. The simulation shows that the proposed DDRO-ILC outperformed the MAIIC method when the crossaxis coupling is strong, and achieved precision tacking with rapid convergence in the presence of random disturbance.

Keywords: Iterative learning control, Mechanical systems/robotics, Optimization
Abstract: Precise trajectory tracking for legged robots can be challenging due to their high degrees of freedom, unmodeled nonlinear dynamics, or random disturbances from the environment. A commonly adopted solution to overcome these challenges is to use optimization-based algorithms and approximate the system with a simplified, reduced-order model. Additionally, deep neural networks are becoming a more promising option for achieving agile and robust legged locomotion. These approaches, however, either require large amounts of onboard calculations or the collection of millions of data points from a single robot. To address these problems and improve tracking performance, this paper proposes a method based on iterative learning control. This method lets a robot learn from its own mistakes by exploiting the repetitive nature of legged locomotion within only a few trials. Then, a torque library is created as a lookup table so that the robot does not need to repeat calculations or learn the same skill over and over again. This process resembles how animals learn their muscle memories in nature. The proposed method is tested on the A1 robot in a simulated environment, and it allows the robot to pronk at different speeds while precisely following the reference trajectories without heavy calculations.

Keywords: Iterative learning control, Modeling, Machine learning
Abstract: We propose a Model-Based Reinforcement Learning (MBRL) algorithm named VF-MC-PILCO, specifically designed for application to mechanical systems where velocities cannot be directly measured. This circumstance, if not adequately considered, can compromise the success of MBRL approaches. To cope with this problem, we define a velocity-free state formulation which consists of the collection of past positions and inputs. Then, VF-MC-PILCO uses Gaussian Process Regression to model the dynamics of the velocity-free state and optimizes the control policy through a particle-based policy gradient approach. We compare VF-MC-PILCO with our previous MBRL algorithm, MC-PILCO4PMS, which handles the lack of direct velocity measurements by modeling the presence of velocity estimators. Results on both simulated (cart-pole and UR5 robot) and real mechanical systems (Furuta pendulum and a ball-and-plate rig) show that the two algorithms achieve similar results. Conveniently, VF-MC-PILCO does not require the design and implementation of state estimators, which can be a challenging and time-consuming activity to be performed by an expert user.

Keywords: Variable-structure/sliding-mode control, Distributed control, Cooperative control
Abstract: This article presents a distributed controller for the formation of unicycle mobile robots whose aim is to follow the leader position maintaining a certain geometry in the horizontal plane. The proposed control law provides the formation of the followers with the leader's position using sliding mode control techniques. The sliding mode controllers are designed using local interactions to ensure the convergence to zero of a couple of suitable sliding variables. The particular design of the sliding variables guarantees that the resulting sliding motion provides the asymptotic convergence of the formation errors to a bounded region around the origin.

Keywords: Variable-structure/sliding-mode control, Fault accomodation, Power electronics
Abstract: Fast and accurate mitigation of dynamic instabilities resulting from grid faults is critical for the safe and reliable operation of microgrids. This paper proposes a non-singular fast terminal sliding mode control (NFTSMC)-based approach to enhance the dynamic stability of wind energy conversion system-based microgrids. The approach combines the fast convergence and robustness of NFTSMC with the fast current controllability of static synchronous compensators (STATCOM) to provide reactive power support and stabilize the grid voltage in the presence of grid faults and mismatched disturbances. The stability of the NFTSMC approach is established using the Lyapunov stability theory. The control approach is implemented in a test microgrid system and assessed in the presence of mismatched disturbances and a symmetrical grid fault. Its dynamic performance is also compared to that of a standard sliding mode controller. The obtained results confirmed the ability of the proposed scheme to effectively mitigate dynamic instabilities resulting from grid faults and provide grid support under faulty conditions.

Keywords: Variable-structure/sliding-mode control
Abstract: In many application domains, navigation of unmanned aerial vehicles (UAVs) requires a planar flight to move along a desired path or to track a moving object under uncertain conditions. In this paper, we propose a robust control approach for quadrotor UAVs performing a nonholonomic-like navigation with a predefined velocity based guidance law. Specifically, the quadrotor model is first recast in the framework of nonholonomic systems, and then an adaptive multiple-surface sliding mode approach, with suboptimal second order sliding mode control, is applied. The robustness features of the proposed approach are discussed and assessed in simulation.

Keywords: Uncertain systems, Variable-structure/sliding-mode control
Abstract: Although literature has presented effective approaches using adaptive control methods to tackle system uncertainties, these methods typically guarantee asymptotic stabilization without a defined convergence time unless the controlled system adheres to the persistent excitation condition. Unfortunately, this condition may not always be applicable in practice. This paper proposes a sliding mode adaptive stabilization architecture that uses nonlinear reference models to control a class of uncertain nonlinear dynamical systems with a quantifiable convergence time. Along with presenting our main results, we also showcase the effectiveness of our approach by providing two illustrative numerical examples.

Keywords: Chaotic systems, Variable-structure/sliding-mode control, Fuzzy systems
Abstract: This work presents a novel chaos synchronization scheme for nonidentical fractional-order chaotic systems. The new scheme, called switched combination synchronization, integrates the concepts of switched synchronization and combination synchronization where two drive systems, called base systems, are swapped using a switching factor and are combined with a third drive system, called the masking system. A response system is synchronized with the resulting multi-drive systems using a neuro-fuzzy sliding mode control (NFSMC) approach. A soft switching algorithm using the neuro-fuzzy switch is designed to ensure the stability of the system during the transition of drive systems. Simulation results confirm the higher performance of the proposed control approach than a regular sliding mode control (SMC) and a proportional integrative derivative (PID) controller in switched combination synchronization of chaotic systems.

Keywords: Observers for Linear systems, Variable-structure/sliding-mode control, Robust control
Abstract: This article presents a robust observer for a class of continuous-time linear time-invariant systems affected by unknown inputs. The sufficient conditions under which this observer allows the estimation error to possess the homogeneity property are studied. Furthermore, the observer algorithm comprises a linear compensation term that enables the observer nonlinear output injection term to provide global finite-time convergence despite bounded unknown inputs and system instability.

Keywords: Modeling, Biological systems, Simulation
Abstract: This work studies the classical pharmacokinetic-pharmacodynamic (PK-PD) model of Propofol for total intravenous anesthesia in response to intraoperative blood loss. Anesthetic and hemodynamic stability are impaired in the setting of trauma surgeries or major procedures with high hemorrhage risk. Blood loss has immediate effects on the cardiovascular system, but also affects the plasma concentration of the perioperatively infused drugs. During perioperative transition periods, when fast blood losses occur, the PK models on which the target-controlled infusion (TCI) is based should be updated. Then, the population-based parameters move towards an individualized strategy that accounts also for the actual blood volume in the patient. This paper evaluates the influence of changing blood volume on the PK model of Propofol, hence on the anesthesia state of the patient. The simulations also account for the hemodynamic responses due to the conflicting interactions of both hemorrhage and anesthetic drug infusion. This model has great potential for inclusion in multiple-closed loop control strategies of anesthesia-hemodynamic states, as it is simple and adapted from well-known PK models, for which control strategies are already mature.

Keywords: Healthcare and medical systems, Biomedical, Control applications
Abstract: This letter presents a novel approach to assure hemodynamic safety in closed-loop controlled critical care. The approach is equipped with safety-preserving control based on control barrier functions to ensure the safety of hemodynamic state, hemodynamic monitoring to estimate hemodynamic state, and probabilistic recursive therapeutic target guidance to direct a patient as closely as possible to a prescribed therapeutic target along a desired trajectory. A notable advantage of the approach is that it can be augmented to single-input-single-output critical care control loops developed in isolation to guard hemodynamic safety against conflicts between them, providing a practical alternative to sophisticated multi-input-multi-output control loop design. The efficacy of the approach was examined in a hemorrhage resuscitation-intravenous sedation case study using realistic virtual patients. The approach as a whole assured the boundedness of hemodynamic state by reconciling conflicts between the two control loops. The recursive therapeutic target guidance directed patients to personalized reachable targets while maintaining the patients’ therapeutic responses near the desired therapeutic trajectory. The approach may serve as an effective means to reconcile multiple critical care control loops and assure holistic hemodynamic safety.

Keywords: Healthcare and medical systems, Stability of nonlinear systems, Network analysis and control
Abstract: Epilepsy affects approximately 50 million people worldwide. Despite its prevalence, the recurrence of seizures can be mitigated only 70% of the time through medication. Furthermore, surgery success rates range from 30% - 70% because of our limited understanding of how a seizure starts. However, one leading hypothesis suggests that a seizure starts because of a critical transition due to an instability. Unfortunately, we lack a meaningful way to quantify this notion that would allow physicians to not only better predict seizures but also to mitigate them. Hence, in this paper, we develop a method to not only characterize the instability of seizures but also to leverage these conditions to stabilize the system underlying these seizures. Remarkably, evidence suggests that such critical transitions are associated with long-term memory dynamics, which can be captured by considering linear fractional-order systems. Subsequently, we provide for the first time tractable necessary and sufficient conditions for the global asymptotic stability of discrete-time linear fractional-order systems. Next, we propose a method to obtain a stabilizing control strategy for these systems using linear matrix inequalities. Finally, we apply our methodology to a real-world epileptic patient dataset to provide insight into mitigating epilepsy and designing future cyber-neural systems.

Keywords: Biomedical, Computational methods, Modeling
Abstract: Multi-actuator magnetic resonance elastography (MRE) has previously been studied for overcoming wave attenuation and generating uniform displacements throughout a targeted imaging region. While the actuators’ locations, relative phase offsets, and angles are known to influence the generated displacements, their effects are dependent on the geometry and properties of the specific target. Experimental optimization of these MRE parameters can be performed but is time-consuming. Alternatively, finite element analysis (FEA) is used for three-dimensional model-specific characterization of displacement fields induced by MRE mechanical excitation loads across varying actuator locations. Cubic, tissue-like homogeneous and heterogeneous models were created and loads were applied to simulate single actuator and multi-actuator cases. Multi-actuator cases were phase-matched to promote constructive interference of the induced waves. An additional investigation was performed by repeating a single multi-actuator configuration with various loading angles in the heterogeneous model. The mean displacement amplitudes and the corresponding standard deviations throughout the imaging target volumes are compared across the multiple configurations. Wave images of selected configurations are presented for comparison. Multi-actuator configurations induced the greatest mean z displacement amplitudes within the imaging target of both models. To further increase the z displacement, the excitation loads can be angled towards the imaging target. The differences in simulated displacement fields demonstrate the potential for future automated parameter optimization for closed-loop MRE driver positioning using more complex FEA models.

Keywords: Biomedical, Emerging control applications, Identification for control
Abstract: The application of control systems principles in behavioral medicine includes developing interventions that can be individualized to promote healthy behaviors, such as sustained engagement in adequate levels of physical activity (PA). This paper presents the use of system identification and control engineering methods in the design of behavioral interventions through the novel formalism of a control-optimization trial (COT). The multiple stages of a COT, from experimental design in system identification through controller implementation, are illustrated using participant data from Just Walk, an intervention to promote walking behavior in sedentary adults. ARX models for individual participants are estimated using multiple estimation and validation data combinations, with the model leading to the best performance over a weighted norm being selected. This model serves as the internal model in a hybrid MPC controller formulated with three degree-of-freedom (3DoF) tuning that properly balances the requirements of physical activity interventions. Its performance in a realistic closed-loop setting is evaluated via simulation. These results serve as proof of concept for the COT approach, which is currently being evaluated with human participants in the clinical trial YourMove.

Keywords: Biomedical, Control applications, Estimation
Abstract: This paper proposes a novel algorithm for human activity recognition that is a combination of a high-gain observer and deep learning-based classification algorithms. The nonlinear high-gain observer designed using Lyapunov analysis accurately estimates the attitude of the chest of a human subject using measurements from a single Inertial Measurement Unit (IMU). The signals processed by the observer are then converted into spectrograms to obtain “images” of the frequency response of the signals. The images for activities from a dataset of 7 human subjects are annotated and used for training/ fine-tuning of several well-known deep learning algorithms for image processing. The results from the best combination of our algorithms shows an exceptional accuracy of 98% for activity recognition.

Keywords: Kalman filtering, Modeling, Estimation
Abstract: Wheel slip control of locomotive traction systems is difficult because of the uncertainty in the non-linear wheel-surface behaviour, the unknown adhesion conditions and the difficulty in obtaining the slip ratio. Continuous controllers can perform better than traditional rule-based controllers if the uncertainty can be reduced using effective estimation. A novel linear state-observable estimator is presented that produces estimates of the slip ratios and adhesion coefficients of each locomotive wheelset. The estimator requires measurements of the locomotive velocity and acceleration. The estimator includes the estimation of the normal forces of each wheelset to increase the adhesion coefficient estimation accuracy.

Keywords: Kalman filtering, Robust control, Uncertain systems
Abstract: Developing accurate and optimum state estimation methods for fractional order systems is highly relevant since it provides vital information related to memory effects. The optimum estimation of these systems can be guaranteed using the Kalman filter (KF) when all parameter matrices are not subject to uncertainties. Nevertheless, this fundamental principle of the filter is violated, and its performance can be degraded when the model is uncertain. In this light and to limit this deterioration, the present study introduces an optimal solution for filtering uncertain fractional order systems, which operates as follows. First, using the robust regularized least-squares (RLSs) problem combined with penalty functions, a robust penalty game approach is proposed. Then, in an independent framework of any auxiliary parameters, unified recursive Riccati equation and optimal robust filter are derived subject to norm-bounded uncertainties of parameter matrices. To accomplish this step, the stability and convergence analysis of the filter are illustrated based on the singular theory conception.

Keywords: Kalman filtering, Quantized systems, Stability of linear systems
Abstract: In this paper, we address the stability of a Quantized Distributed-Consensus Kalman Filter (Q-DCKF) operating in a limited communication environment. In the QDCKF, agents share a quantized version of their state estimates with neighboring nodes, as they reach a consensus on the state of a mobile target. Even though the stability of the single and distributed Kalman filters has been studied in the past, the effect of quantization of the states and resulting estimation error covariances have not been characterized for the distributed setting considered in this paper. We show, via passivity theory, that the Q-DCKF is stable under mild assumptions and validate the theoretical results obtained via numerical experiments.

Keywords: Quantum information and control, Kalman filtering, Control applications
Abstract: Research in the field of quantum control usually assumes complete knowledge of the state and parameters. In this paper, a driven and damped two-level quantum system under continuous observation is considered. Its time evolution is governed by an operator-valued stochastic master equation and conditioned on the recorded measurement data. The system is transformed to state space representation and its observability is proven analytically. An extended Kalman filter is employed in order to both reconstruct the density operator describing the full state of the system, and to dynamically identify key parameters. Convincing results are obtained in numerical simulations. Overall, a practical engineering approach to quantum control is presented.

Keywords: Kalman filtering, Biomedical, Control applications
Abstract: This paper is motivated by peritoneal perfusion: the circulation of fluid through the abdomen of a patient or laboratory animal. Peritoneal perfusion applications include dialysis, drug delivery, and potentially providing supplemental oxygen to patients with respiratory failure. If an excessive fluid volume is retained in the abdomen during perfusion, medical complications, such as intra-abdominal hypertension and abdominal compartment syndrome, may arise. Previous work by the authors presents a state-space model of the abdominal cavity pressure dynamics causing such complications and proposes an extended Kalman filter (EKF) that uses these dynamics for retained volume estimation. In this paper, the authors aim to validate the EKF's performance using data from clinical experiments on two Yorkshire swine, which are different from the animal originally used for system identification and EKF design. In both experiments, the EKF runs online as perfusion takes place. The EKF-based volume estimate is then compared to a weight sensor-based estimate of the total fluid supplied to the animal plus the tubing connected to the animal. The two volume estimates correlate linearly, with an encouraging coefficient of determination of 91.6% for both animal experiments.

Keywords: Kalman filtering, Estimation, Observers for nonlinear systems
Abstract: The concept of transmissibility operators refers to the mathematical relationships between system outputs. They can be used to estimate the independent output of a system based on sensor measurements only. In this case, the output estimation is independent of the process noise or unmodeled dynamics. This allows for the estimation of process noise regardless of its probability distribution. The proposed approach takes into account the possibility of using the Kalman filter theme in the filtering of output noise regardless of the process noise distribution. The proposed approach does not require the covariance estimation of the process noise. Since the proposed approach considers the ability to formulate unmodeled dynamics or parameter uncertainties as non-Gaussian process noise, it can handle both. The potential of this approach is demonstrated by implementing it in a group of connected autonomous robots.

Keywords: Identification, Maritime control, Uncertain systems
Abstract: Linear and nonlinear models of a modified commercially available unmanned surface vessel are identified without actuator calibration. The unknown actuator calibration is represented by a piecewise linear function of the normalized force, the actuator force divided by the unknown maximum force. The drag coefficients are estimated in terms of the normalized force using the experimental steady-state response and the maximum force is estimated using the experimental transient response. The models are validated via simulation and by comparison with a previously-developed model for an unmodified version of the unmanned surface vessel.

Keywords: Identification, Modeling, Energy systems
Abstract: To develop a full battery model in view to accurate battery management, Li-ion cell dynamics is modelled by a capacitor in series with a simplified Randles circuit. The open circuit voltage is the voltage at the capacitor terminals, allowing, in this way, for the dependence of the open circuit voltage on the state-of-charge to be embedded in its capacitance. The Randles circuit is recognised as a trusty description of a cell dynamics. It contains a semi-integrator of the current, known as the Warburg impedance, that is a special case of a fractional integrator. To enable the formulation of a time-domain system identification algorithm, the Warburg impedance impulse response was calculated and normalised, in order to derive a finite order state-space approximation, using the Ho-Kalman algorithm. Thus, this Warburg impedance LTI model, with known parameters (normalised impedance) in series with a gain block, is suitable for system identification, since it has only one unknown parameter. A LTI System identification Algorithm was formulated to estimate the model parameters and the initial values of both the open circuit voltage and the states of the normalised Warburg impedance. The performance of the algorithm was very satisfactory on the whole state-of-charge region and when compared with low order Thévenin models. Once it is understood the parameters variability on the state-of-charge, temperature and ageing, we envisage to continue the work using parameter-varying algorithms.

Keywords: Model/Controller reduction, Robust control, Linear systems
Abstract: Recently, the fractional-order element has been integrated into the Robust Control Framework considering the Oustaloup method. As such, the resulting infinite impulse response approximation manages to satisfy the robust stability and the robust performance criteria according to a given uncertainty block. However, the recommended approximation order for each fractional-order element is the number of decades of the frequency range where the approximation is valid, which can lead to a high-order controller. The current paper describes an optimization-based technique to find a low-order approximation of a fractional-order controller such that the resulting controller maintains the robust stability and robust performance as well. A set of numerical experiments have also been performed in order to illustrate the proposed method.

Keywords: Queueing systems, Network analysis and control, Stochastic systems
Abstract: A graph-theoretic analysis of the steady-state behavior of an open Jackson queueing network is developed. In particular, a number of queueing-network performance metrics are shown to exhibit a spatial dependence on local drivers (e.g. increments to local exogenous arrival rates), wherein the impacts fall off across graph cutsets away from a target queue. This graph-theoretic analysis is also used to motivate a structure-preserving model reduction algorithm, and an algorithm that exactly matches performance statistics of the original model is proposed. The graph-theoretic results and model-reduction method are evaluated via simulations of an example queueing-network model.

Keywords: Control of networks, Network analysis and control, Biological systems
Abstract: We study the endemic behavior of a multi-competitive networked susceptible-infected-susceptible (SIS) model. In particular, we focus on the case where there are three competing viruses (i.e., tri-virus system). First, we show that the tri-virus system is not monotone. Thereafter, we identify necessary conditions and a sufficient condition for local exponential convergence to a boundary equilibrium (exactly one virus is alive, the other two are dead) and identify a special case that admits the existence and local exponential attractivity of a line of coexisting equilibria (at least two viruses are active). Finally, we identify a particular case (subsumed by the aforementioned special case) such that for all nonzero initial infection levels, the dynamics of the tri-virus system converge to a plane of coexisting equilibria.

Keywords: Fluid flow systems, Uncertain systems, Reduced order modeling
Abstract: This work builds upon recent work exploiting the notion of structured singular values to capture nonlinear interactions in the analysis of wall-bounded shear flows. In this context, the structured uncertainty can be interpreted in terms of the flow structures most likely to be amplified (the optimal perturbations). Here we further analyze these perturbations through a problem reformulation that decomposes this uncertainty into three components associated with the streamwise, wall-normal and spanwise velocity correlations. We then demonstrate that the structural features of these correlations are consistent with nonlinear optimal perturbations and results from secondary stability analysis associated with streamwise streaks. These results indicate the potential of structured input-output analysis for gaining insight into both linear and nonlinear behavior that can be used to inform sensing and control strategies for transitional wall-bounded shear flows.

Keywords: Game theory, Network analysis and control, Large-scale systems
Abstract: We consider network games where a large number of agents interact according to a network sampled from a random network model, represented by a graphon. By exploiting previous results on convergence of such large network games to graphon games, we examine a procedure for estimating unknown payoff parameters, from observations of equilibrium actions, without the need for exact network information. We prove smoothness and local convexity of the optimization problem involved in computing the proposed estimator. Additionally, under a notion of graphon parameter identifiability, we show that the optimal estimator is globally unique. We present several examples of identifiable homogeneous and heterogeneous parameters in different classes of linear quadratic network games with numerical simulations to validate the proposed estimator.

Keywords: Game theory, Optimization algorithms
Abstract: Stackelberg games have been widely used to model interactive decision-making problems in a variety of domains such as energy systems, transportation, cybersecurity, and human-robot interaction. However, existing algorithms for solving Stackelberg games often require knowledge of the follower's cost function or learning dynamics and may also require the follower to provide an exact best response, which can be difficult to obtain in practice. To circumvent this difficulty, we develop an algorithm that does not require knowledge of the follower's cost function or an exact best response, making it more applicable to real-world scenarios. Specifically, our algorithm only requires the follower to provide an approximately optimal action in response to the leader's action. The inexact best response is used in computing an approximate gradient of the leader's objective function, with which zeroth-order bilevel optimization can be applied to obtain an optimal action for the leader. Our algorithm is proved to converge at a linear rate to a neighborhood of the optimal point when the leader's cost function under the follower's best response is strongly convex and smooth.

Keywords: Game theory, Sensor networks, Fault detection
Abstract: We consider a two-player zero-sum inspection game, in which a limited number of detectors are coordinated in an infrastructure system according to a probability distribution to detect multiple attacks from a strategic opponent. Detection is assumed to be imperfect and depends on the detectors' technology and the infrastructure's properties. We analytically characterize Nash equilibria of this large-scale game for problem instances where each component is detected from one detector location and the attacker has limited resources. Our equilibrium analysis provides a new criticality assessment of the infrastructure's components in strategic settings. It also demonstrates new equilibrium behavior from the players that intricately depends on their amount of resources, as well as the detection technology and infrastructure topology.

Keywords: Mean field games, Stochastic systems, Network analysis and control
Abstract: Crowd-sourcing models, which leverage the collective opinions/signals of users on online social networks (OSNs), are well-accepted for fake post detection; however, motivating the users to provide the crowd signals is challenging, even more so in the presence of adversarial users.

We design a participation (mean-field) game where users of the OSN are lured by a reward-based scheme to provide the binary (real/fake) signals such that the OSN achieves (theta, delta)-level of actuality identification (AI) - not more than delta fraction of non-adversarial users incorrectly judge the real post, and at least theta fraction of non-adversarial users identify the fake post as fake. An appropriate warning mechanism is proposed to influence the decision-making of the users such that the resultant game has at least one Nash Equilibrium (NE) achieving AI. We also identify the conditions under which all NEs achieve AI. Further, we numerically illustrate that one can always design an AI game if the normalized difference in the innate identification capacities of the users is at least 1%, when desired theta = 75%.

Keywords: Multivehicle systems, Game theory, Neural networks
Abstract: Decision-making plays a critical role in autonomous driving, connecting the upstream perception task and the downstream planning task. The interaction among vehicles and the uncertainty of driving intentions are two main challenges of lane change decision-making. To meet these challenges, a game theory method based on the LSTM (Long Short-Term Memeory) neural network is proposed. The game theory method is adopted to model the interaction among vehicles and the LSTM network is used to precisely fit the complex nonlinear relationship between payoffs and features. For highway scenarios with ramps, discretionary and mandatory lane change scenarios are specifically extracted and the lane priority is added to features. The improved GPSO-DE optimizer is used to accelerate network training and reduce the local optimal solutions. Finally, experiments on real-world dataset NGSIM I-80 show that the prediction accuracy of other vehicles’ intentions and the decision-making accuracy of ego vehicles have reached state-of-the-art performance. Moreover, the model is capable of improving the robustness of decision-making and reducing unreasonable jumps effectively.

Keywords: Smart grid, Game theory, Optimization
Abstract: With the proliferation of distributed generations, traditional passive consumers in distribution networks are evolving into ``prosumers", which can both produce and consume energy. Energy trading with the main grid or between prosumers is inevitable if the energy surplus and shortage exist. To this end, this paper investigates the peer-to-peer (P2P) energy trading market, which is formulated as a generalized Nash game. We first prove the existence and uniqueness of the generalized Nash equilibrium (GNE). Then, an distributed online algorithm is proposed to track the GNE in the time-varying environment. Its regret is proved to be bounded by a sublinear function of learning time, which indicates that the online algorithm has an acceptable accuracy in practice. Finally, numerical results with six microgrids validate the performance of the algorithm.

Keywords: Adaptive control, Constrained control, Closed-loop identification
Abstract: We propose a certainty-equivalence scheme for adaptive control of scalar linear systems subject to additive, i.i.d. Gaussian disturbances and bounded control input constraints, without requiring prior knowledge of the bounds of the system parameters, nor the control direction. Assuming that the system is at-worst marginally stable, mean square boundedness of the closed-loop system states is proven. Lastly, numerical examples are presented to illustrate our results.

Keywords: Adaptive control, Automotive control, Fault tolerant systems
Abstract: This paper proposes a hierarchical control architecture to mitigate faults and modeling errors in an engine system. A hybrid approach is used to model the complete engine system with the main cylinder combustion process represented using a neural network model and the rest of the system is modeled using well-studied physics-based analytical equations. A control calibration map that consists of the optimal engine control parameters to maintain the desired engine torque using the minimum fuel consumption rate is generated offline by performing Bayesian optimization on this high-fidelity hybrid engine model. We then use proportional-integral (PI) and extremum seeking (ES) controllers on top of the offline map to compensate for any engine faults and modeling errors for online calibration. The work is motivated by optimally reconfiguring autonomous systems. We test three different scenarios through numerical simulations which require online calibration of the engine control parameters. It is shown that the PI+ES controller can overcome the fault by maintaining the desired torque and also lowers the fuel consumption rate compared to a PI controller.

Keywords: Adaptive control, Aerospace, Lyapunov methods
Abstract: The interest in multirotor systems has significantly increased over the last decade, with considerable further potential application scenarios in the future. Multiple adaptive control strategies have been developed to account for uncertainties and disturbances during operation. In this paper, we derive an adaptive backstepping position controller by utilizing the tuning functions methodology. This allows compensating for both matched and unmatched disturbances in the system. Asymptotic stability of the reference model is proved with Lyapunov's second method. The derived control laws are implemented and finally validated during flight tests with a hexacopter system.

Keywords: Adaptive control, Constrained control, Uncertain systems
Abstract: This paper deals with the control of uncertain constrained linear systems. The plant's dominant dynamics are controlled via a simple linear control law, while uncertainties are handled by an adaptive strategy that appropriately modifies the law by monitoring the system state in accordance with some desired dynamics. The closed-loop system is augmented with a robust command governor scheme to enforce state and input constraints by modifying the reference point-wisely. Thanks to the adaptive law performance guarantees, large uncertainties can be handled and the computational complexity of the governor's optimization problem is limited compared to the standard strategy. Stability and feasibility are discussed. Numerical simulations illustrate the methodology applied to a geostationary satellite. Discussions and future perspectives conclude the paper.

Keywords: Direct adaptive control, Adaptive control
Abstract: This paper concerns the adaptive control of a class of discrete-time nonlinear systems with all states accessible. Recently, a high-order tuner algorithm was developed for the minimization of convex loss functions with time-varying regressors in the context of an identification problem. Based on Nesterov's algorithm, the high-order tuner was shown to guarantee bounded parameter estimation when regressors vary with time, and to lead to accelerated convergence of the tracking error when regressors are constant. In this paper, we apply the high-order tuner to the adaptive control of a particular class of discrete-time nonlinear dynamical systems. First, we show that for plants of this class, the underlying dynamical error model can be causally converted to an algebraic error model. Second, we show that using this algebraic error model, the high-order tuner can be applied to provably stabilize the class of dynamical systems around a reference trajectory.

Keywords: Adaptive control, Direct adaptive control, Adaptive systems
Abstract: This paper develops an approach to static output feedback under the assumption that a stabilizing static-output-feedback gain is known for an approximate plant model. This approach is motivated by the fact that system identification may be used to obtain an approximate plant model, and offline optimization can be used to obtain a stabilizing static-output-feedback gain. This gain provides the initial guess for the adaptive static-output-feedback control law, which iteratively refines the gain based on the response of the actual system dynamics.

Keywords: Stability of nonlinear systems, Adaptive control, Optimization
Abstract: This work extends the existing fast extremum seeking control (ESC) for a class of Hammerstein systems to a class of generalized Hammerstein systems, in which the nonlinear affine dynamic system is connected directly after a given cost function. With the relative degree information of the unknown nonlinear dynamics, a new output is generated. The mapping between the new output and the input has two parts. The first part is proportional to the cost function and the second part is related to the state. By inserting a fast dither signal, the proposed ESC can seek the optimum of this cost function without time-scale separation. Our main results show that with proper selection of tuning parameters, this scheme can achieve arbitrarily fast semi-global practical asymptotic (SPA) convergence. Simulation results support the theoretical findings.

Keywords: Stability of nonlinear systems, Robust control, LMIs
Abstract: This letter presents a framework for synthesizing a robust full-state feedback controller for systems with unknown nonlinearities. Our approach characterizes input-output behavior of the nonlinearities in terms of local norm bounds using available sampled data corresponding to a known region about an equilibrium point. A challenge in this approach is that if the nonlinearities have explicit dependence on the control inputs, an a priori selection of the control input sampling region is required to determine the local norm bounds. This leads to a "chicken and egg" problem, where the local norm bounds are required for controller synthesis, but the region of control inputs needed to be characterized cannot be known prior to synthesis of the controller. To tackle this issue, we constrain the closed-loop control inputs within the sampling region while synthesizing the controller. As the resulting synthesis problem is non-convex, three semi-definite programs (SDPs) are obtained through convex relaxations of the main problem, and an iterative algorithm is constructed using these SDPs for control synthesis. Two numerical examples are included to demonstrate the effectiveness of the proposed algorithm.

Keywords: Stability of nonlinear systems, Nonlinear output feedback, LMIs
Abstract: This letter presents a framework for the gain scheduling of QSR-dissipative systems and quantifies the resulting QSR-dissipative properties of the overall gain-scheduled system. This work constitutes a generalization of prior work in the literature involving the gain scheduling of passive and conic systems, providing a practical extension to non-square QSR-dissipative systems. The derived results are presented for two classes of systems that account for many well-known special cases of QSR-dissipative systems, including passive, conic, and finite L2 gain systems. Special cases of the developed theory are shown to match closely to existing results in the literature. A numerical example is included that demonstrates the benefits of the derived results within the context of gain-scheduled control, with a comparison to a passivity-based control.

Keywords: Algebraic/geometric methods, Stability of nonlinear systems, Lyapunov methods
Abstract: This paper focuses on stability analysis of discrete-time dynamical systems having a continuum of equilibria. Two notions that are of particular relevance to such systems are convergence and semistability. In this paper, we develop Lyapunov-based tests for convergence using the notion of nontangency between the vector field and invariant subsets of the level and sublevel sets of the Lyapunov function and its difference. Specifically, we study nontangency of the vector field to the set of equilibria and provide sufficient conditions for convergence. Moreover, a relationship between Lyapunov stability of an equilibrium point and convergence is provided.

Keywords: Stability of nonlinear systems, Uncertain systems, Control applications
Abstract: Projection-to-state safety (PSSf) is a special case of input-to-state safety (ISSf), which uses projections to create a low-dimensional representation of the uncertainties and allows quantifying the impact of the projected disturbance on the safety guarantees in a low-dimensional space. In this paper, rather than reasoning PSSf as a characterization of safety in terms of projected uncertainties, we interpret it as a property of the original dynamical system that is guaranteed by ISSf of the projected dynamical system. This new perspective allows for simplifying controller synthesis via projected dynamical systems and quantifying the impact of uncertainties on the safety of the original dynamical systems. Moreover, we extend the results of PSSf to deal with high relative degree constraints via a coordination transformation strategy, which makes it also applicable to some high-order systems. To exhibit the efficacy of the new perspective, a robotic arm application, and its corresponding numerical results are provided for validation.

Keywords: Stability of nonlinear systems, Stochastic systems, Markov processes
Abstract: The COVID-19 pandemic has witnessed the role of online social networks (OSNs) in the spread of infectious diseases. The rise in severity of the epidemic augments the need for proper guidelines, but also promotes the propagation of fake news-items. The popularity of a news-item can reshape the public health behaviors and affect the epidemic processes. There is a clear inter-dependency between the epidemic process and the spreading of news-items. This work creates an integrative framework to understand the interplay. We first develop a population-dependent `saturated branching process' to continually track the propagation of trending news-items on OSNs. A two-time scale dynamical system is obtained by integrating the news-propagation model with SIRS epidemic model, to analyze the holistic system. It is observed that a pattern of periodic infections emerges under a linear behavioral influence, which explains the waves of infection and reinfection that we have experienced in the pandemic. We use numerical experiments to corroborate the results and use Twitter and COVID-19 data-sets to recreate the historical infection curve using the integrative model.

Keywords: Observers for Linear systems, Agents-based systems, Uncertain systems
Abstract: This paper proposes a novel distributed interval observer design for linear time-invariant (LTI) discrete-time systems subject to bounded disturbances. In the proposed observer algorithm, each agent in a networked group, exchanges locally computed framers or interval-valued state estimates with neighbors and coordinates its update via an intersection operation. We show that the proposed framers are guaranteed to bound the true state trajectory of the system by construction, i.e., without imposing any additional assumptions or constraints. Moreover, we provide necessary and sufficient conditions for the collective stability of the distributed observer, i.e., to guarantee the uniform boundedness of the observer error sequence. In particular, we show that such conditions can be tractably satisfied through a constructive and distributed approach. Moreover, we provide an algorithm to verify some structural conditions for a given system, which guarantee the existence of the proposed observer. Finally, simulation results demonstrate the effectiveness of our proposed method compared to an existing distributed observer in the literature.

Keywords: Observers for Linear systems, Estimation, Control applications
Abstract: This paper investigates cell-level state of charge (SOC) estimation in a parallel connected lithium-ion (Li-ion) battery pack under a reduced sensing scenario. The internal states of individual cells within a battery pack are likely to differ due to cell inconsistencies caused by manufacturing tolerances and usage conditions. This creates a need for cell level estimation in a parallel connected battery pack. The dynamics of parallel connected battery packs require solving differential algebraic equations (DAEs). This paper considers the reduced sensing scenario, measuring only the total current and voltage for estimating individual cell SOCs and local currents in a battery pack. A novel functional observer, designed under milder conditions, is proposed and the observer design is formulated in terms of a feasible linear matrix inequality (LMI) problem. In the simulation, the SOC of two cylindrical Li-ion battery cells are estimated, and the results illustrate a fast convergence and hence the effectiveness of our approach.

Keywords: Observers for Linear systems, Intelligent systems, Estimation
Abstract: We consider the problem of signal reconstruction for a system under sparse signal corruption by a malicious agent. The reconstruction problem follows the standard error coding problem that has been studied extensively in the literature. We include a new challenge of robust estimation of the attack support. The problem is then cast as a constrained optimization problem merging promising techniques in the area of deep learning and estimation theory. A pruning algorithm is developed to reduce the ``false positive" uncertainty of data-driven attack localization results, thereby improving the probability of correct signal reconstruction. Sufficient conditions for the correct reconstruction and the associated reconstruction error bounds are obtained for both exact and inexact attack support estimation. Moreover, a simulation of a water distribution system is presented to validate the proposed techniques.

Keywords: Observers for Linear systems, Optimization algorithms, Estimation
Abstract: This paper considers the design of a distributed state observer for discrete-time Linear Time Invariant (LTI) systems in the presence of sensor attacks. We assume there is a network of observer nodes, communicating with each other over an undirected graph, each with partial measurements of the output corrupted by some adversarial attack. We address the case of sparse attacks where the attacker targets a small subset of sensors. An algorithm based on Alternating Direction Method of Multipliers (ADMM) is developed which provides an update law for each observer that ensures convergence of each observer node to the actual state asymptotically.

Keywords: Observers for Linear systems, Switched systems, Fault tolerant systems
Abstract: The design of safe-critical control algorithms for systems under Denial-of-Service (DoS) attacks on the system output is studied in this work. We aim to address scenarios where attack-mitigation approaches are not feasible, and the system needs to maintain safety under adversarial attacks. We propose an attack-recovery strategy by designing a switching observer and characterizing bounds in the error of a state estimation scheme by specifying tolerable limits on the time length of attacks. Then, we propose a switching control algorithm that renders forward invariant a set for the observer. Thus, by satisfying the error bounds of the state estimation, we guarantee that the safe set is rendered conditionally invariant with respect to a set of initial conditions. A numerical example illustrates the efficacy of the approach.

Keywords: Energy systems, Automotive control, Optimization
Abstract: This paper presents an optimal controller for an electric vehicle’s mechanical braking system to maximize energy regeneration during braking. First an EV powertrain system model is developed using a DC motor, an equivalent circuit battery, and a vehicle dynamics model. An open-loop speed controller is then derived for precise drive cycle tracking. Using the electromechanical DC motor equations, an optimal control policy is developed for motor voltage and the friction brake system to maximize motor power during energy regeneration. Simulation results indicate that the addition of the mechanical brake in an optimal way can improve energy recovery during braking periods. However, the amount of energy recovery is highly dependent on the deceleration rate and the parameters of the electric motor including the back-emf constant and the coil resistance.

Keywords: Automotive control, Energy systems, Optimization
Abstract: This paper proposes a control barrier function (CBF) approach for fast charging of batteries under temperature, charge and terminal voltage constraints. To improve numerical efficiency, we derive a cascade CBF formulation, which divides this safety problem into multiple layers that are easier to formulate and implement. Experimental results demonstrate the effectiveness of the fast charging algorithm, decreasing charging time by 22% when compared to state-of-art constant current, constant voltage (CC-CV) methods and without violating electro-thermal safety constraints.

Keywords: Energy systems, Building and facility automation, Automotive systems
Abstract: Plug-in electric vehicles have seen unprecedented market growth, while charging facility infrastructure is falling behind. Worse still, these limited charging resources are being utilized quite uneconomically - commonly occupied by fully charged PEVs for a long time, known as overstay. In this paper, we propose a charging facility and operation innovation to tackle this challenge. We introduce the idea of Robo-chargers, an automated charger that can proactively rotate among PEVs for charging service. We develop an operation model for management in a mixed-type charger charging station, equipped with both Fixed-chargers and Robo-chargers. The model incorporates the combinatorial nature of vehicle-charger assignments, charging dynamics, and customer waiting behavior in order to maximize the station’s revenue. We further reformulate the model as a mixed integer linear programming problem. In numerical studies based on real-world data, we find that incorporating Robo-chargers into a charging station is profitable when heavy overstay occurs, justifying the increased capital cost. For a given budget, a mix of Fixed chargers and Robo-chargers can achieve the best operation performance by balancing robo-charger flexibility, cost, and total charging points.

Keywords: Predictive control for nonlinear systems, Energy systems, Estimation
Abstract: In this paper, we consider the problem of controlling a hybrid thermal management system (TMS) in which thermal energy may be temporarily rejected to a phase change material (PCM)-based energy storage device. We define the state of charge (SOC) as the amount of thermal energy that can yet be absorbed by the PCM at that instant. The hybrid TMS control objective is to optimally determine when and by how much heat should be rejected to (discharge) the PCM, or removed from (recharge) it during the operation, while meeting some system performance specification. In order to design the feedback control scheme, we require knowledge of the temperature and/or melt fraction across the PCM volume to determine SOC at each sampling instant. Using a graph-based diffusion model of the heat transfer in the PCM volume, we show that the temperature distribution across the PCM may be estimated using a State-Dependent Riccati Equation Estimator (SDRE). Thus, we develop a model predictive control (MPC) scheme in which the SDRE is used to estimate the temperature distribution, and hence the SOC. The MPC is designed to minimize the system’s pump energy requirement, maximize the SOC at the end of the operation period, and satisfy critical temperature constraints. Through simulation results, we demonstrate the importance of the SOC estimate in achieving control objectives in a hybrid thermal management system.

Keywords: Energy systems, Model Validation, Predictive control for nonlinear systems
Abstract: Because thermal events in battery systems can evolve quickly, any response to prevent thermal runaway propagation and re-ignition will need to be fast, including an emergency fast discharge. However, a fast discharge can create internal heat generation and lead to high temperatures where gas generation and venting of the flammable electrolyte can occur. This work formulates the fast discharge as a multi-objective, nonlinear model predictive control problem that leverages an electro-thermo-mechanical model. Constraints are placed on temperature and pressure to avoid cell venting. The controller is applied to simulate a fast discharge of a fully-charged, 4.6 Ah pouch cell under three constraint scenarios. When the maximum temperature is set to 45 degC, representative of an upper limit during normal operation, discharging down to 60%SOC took 13 minutes. When the constraint was increased to 80 degC, discharging to 60%SOC was four times faster, but the cell vented after 14 minutes. Adding a pressure constraint to the latter case allowed the cell to discharge to 60%SOC equally as fast while also avoiding cell venting in the future, achieving a safe emergency discharge. This is the first work that applies a nonlinear controller with venting considerations to manage abnormal battery behavior for mitigating thermal runaway in a Li-ion battery.

Keywords: Energy systems, Distributed control, Power systems
Abstract: This paper proposes a distributed secondary control for heterogeneous battery energy storage systems (BESSs) to achieve finite-time consensus in frequency and active power while maintaining a balanced energy-level. The proposed scheme incorporates heterogeneity in electrical as well as control aspects and models heterogeneous BESS-based islanded AC microgrid as a multi-agent system with agents interacting according to a detail-balanced topology with heterogeneous edge weights. The finite-time stability of the closed-loop system, under the proposed controllers, is rigorously proved by considering a single composite homogeneous Lyapunov function, thereby calculating an upper limit on convergence time. Efficacy of the proposed controllers is illustrated by simulating a BESS-based microgrid in a Simulink environment.

Keywords: Energy systems, Control applications
Abstract: Within the rapidly growing wind energy sector, floating offshore wind turbines are expected to be the fastest growing portion. This is largely driven by the immense offshore wind resources that are mostly over deep water, where fixed-bottom concepts become cost-prohibitive. However, compared to fixed-bottom wind turbines, floating wind turbines are more dynamic and exhibit potential instabilities, which requires advanced control technologies to ensure a safe and efficient operation. Beyond their existing objectives of maximizing power production while minimizing structural loads, floating wind turbine controllers must also avoid large platform oscillations and accommodate ocean wave and current disturbances. This paper provides an overview of the challenges and opportunities in the control of floating offshore wind energy systems.

Keywords: Energy systems
Abstract: Feedback control of land-based wind turbines is well-established in both industry and academia, however, the same control strategies do not necessarily perform well when applied to floating offshore wind turbines (FOWTs). Multi-loop feedback has been investigated to address the challenges of FOWT control, but the various proposed auxiliary feedback architectures are seldom compared under a unified study. Four multi-loop control approaches are analyzed in this work and evaluated for their ability to improve FOWT performance metrics, including power quality, generator-speed tracking, and structural loading. Each control law is analyzed in the context of closed-loop system stability using root locus methods and tuned using a frequency-based stability margin. The controllers are evaluated using the nonlinear aero-servo-hydro-elastic simulation tool OpenFAST to validate performance benefits compared to a single-loop baseline controller.

Keywords: Energy systems, Predictive control for nonlinear systems, Flexible structures
Abstract: Lidar-assisted control is very promising to reduce the cost of energy for large floating offshore wind turbines by reacting proactive to wind changes. This paper presents a tutorial on how to develop and test a lidar-assisted controller using examples of a 15 MW floating reference wind turbine.

Keywords: Energy systems, Control applications, Mechatronics
Abstract: This paper overviews a wind farm control technique via turbine repositioning, which is exclusively applied to floating offshore wind turbines. The wind turbines are repositioned to modify the wind farm layout based on the wind condition and the power demand, in order to maximize the wind farm efficiency. The repositioning mechanism which manipulates the aerodynamic force by means of conventional wind turbine control inputs is explained. Potential advantages of the turbine repositioning for wind farm control are demonstrated in simulations using the medium-fidelity wind farm simulator FAST.Farm developed by the National Renewable Energy Laboratory (NREL) and an example floating offshore wind farm which consists of three NREL 5MW semi-submersible baseline wind turbines. Finally, potential future research directions in this wind farm control technique are provided.

Keywords: Stochastic optimal control, Autonomous systems, Machine learning
Abstract: We present an empirical, gradient-based method for solving data-driven stochastic optimal control problems using the theory of kernel embeddings of distributions. By embedding the integral operator of a stochastic kernel in a reproducing kernel Hilbert space (RKHS), we can compute an empirical approximation of stochastic optimal control problems, which can then be solved efficiently using the properties of the RKHS. Existing approaches typically rely upon finite control spaces or optimize over policies with finite support to enable optimization. In contrast, our approach uses kernel-based gradients computed using observed data to approximate the cost surface of the optimal control problem, which can then be optimized using gradient descent. We apply our technique to the area of data-driven stochastic optimal control, and demonstrate our proposed approach on a linear regulation problem for comparison and on a nonlinear target tracking problem.

Keywords: Stochastic optimal control, Control system architecture, Networked control systems
Abstract: This paper presents a novel approach for achieving safe stochastic optimal control in networked multi-agent systems (MASs). The proposed method incorporates barrier states (BaSs) into the system dynamics to embed safety constraints. To accomplish this, the networked MAS is factorized into multiple subsystems, and each one is augmented with BaSs for the central agent. The optimal control law is obtained by solving the joint Hamilton-Jacobi-Bellman (HJB) equation on the augmented subsystem, which guarantees safety via the boundedness of the BaSs. The BaS-based optimal control technique yields safe control actions while maintaining optimality. The safe optimal control solution is approximated using path integrals. To validate the effectiveness of the proposed approach, numerical simulations are conducted on a cooperative UAV team in two different scenarios.

Keywords: Stochastic optimal control, Estimation, Machine learning
Abstract: Partially observable Markov decision process (POMDP) is a general framework for decision making and control under uncertainty. A large class of POMDP algorithms follows a two-step approach, in which the first step is to estimate the belief state, and the second step is to solve for the optimal policy taking the belief state as input. The optimality guarantee of their combination relies on the so-called separation principle. In this paper, we propose a new path to prove the separation principle for infinite horizon general POMDP problems under both discounted cost and average cost. We use a nominal horizon to split a virtual objective function into two parts and prove that it converges to the optimal state-value function. Based on the separation principle, we design a two-step POMDP algorithm called Belief State Actor-Critic (BSAC), which first estimates the belief state and then takes it as input to solve for the optimal policy. The belief state is learned using variational inference, and the policy is learned through model-based reinforcement learning. We test our algorithm in a partially observable multi-lane autonomous driving task. Results show that our algorithm achieves lower costs than the baselines and learns safe, efficient, and smooth driving behaviors.

Keywords: Stochastic optimal control, Neural networks, Autonomous vehicles
Abstract: Autonomous systems are required to operate in different environments, but recognizing the current environment is often challenging. For example, an autonomous vehicle should stop or obey a speed limit according to a traffic sign, but state-of-the-art perception modules (e.g., neural networks) do not guarantee the correctness of their reading of the traffic sign. Considering such uncertain outputs of a perception module, which in effect determines modes, we propose a chance-constrained control formulation that with high probability guarantees the satisfaction of a set of constraints associated with the possible modes. To do this, we present a method based on the Bayes rule and sampling to calculate the probability of each mode. We prove that our approach can ensure satisfying constraints of novel situations, which have not been used during training of the perception module. Also, to account for the error due to limited data, we present a robust formulation that guarantees constraint satisfaction with high confidence. In an autonomous vehicle example, we train a neural network that classifies traffic signs and show that given each output of the neural network, our motion planning approach guarantees the constraint satisfaction with high probability.

Keywords: Stochastic optimal control, Optimal control, Estimation
Abstract: Probabilistic inference approaches to stochastic optimal control have attracted significant interest from researchers in the past decade. Existing inference-based optimal control approaches are limited to linear controllers in a finite-horizon model-based setting. Since nonlinear systems typically admit nonlinear optimal controllers, linear controllers may yield sub-optimal trajectories when applied to nonlinear systems. In this paper, we propose a new Expectation-Maximization (EM) based inference algorithm for stochastic optimal control. The algorithm employs nonlinear basis functions to infer nonlinear controllers. We formulate the estimation problem of optimal control as a parameter inference problem. We demonstrate the effectiveness of the algorithm on a simulated nonlinear oscillator system for nonlinear control and a linear thermal system for structured control.

Keywords: Stochastic optimal control, Optimization, Predictive control for nonlinear systems
Abstract: In this paper we propose an formulation for approximate constrained nonlinear output-feedback stochastic model predictive control. Starting from the ideal but intractable stochastic optimal control problem (OCP), which involves the optimization over output-dependent policies, we use linearization with respect to the uncertainty to derive a tractable approximation which includes knowledge of the output model. This allows us to compute the expected value for the outer functions of the OCP exactly. Crucially, the dual control effect is preserved by this approximation. In consequence, the resulting controller is aware of how the choice of inputs affects the information available in the future which in turn influences subsequent controls. Thus, it can be classified as a form of implicit dual control.

Keywords: Stochastic optimal control, Optimization, Uncertain systems
Abstract: In this paper, we study the covariance steering (CS) problem for discrete-time linear systems subject to multiplicative and additive noise. Specifically, we consider two variants of the CS problem. The goal of the first problem, which is called the exact CS problem, is to steer the mean and covariance of the state process to their desired values in finite time. In the second problem, which is called the ``relaxed'' CS problem, the covariance assignment constraint is relaxed into a positive semi-definite constraint. We show that after applying suitable variable transformations and constraint relaxations, the relaxed CS problem can be cast as an equivalent convex semi-definite program (SDP). Furthermore, we propose a two-step solution procedure for the exact CS problem based on the relaxed problem formulation which returns a feasible solution, if there exists one. Finally, results from numerical experiments are provided to show the efficacy of the proposed solution methods.

Keywords: Stochastic optimal control, Randomized algorithms, Networked control systems
Abstract: Distributed resource allocation arises in many application domains, such as smart energy systems, intelligent transportation systems, cloud computing, edge computing, etcetera. To realize many of these applications, agents in a network may require multiple shared resources to complete a task and aim to maximize the network utility. Additionally, they may demand resources based on their preferences. Furthermore, they may not wish to share their cost functions, partial derivatives of the cost functions, etc., with other agents or a central server; however, they share their resource demands with the central server that aggregates the demands and sends one-bit resource-capacity constraint notification in the network. The single resource allocation algorithms are inefficient and provide sub-optimal solutions for multi-resource allocations, especially when the cost functions are multi-variate and non-separable. We present additive increase and multiplicative decrease algorithm (AIMD)-based distributed solutions for multi-resource allocation. We formulate the resource allocations problem over finite window sizes and model the system as a homogeneous Markov chain with place-dependent probabilities. We show that the time-averaged allocations over the finite window size converge to a unique invariant measure. We also show that the ergodic property holds for the model.

Keywords: Stochastic optimal control, Stochastic systems, Predictive control for linear systems
Abstract: We propose an open loop control scheme for linear systems with time-varying random elements in the state matrix. This paper focuses on joint chance constraints for potentially time-varying target sets. Under assumption of finite and known expectation and variance, we use the one-sided Vysochanskij–Petunin inequality to reformulate joint chance constraints into a tractable form. We demonstrate our methodology on a two-bus power system with stochastic load and wind power generation. We compare our method with situation approach. We show that the proposed method had superior solve times and favorable optimally considerations.

Keywords: Stochastic optimal control, Stochastic systems, Uncertain systems
Abstract: This article extends the optimal covariance steering (CS) problem for discrete time linear stochastic systems modeled using moment-based ambiguity sets. To hedge against uncertainty in the state distributions while performing covariance steering, distributionally robust risk constraints are employed during the optimal allocation of the risk. Specifically, a distributionally robust iterative risk allocation (DR-IRA) formalism is used to solve the optimal risk allocation problem for the CS problem using a two-stage approach. The upper-stage of DR-IRA is a convex problem that optimizes the risk, while the lower-stage optimizes the controller with the new distributionally robust risk constraints. The proposed framework results in solutions that are robust against arbitrary distributions in the considered ambiguity set. Finally, we demonstrate our proposed approach using numerical simulations. Addressing the covariance steering problem through the lens of distributional robustness marks the novel contribution of this article.

Keywords: Predictive control for nonlinear systems, Identification for control, Control applications
Abstract: Functional Electrical Stimulation (FES) is an effective method to restore the normal range of ankle motion in people with Drop Foot. This paper aims to develop a real-time, data-driven MPC scheme of FES for drop foot correction (DFC). We utilize a Koopman operator-based framework for system identification required for setting up the MPC scheme. We use inertial measurement units (IMUs) for collecting the foot pitch and roll rate state information to build an approximate linear predictor. In doing so, we also account for the implicit muscle actuation dynamics which are dependent on the activation and fatigue levels of the Tibialis Anterior muscle. Hence, contribution and develop a relationship between FES input parameters and ankle motion, tailored to an individual user. Using the Koopman operator we can fully capture the nonlinear dynamics through an infinite dimensional linear operator describing the evolution of functions of state space. The approximation, although computationally expensive, leads to reformulating the optimization problem as a quadratic program for the MPC problem. Further, we show the closed-loop system's recursive feasibility and asymptotic stability analysis. Simulation and experimental results from a subject with Multiple Sclerosis show the effectiveness of the data-driven MPC scheme of FES for DFC.

Keywords: Predictive control for nonlinear systems, Lyapunov methods, Stability of nonlinear systems
Abstract: In recent years, economic nonlinear model predictive control (eNMPC) has emerged as a viable alternative for distributed control systems. Because eNMPC involves the solution of a dynamic programming problem, it provides the control actions that lead the system to the most economical transient operations, which may be periodic instead of converging to a steady statecite{angeli2012}. Since eNMPC has been typically used for stand-alone unit operations instead of plantwide control, an unsteady operation of a unit may lead to undesirable operations of downstream units. This work proposes a self-stabilizing eNMPC formulation, in which a pre-calculated steady-state condition is not required. Lyapunov functions with embedded steady-state optimal conditions are employed as additional constraints of the eNMPC formulation, so that the asymptotically stable behavior can be achieved. The performance of the proposed eNMPC is demonstrated with two case studies of a membrane reactor for natural gas utilization. In the first case study, the proposed eNMPC can effectively bring the system toward the feasible steady-state optimal operation. In the second case study, a cost-optimal steady-state does not exist due to the time-varying disturbance, and the closed-loop behavior is shown to be bounded if the disturbance is also bounded.

Keywords: Predictive control for nonlinear systems, Machine learning, Robotics
Abstract: This paper develops computationally efficient data-driven model predictive control (MPC) for Agile quadrotor flight. Agile quadrotors in high-speed flights can experience high levels of aerodynamic effects. Modeling these turbulent aerodynamic effects is a cumbersome task and the resulting model may be overly complex and computationally infeasible. Combining Gaussian Process (GP) regression models with a simple dynamic model of the system has demonstrated signif- icant improvements in control performance. However, direct integration of the GP models to the MPC pipeline poses a significant computational burden to the optimization process. Therefore, we present an approach to separate the GP models to the MPC pipeline by computing the model corrections using reference trajectory and the current state measurements prior to the online MPC optimization. This method has been validated in the Gazebo simulation environment and has demonstrated of up to 50% reduction in trajectory tracking error, matching the performance of the direct GP integration method with improved computational efficiency

Keywords: Predictive control for nonlinear systems, Modeling, Numerical algorithms
Abstract: A two-stage nonlinear model predictive controller for the task of power tracking with a fuel cell system is presented. In the first stage, an economic optimization problem is solved for optimal steady states and inputs, which are tracked in the subsequent stage. For the dynamic tracking using MPC, a nonlinear, stiff ordinary differential equation must be discretized. A numerical study of different integration schemes reveals that the first order implicit Runge-Kutta integration scheme is appropriate for discretization. Compared to a high accuracy numerical integration and the standard explicit Runge-Kutta method of order four, the computation time on embedded hardware can be reduced by more than 30% and 10% respectively without loss in closed-loop cost.

Keywords: Predictive control for nonlinear systems, Nonlinear output feedback, Constrained control
Abstract: It is well known that, for some systems, stabilization can be achieved by open-loop control in the form of high-frequency vibrations. Vibrational control is attractive since it requires no sensors. On the other hand, however, vibrational control requires careful selection of the frequency and amplitude of the input. The present paper is aimed at understanding the robustness of vibrational control and the required control effort by applying nonlinear model predictive control to the classical Kapitza pendulum. A numerical investigation shows that closed-loop control using nonlinear model predictive control is significantly more efficient than open-loop vibrational control with respect to signal power.

Keywords: Predictive control for nonlinear systems, Optimal control, Autonomous systems
Abstract: This paper presents a new control approach for guaranteed safety (remaining in a safe set) subject to actuator constraints (the control is in a convex polytope). The control signals are computed using real-time optimization, including linear and quadratic programs subject to affine constraints, which are shown to be feasible. The control method relies on a new soft-minimum barrier function that is constructed using a finite-time-horizon prediction of the system trajectories under a known backup control. The main result shows that: (i) the control is continuous and satisfies the actuator constraints, and (ii) a subset of the safe set is forward invariant under the control. We also demonstrate this control on numerical simulations of an inverted pendulum and a double-integrator ground robot.

Keywords: Predictive control for nonlinear systems, Optimal control, Optimization algorithms
Abstract: The predictive energy management (PEM) problem for hybrid electric powertrains is challenging to solve in real time, mainly due to the nonconvexity from the battery state of energy (SOE) model, which is nonlinear. This study proposes a control-oriented battery model consisting of a stochastic linear SOE model and a quadratic power loss model to realize real-time PEM. The stochastic linear model describes the SOE trajectory from an average point of view. The quadratic power loss model describes the nonlinear power loss that the stochastic linear SOE model cannot consider. By replacing the nonlinear SOE model with the control-oriented model, the PEM problem is reformulated into quadratic programming (QP), which can be easily solved in real time by a QP solver. Simulation results obtained using a fuel cell-powered unmanned aerial vehicle (UAV) show that the proposed model predicts the trend of the SOE trajectory well, even for long prediction horizons (maximum of 750 s). In addition, PEM based on the proposed model results in near-optimal performance (0.36 % difference from the global solution) with real-time capability (solved within 0.27 s).

Keywords: Predictive control for nonlinear systems, Optimization, Uncertain systems
Abstract: This paper proposes a reactive approach based on the moving horizon estimation method for optimization in the presence of parametric uncertainty. The moving horizon estimation scheme uses measurable outputs in order to estimate the states and uncertain parameters jointly where the full states are not measurable. It has been shown that the deterministic certainty-equivalent model predictive control based on estimated states and parameters is less conservative and significantly faster. However, the method's performance deteriorates in transition periods, particularly when the system's parameters change rapidly. Nevertheless, when the estimations converge to the actual values, the adaptive MPC will be adjusted quickly to respect the constraints. These promising features make the adaptive method suitable for circumstances where high performance is more desirable than robustness fulfillment of constraint. The other aspects of the method and its applicability are also discussed thoroughly.

Keywords: Predictive control for nonlinear systems, Simulation, Kalman filtering
Abstract: The Unscented Transform which is the basis of the Unscented Kalman Filter, UKF, is used here to develop a novel predictive controller for non-linear plants, called the Unscented Transform Controller, UTC. The UTC can be seen as the dual of the UKF, the same way as the LQG regulator and the Kalman Filter are related. The UTC is demonstrated on the control of complex maneuvers in free fall of a virtual skydiver the model of which was verified in wind tunnel and free fall experiments.

Keywords: Predictive control for nonlinear systems, Stochastic optimal control, Uncertain systems
Abstract: Due to their ability to model complex functions and their suitability for control design, Gaussian Processes (GPs) have recently found widespread use to learn residual dynamics that account for the mismatch between the nominal system model and the true underlying system dynamics. However in cases where the residual dynamics differ drastically over regions of the state/input space, a single GP-based residual model could be inaccurate. When used to design controllers, this could result in controllers with poor performance that could violate state/input constraints. We propose the use of GP-based hybrid residual dynamics model, which switches between different residual models across regions of the state and input space of a dynamics model. We also design a Model Predictive Controller (MPC) that can leverage this hybrid residual dynamics model to ensure probabilistic constraint satisfaction. Through numerical studies, we demonstrate how the proposed controller outperforms a baseline single GP-based MPC baseline. Simulations show a 45% improvement in control performance in the best-case and probability of constraint violations within the desired threshold in contrast to the baseline approach.

Keywords: Autonomous systems, Autonomous robots, Robotics
Abstract: We propose a continuous feedback control strategy that steers a point-mass vehicle safely to a desired destination, in a quasi-optimal manner, from almost all initial conditions in an n-dimensional Euclidean space cluttered with spherical obstacles. The main idea consists in avoiding each obstacle via the shortest path within the cone enclosing the obstacle, and moving straight towards the target when the vehicle has a clear line of sight to the target location. The proposed control strategy ensures safe navigation with almost global asymptotic stability of the equilibrium point at the target location. Simulation results, illustrating the effectiveness of the proposed approach, are presented.

Keywords: Autonomous systems, Cooperative control, Decentralized control
Abstract: Flip, flex, and reflection ambiguities, which can arise in bearing-only formation control with elevation angle rigid configurations, are addressed in this paper. Elevation angle rigidity achieves formation control in agents' local co-ordinate system using bearing-only sensors, without any orientation synchronization or estimation algorithm. Considering elevation angle constraints to determine the formation shape, and then using a gradient based control law offers the benefit of a co-ordinate free control. However, flip, flex, and reflection ambiguities might be present in the final formation shape. To tackle this, we first develop sign-elevation angle rigidity theory to uniquely (locally) characterize formation shapes up-to a translation and rotation using elevation angle and signed area/volume constraints. Thereafter, a formation control law is proposed (for 2-D and 3-D) using bearing-only information for single integrator systems, and local exponential stability is proved for formation tracking error. Finally, simulations validate the presented results.

Keywords: Autonomous systems, Distributed control, Learning
Abstract: In this paper, we investigate the problem of time-varying sensor selection for linear time-invariant (LTI) dynamical systems. We develop a framework to design a sparse sensor schedule for a given large-scale LTI system with guaranteed performance bounds using a learning-based algorithm. We show how the observability Gramian matrix of an LTI system can be interpreted as the sum of rank-1 matrices indicating the contribution of the available sensors distributed in time. We then employ a regret minimization framework over density matrices to sparsify this sum of rank-1 matrices to approximate fully sensed LTI dynamics up to a multiplicative factor in some certain observability senses. Our main result provides a linear-sized (in dimension of system) sensor schedule that on the average activates only a constant number of sensors at each time step and significantly improves the previous linearithmic results. Our results naturally apply to the dual problem of actuator selection where a guaranteed approximation to the controllability Gramian will be provided.

Keywords: Autonomous systems, Formal verification/synthesis, Cooperative control
Abstract: We develop a cooperative sampling-based motion planning algorithm for two autonomous agents under coupled tasks expressed as signal temporal logic constraints. The algorithm builds incrementally two spatio-temporal trees, one for each agent, by sampling points in an extended space, which consists of a compact subset of the time domain and the physical space of the agents. The trees are built by checking if newly sampled points form edges in time and space that satisfy certain parts of the coupled task. Therefore, the constructed trees represent time-varying trajectories in the agents’ state space that satisfy the task. The algorithm is distributed in the sense that the agents build their trees individually by communicating with each other. The proposed algorithm inherits the properties of probabilistic completeness and computational efficiency of the original sampling-based procedures.

Keywords: Autonomous systems, Nonholonomic systems, Robotics
Abstract: The paper focuses on the generation of planar trajectories using an autonomous agent modelled as a unicycle. The agent can be controlled using its linear and angular speeds. It is assumed that only range information is available to the agent with respect to a stationary point, known as the target. The latter could be representative of any beacon, a building of interest or a landmark in real world scenarios. Both of the speeds are designed as continuous functions of range with the linear speed constrained to be positive. We present a complete characterisation of agent trajectories in the given framework which shows that the trajectories can remain bounded or become unbounded depending on both the control inputs and the initial conditions. We also present the conditions necessary to generate each kind of the above mentioned trajectories. Finally, numerical simulation have been presented to elucidate the results.

Keywords: Autonomous systems, Robust control, Intelligent systems
Abstract: Many modern autonomous systems, particularly multi-agent systems, are time-critical and need to be robust against timing uncertainties. Previous works have studied left and right time robustness of signal temporal logic specifications by considering time shifts in the predicates that are either only to the left or only to the right. We propose a combined notion of temporal robustness which simultaneously considers left and right time shifts. For instance, in a scenario where a robot plans a trajectory around a pedestrian, this combined notion can now capture uncertainty of the pedestrian arriving earlier or later than anticipated. We first derive desirable properties of this new notion with respect to left and right time shifts and then design control laws for linear systems that maximize temporal robustness using mixed-integer linear programming. Finally, we present two case studies to illustrate how the proposed temporal robustness accounts for timing uncertainties.

Keywords: Optimal control, Game theory, Neural networks
Abstract: This paper presents a novel hybrid learning-based optimal tracking method to address zero-sum game problems for partially uncertain nonlinear discrete-time systems. An augmented system and its associated discounted cost function are defined to address optimal tracking. Three multi-layer neural networks (NNs) are utilized to approximate the optimal control and the worst-case disturbance inputs, and the value function. The critic weights are tuned using the hybrid technique, whose weights are updated once at the sampling instants and in an iterative manner over finite times within the sampling instants. The proposed hybrid technique helps accelerate the convergence of the approximated value functional to its actual value, which makes the optimal policy attain quicker. A two-layer NN-based actor generates the optimal control input, and its weights are adjusted based on control input errors. Moreover, the concurrent learning method is utilized to ease the requirement of persistent excitation. Further, the Lyapunov method investigates the stability of the closed-loop system. Finally, the proposed method is evaluated on a two-link robot arm and demonstrates promising results.

Keywords: Optimal control, Optimization algorithms, Computational methods
Abstract: Strongly contracting dynamical systems have numerous properties (e.g., incremental ISS), find widespread applications (e.g., in controls and learning), and their study is receiving increasing attention. This work starts with the simple observation that, given a strongly contracting system on a normed space, its adjoint dynamical system is also strongly contracting, with the same rate, with respect to the dual norm, under time reversal. As main implication of this dual contractivity, we show that the classic Method of Successive Approximations (MSA), an indirect method in optimal control, is a contraction mapping for short optimization intervals or large contraction rates. Consequently, we establish new convergence conditions for the MSA algorithm, which further imply uniqueness of the optimal control and sufficiency of Pontryagin's minimum principle under additional assumptions.

Keywords: Optimal control, Predictive control for nonlinear systems, Automotive control
Abstract: This paper proposes an algorithm for solving perturbed dynamic programs, where first-order corrections are applied to a pre-computed optimal strategy and its corresponding value function using local quadratic approximation. The technique is developed to handle perturbations of external inputs and parameters affecting system dynamics, objective and constraint functions, allowing the application to a wide variety of perturbed problems. The method is applied to the energy optimization of an electric vehicle thermal management system, formulated as a constrained dynamic program where external conditions and target set-point are perturbed from their nominal values. Simulations result show 80% reduction in computation time from a Dynamic Programming (DP) solution, with only minimal effect on the overall controller performance

Keywords: Optimal control, Game theory
Abstract: A finite horizon nonlinear optimal control problem is considered for which the associated Hamiltonian satisfies a uniform semiconcavity property with respect to its state and costate variables. It is shown that the value function for this optimal control problem is equivalent to the value of a min-max game, provided the time horizon considered is sufficiently short. This further reduces to maximization of a linear functional over a convex set. It is further proposed that the min-max game can be relaxed to a type of stat (stationary) game, in which no time horizon constraint is involved.

Keywords: Optimal control, Control applications, Robotics
Abstract: Potentially, cooperative control of functional electrical stimulation (FES) and electric motors in a hybrid exoskeleton can perform stair ascent while adapting to a user’s locomotion. Towards this goal, it would be essential to determine the time-varying impedance model parameters of each user while ensuring the stability of the closed loop system. While some previous studies address the stability problem when estimating time-varying impedance model parameters, constraints on the parameters to their physiological values are not guaranteed. In this paper, we develop a model predictive control (MPC) based approach to prescribe physiologically constrained time-varying stiffness and damping parameters for an impedance model. A terminal cost and controller for the stiffness and damping are designed to ensure the MPC problem is recursively feasible, satisfy physiological constraints, and is asymptotically stable. Another MPC-based cooperative control approach is then used to ensure that the knee joint follows the knee trajectory generated via the impedance model with optimized parameters. Simulations results show foot, knee joint, and impedance model tracking while allocating inputs between FES and motors during stair ascent and adequate foot clearance and placement.

Keywords: Optimal control, Time-varying systems, Control applications
Abstract: Controllability metrics are used to determine or incentivise the ease with which a system can be driven to a specified target. Such metrics stemming from the controllability gramian are currently used to analyse the local controllability of nonlinear systems about precomputed trajectories. This paper introduces an alternative application of these metrics to generate an optimal trajectory that directly incentivises the local controllability of a nonlinear system. Such optimal trajectory design techniques would be useful for reducing the additional control energy requirement necessary to achieve control objective satisfaction in the presence of unmodelled disturbances. We present an approach in which the LTV controllability gramian is used to construct an augmented optimal control problem that incentivises the local controllability of a nonlinear system about the optimal trajectory. A modified form of Zermelo's boat problem is used to demonstrate the approach, showing that trajectories generated by solution of the augmented optimal control problem require the system to expend less additional control energy to recover the optimal terminal state following perturbation due to an unmodelled disturbance.

Keywords: Iterative learning control, Neural networks, Uncertain systems
Abstract: Growing demands in today's industry results in increasingly stringent performance and throughput specifications. For accurate positioning of high-precision motion systems, feedforward control plays a crucial role. Nonetheless, conventional model-based feedforward approaches are no longer sufficient to satisfy the challenging performance requirements. An attractive method for systems with repetitive motion tasks is iterative learning control (ILC) due to its superior performance. However, for systems with non-repetitive motion tasks, ILC is {generally} not applicable, {despite of some recent promising advances}. In this paper, we aim to explore the use of deep learning to address the task flexibility constraint of ILC. For this purpose, a novel Task Analogy based Imitation Learning (TAIL)-ILC approach is developed. To benchmark the performance of the proposed approach, a simulation study is presented which compares the TAIL-ILC to classical model-based feedforward strategies and existing learning-based approaches, such as neural network based feedforward learning.

Keywords: Robust control, Flight control, Machine learning
Abstract: Morphing aircraft is the key component of intelligent control of aircraft. In this paper, a complete framework and process are established to model, analyze and control a morphing aircraft, so that the aircraft can achieve the tracking ability for a certain trajectory. In the control framework, the decoder method is used to reduce the size of the value function network of reinforcement learning, which leads to that the learning becomes easier to converge and the calculation speed is faster. First, the aircraft is designed by using CATIA software and 3D modeled. Then, the different variants of the morphing aircraft were imported into ansys--fluent for force analysis. Finally, a real physical model is built according to the obtained dynamics data, and a complete reinforcement leaning-based control algorithm is proposed to realize the trajectory tracking of the morphing aircraft.

Keywords: PID control, Chemical process control, Machine learning
Abstract: Proportional-integral-derivative (PID) controllers have been widely used in the process industry. However, the satisfactory control performance of a PID controller depends strongly on the tuning parameters. Conventional PID tuning methods require extensive knowledge of the system model, which is not always known especially in the case of complex dynamical systems. In contrast, reinforcement learning-based PID tuning has gained popularity since it can treat PID tuning as a black-box problem and deliver the optimal PID parameters without requiring explicit process models. In this paper, we present a novel entropy-maximizing twin-delayed deep deterministic policy gradient (EMTD3) method for automating the PID tuning. In the proposed method, an entropy-maximizing stochastic actor is employed at the beginning to encourage the exploration of the action space. Then a deterministic actor is deployed to focus on local exploitation and discover the optimal solution. The incorporation of the entropy-maximizing term can significantly improve the sample efficiency and assist in fast convergence to the global solution. Our proposed method is applied to the PID tuning of a second-order system to verify its effectiveness in improving the sample efficiency and discovering the optimal PID parameters compared to traditional TD3.

Keywords: Robust adaptive control, Machine learning, Optimization
Abstract: Plasma medicine has emerged as a promising approach for treatment of biofilm-related and virus infections, assistance in cancer treatment, and treatment of wounds and skin diseases. Despite advances in learning-based and predictive control of plasma medical devices, there remains major challenges towards personalized and point-of-care plasma medicine. In particular, an important challenge arises from the need to adapt control policies after each treatment using (often limited) observations of therapeutic effects that can only be measured in-between treatments. Control policy adaptation is necessary to account for variable characteristics of plasma and target surfaces across different subjects and treatment scenarios, thus personalizing the plasma treatment to enhance its efficacy. To this end, this paper presents a data-efficient, ``globally'' optimal strategy to adapt deep learning-based controllers that can be readily embedded on resource-limited hardware for portable medical devices. The proposed strategy utilizes multi-objective Bayesian optimization (MOBO), a derivative-free, ``global'' optimization method, to use observations of closed-loop performance measures in order to adapt parameters of a deep neural network (DNN)-based control laws. The proposed strategy for adaptive DNN-based control is demonstrated experimentally on a cold atmospheric plasma jet with prototypical applications in plasma medicine.

Keywords: Process Control, Stochastic systems
Abstract: Colloidal self-assembly systems are generally difficult to control due to their highly nonlinear and stochastic dynamics and sparse rewards. These systems are also inherently deceptive, as successful control policies must be able to smooth out unavoidable defects and therefore temporarily move farther away from their goal in order to eventually realize the desired goal. This paper investigates the viability of evolutionary reinforcement learning (RL) based on novelty search, wherein behavioral novelty alone is used to learn control policies that can systematically mitigate deceptive dynamics. As such, for stochastic nonlinear systems that are prone to a deceptive behavior, novelty search is a promising alternative to the widely used objective search RL, where merely progress towards a pre-defined goal is used to learn and update control policies. In this work, we pair novelty search RL with a complexifying algorithm that simultaneously learns the neural network architecture and parameters of a control policy. This complexifying algorithm principles the novelty search by ensuring that simple behaviors must be discovered before more complex ones. We evaluate the performance of evolutionary RL based on objective search and novelty search on a benchmark in-silico colloidal self-assembly problem.

Keywords: Stability of linear systems, Learning, Linear systems
Abstract: In this paper, we study the impact of clock offsets among different components of cyber-physical systems on data-driven off-policy reinforcement learning (RL) for linear quadratic regulation (LQR). Our results show that under certain conditions the control policies generated by data-driven off-policy RL with clock offsets are stabilizing policies. With clock offsets what directly influences the learning behavior is not only the values of clock offsets but also the dynamics change caused by clock offsets. In particular, larger values of clock offsets do not necessarily lead to non-stabilizing policies. The proposed conclusions are illustrated by numerical simulations.

Keywords: Sampled-data control, Linear systems, Quantized systems
Abstract: We show that the homomorphic property, a desired property in encrypted control, can lead to failure in the cyber defense of a dynamical control system from undetectable attacks, even though individual signal sequences remain unknown to the attacker. We consider an encryption method based on the Learning with Errors (LWE) problem and demonstrate how model-free undetectable attacks on linear systems over integers can be computed from sampled inputs and outputs that are encrypted. Previous work has shown that computing such attacks is possible on nonencrypted systems. Applying this earlier work to our scenario, with minor modifications, typically amplifies the error in encrypted messages unless a short vector problem is solved. Given that an attacker obtains a short vector, we derive the probability that the attack is detected and show how it explicitly depends on the encryption parameters. Finally, we simulate an attack obtained by our method on an encrypted linear system over integers and conduct an analysis of the probability that the attack will be detected.

Keywords: Sampled-data control, Nonholonomic systems, Autonomous vehicles
Abstract: In this paper, on the basis of a recently proposed discrete-time port-Hamiltonian representation of sampled-data dynamics, we propose a new time-varying digital feedback for steering mobile robots. The quality of the proposed passivity-based control is validated and compared through simulations with the existing literature and the continuous-time implementation using the unicycle as a case study.

Keywords: Information theory and control, Sampled-data control, Machine learning
Abstract: We define the complexity of a continuous-time linear system to be the minimum number of bits required to describe its forward increments to a desired level of fidelity, and compute this quantity using the rate distortion function of a Gaussian source of uncertainty in those increments. The complexity of a linear system has relevance in control-communications contexts requiring local and dynamic decision-making based on sampled data representations. We relate this notion of complexity to the design of attention-varying controllers, and demonstrate a novel methodology for constructing source codes via the endpoint maps of so-called emulating systems, with potential for non-parametric, data-based simulation and analysis of unknown dynamical systems.

Keywords: Behavioural systems, Linear systems, Sampled-data control
Abstract: This work develops a data-based construction of inverse dynamics for LTI systems. Specifically, the problem addressed here is to find an input sequence from the corresponding output sequence based on pre-collected input and output data. The problem can be considered as a reverse of the recent use of the behavioral approach, in which the output sequence is obtained for a given input sequence by solving an equation formed by pre-collected data. The condition under which the problem gives a solution is investigated and turns out to be L-delay invertibility of the plant and a certain degree of persistent excitation of the data input. The result is applied to form a data-driven disturbance observer. The plant dynamics augmented by the data-driven disturbance observer exhibits disturbance rejection without the model knowledge of the plant.

Keywords: Power electronics, Stability of nonlinear systems, Sampled-data control
Abstract: Stability guarantees are critical for cycle-by-cycle controlled dc-dc converters in consumer electronics and energy storage systems. Traditional stability analysis on cycle-by-cycle dc-dc converters is incomplete because the inductor current ramps are considered fixed; but instead, inductor ramps are not fixed because they are dependent on the output voltage in large-signal transients. We demonstrate a new large-signal stability theory which treats cycle-by-cycle controlled dc-dc converters as a particular type of feedback interconnection system. An analytical and practical stability criterion is provided based on this system. The criterion indicates that the L/R and RC time constants are the design parameters which determine the amount of coupling between the current ramp and the output voltage.

Keywords: Feedback linearization, Observers for nonlinear systems, Sampled-data control
Abstract: In this article, we present data-driven feedback linearization for nonlinear systems with periodic orbits in the zero-dynamics. This scenario is challenging for data-driven control design because, the higher-order terms of the internal dynamics in the discretization appear as disturbance inputs to the controllable subsystem of the normal form. Our design consists of two parts: a data-driven feedback linearization-based controller and a two-part estimator that can reconstruct the unknown nonlinear terms in the normal form of a nonlinear system. We investigate the effects of coupling between the subsystems in the normal form of the closed-loop nonlinear system and conclude that the presence of such a coupling prevents asymptotic convergence of the controllable states. We also show that the estimation error in the controllable states scales linearly with the sampling time. Finally, we present a simulation-based validation of the proposed data-driven feedback linearization.

Keywords: Flight control, Aerospace, Spacecraft control
Abstract: We research control schemes for unmanned aerial vehicles (UAVs) with propulsion, steering and power modules. Physical limits, aerodynamic instabilities, blade flapping, cross-axis coupling, data heterogeneity and other factors affect design. In multirotor UAVs, the differential thrust is regulated by changing the angular velocity of propellers, rotated by brushless electric motors. Voltages applied, phase currents, propeller speed and thrust cannot exceed specific limits. To accomplish aerial photography, airborne intelligence, surveillance, reconnaissance and support missions, multirotor and fixed-wing vehicles integrate active electronically scanned array radar, light detection and ranging modules, transceivers, controllers-drivers, steered pylon mounts, dc-dc regulators, battery pack, charger, etc. The differential thrust is regulated by changing propellers’ angular velocity. We design constrained tracking control laws to govern aerial systems regulating state and error dynamics. Minimizing design-consistent functionals with range-restricted descriptive bounded functions, limits are accounted for by integrands, and control laws are analytically designed. Nonquadratic functionals with domain-specific positive-definite integrands and Hamiltonians admit closed-form solutions. The Hamilton-Jacobi equation is satisfied by continuous positive-definite return functions. Descriptive state-space models and error governance support a design to ensure optimal tracking error evolution. Bounded algorithms with state and tracking error feedback guarantee system optimality subject to minimized functionals. Control schemes, optimization tools, and algorithms are experimentally substantiated for a quadrotor helicopter. Controllers are designed and characterized for flight control systems, direct-drive steering mount pylons, brushless motors, and dc-dc switching regulators.

Keywords: Flight control, Control system architecture, Nonlinear output feedback
Abstract: This paper introduces a unified approach to attitude control of tilt-rotor aircraft. The method utilizes moments-based actuation, based on real-time local linearization and LTI feedback systems. The main advantage of our approach is that it relies on fixed gain control laws throughout the entire flight envelope, including the transition from hover to cruise. This is achieved through sophisticated control allocation and model-matching algorithms. The method is designed with simple reconfiguration in case of an actuator failure, minimal computing power and future certification in mind. As a result, the developed algorithms were included in the development of the fly-by-wire system by a collaboration company.

Keywords: Flight control, Linear parameter-varying systems, Aerospace
Abstract: This paper presents a novel approach for trajectory planning and tracking control of Vertical-TakeOff-and-Landing (VTOL) aircraft with tilt-rotors during the transition phase. The proposed method employs the multiple shooting method (MSM) on a nonlinear dynamic model to determine the optimal trajectory, with given initial and final states, constraints of states and inputs, as well as the objective of minimizing a weighted cost function. Unlike other trajectory planning techniques that yield quasi-equilibrium points, MSM generates dynamic state-control trajectories in time sequences. Subsequently, the nonlinear model is converted into a Linear Parameter-Varying (LPV) representation by treating velocity, pitch rate, and rotor tilt angle as scheduling parameters, which is then used in LPV Model Predictive Control (LPV-MPC) to track the planned trajectory. The LPV-MPC efficiently updates predictive models in future horizons based on predictions of scheduling parameters. The proposed systematic approach is verified through simulation on a tiltable quadrotor VTOL aircraft, where the MSM generates a smooth transition from vertical take-off to level flight, and the LPV-MPC accurately tracks the trajectory despite measurement noise.

Keywords: Flight control, Machine learning, Algebraic/geometric methods
Abstract: This paper presents an equivariant reinforcement learning framework for quadrotor unmanned aerial vehicles. Successful training of reinforcement learning often requires numerous interactions with the environments, which hinders its applicability especially when the available computational resources are limited, or when there is no reliable simulation model. We identified an equivariance property of the quadrotor dynamics such that the dimension of the state required in the training is reduced by one, thereby improving the sampling efficiency of reinforcement learning substantially. This is illustrated by numerical examples with popular reinforcement learning techniques of TD3 and SAC.

Keywords: Flight control, Modeling, Simulation
Abstract: For tethered multi-rotor autogyros to be viable energy efficient unmanned aerial vehicles (UAVs), control analysis and stability investigation of autorotative flight are vital. In this paper, a simplified model-based altitude control technique is presented which is effective in the presence of both uniform and variable wind profile. A two-rotor autogyro, tethered to the ground and constrained to move in the 2D plane of the wind direction, is adopted for the study. The reduction to 2D simplifies the system and helps focus on the feasibility of altitude control and pitch modulation by exclusively using differential braking, which is a novel concept. In this arrangement, control inputs are the braking torques in each of the two rotors. The assumption is that with another two rotors in the lateral direction the roll and yaw motion of the system can be controlled when extended to 3D. The aerodynamics and tether modeling are based on Blade Element Momentum (BEM) method and catenary mechanics respectively. The characteristics of the equilibria of the tethered multi-rotor autogyro are investigated. For the aforementioned set-up, the differential rotor braking input is designed based on a proportional feedback law, and is effective in controlling the autogyro's altitude with the help of restoring effect provided by the tether tension.

Keywords: Flight control, Predictive control for linear systems, Linear parameter-varying systems
Abstract: A quasi-linear model predictive controller (qLMPC) based on linear parameter-varying (LPV) systems is proposed for a flexible aircraft. The dynamics of flexible aircraft vary substantially with the flight condition such that LPV systems depending on time-varying scheduling parameters provide a natural modeling framework. A recently proposed velocity algorithm is used for controller design. A suitable LPV system is obtained by applying Jacobian linearization, model order reduction, and state augmentation. The efficiency is increased by approximating the control trajectory with Laguerre functions. An observer is designed to estimate non-measurable states. The controller achieves good tracking performance in nonlinear simulations for aggressive maneuvers during varying flight conditions with and without stability guarantees. The use of Laguerre functions is further demonstrated to significantly decrease the computing time.

Keywords: Biological systems, Systems biology, Biomolecular systems
Abstract: The overexpression of many proteins can often have a detrimental impact on cellular growth. This expression-growth coupling leads to positive feedback - any increase of intracellular protein concentration reduces the growth rate of cell size expansion that in turn enhances the concentration via reduced dilution. We investigate how such feedback amplifies intrinsic stochasticity in gene expression to drive a skewed distribution of the protein concentration. Our research provides the analytical expression of the distribution after solving the associated Chapman-Kolmogorov equation. With these results, we quantify the enhancement of noise/skewness as a function of expression-growth coupling. This analysis has important implications for the expression of stress factors, where high levels provide protection from stress, but come at the cost of reduced cellular proliferation. Finally, we connect these analytical results to the case of an actively degraded gene product, where the degradation machinery is working close to saturation.

Keywords: Biological systems, Modeling, Identification
Abstract: This paper discusses reliable yet minimal computational models for predicting the patient’s response to anticancer multi-drug combined therapy. The distribution of the drugs into the local heterogeneity of healthy-tumor tissues can be translated into mathematical models. Ideally, these should best describe the physiological processes and physical mechanisms, together with the interactions between the contributing components of the tumor growth dynamic system. Our previously proposed pharmacokinetic-pharmacodynamic (PKPD) mathematical model is revisited for different spatiotemporal fractional drug diffusion patterns. In particular, we examine the specific diffusion-related factors that limit drug effect through the tumor’s surface. The ability of the tumor growth PKPD model to predict patient responsiveness was evaluated using prior radiation therapy data in a patient with lung cancer. This study shows that the effect of anomalous diffusion mechanisms within tumor tissue should be considered while modeling the dose-response relationship for optimal results of cancer therapies.

Keywords: Biomedical, Modeling, Predictive control for linear systems
Abstract: Patients suffering from tremors have difficulty performing activities of daily living. The development of a model of a limb with tremors can pave the way for non-surgical tremor suppression control techniques. Nevertheless, nonlinearity and actuator saturation make it difficult to develop an accurate model and a tremor suppression control method. Towards addressing this issue, this paper describes a Koopman-based method for system identification and its application to the design of a model predictive control (MPC) scheme to suppress tremors. Since model prediction accuracy is critical to the performance of an MPC, it is essential to update the model online if the predictions are not sufficiently accurate. We propose a recursive least squares (RLS) algorithm to improve control performance with low computational complexity. Finally, for the first time, stability analysis and recursive feasibility of the Koopman-based MPC (KMPC) closed-loop updated system are presented. The proposed modeling and control approach have been validated by experimental data and simulation results.

Keywords: Biomedical, Robust control, Optimal control
Abstract: Wide variability of patient response to vasoactive drugs, and mechanical limits of infusion pumps lead to difficulties in achieving robust Closed-Loop Blood Pressure Control (CLBPC). Our goal is to refine a previously proposed CLBPC system which emphasizes the incorporation of mechanistic cardiovascular models, design simple Model Predictive Control (MPC) and Proportional-Integral-Derivative (PID) controllers, and assess their robustness to estimation errors in physiological parameters of patients that are expected to vary widely within a patient population. A pharmacokinetic-pharmacodynamic (PK-PD) model that quantifies the impact of drugs, phenylephrine and nicardipine, on a patient's blood pressure is provided. A state space model is then formulated which incorporates the full dynamics of a patient's blood pressure. We then implement MPC and PID control to simulate regulation of blood pressure and explore the robustness of such controllers to errors in estimates of patient physiological parameters.

We show that parameter estimation errors impact the performance of both CLBPC systems, and pinpoint which parameters are pivotal to estimate in clinical scenarios. We also show that the robustness is significantly improved if drug infusion rates can be updated more rapidly than what is recommended for state-of-the-art programmable infusion pumps. Our results provide support for the estimation of PK and PD parameters in CLBPC systems and emphasize the importance of improving programmable infusion pumps to allow for more rapid updates of infusion rates.

Keywords: Biologically-inspired methods, Filtering, Optimization
Abstract: We propose a novel approach for filtering that is inspired by Complex Cell Networks (CCN) in the primary visual cortex of mammals; our aim is to emulate the robustness of the latter, showing graceful degradation in face of gross deterioration of the input. Instead of relying on energy minimization as in frequency-based filter design, or on Bayes' theorem as in statistical filtering, our formulation is founded on three principles that have been recognized in biological systems: 1)Winner-take-all, where perceptual ambiguity is solved by focusing on the strongest signal; 2)Persistence, where information is fused across time to lessen the impact of noise, outliers, and temporary cancellations in the input data; and 3)Boundedness, where the responses in the filter are bounded to be non-negative and below a maximum value. In neuroscience, the typical goal is to find models that match and explain measurements from biological system. In this paper, we take an engineering approach, where we encode the three properties above as mathematical constraints, and find filter parameters that guarantee convergence of the filter (for constant, bounded inputs), optimizing bounds on the convergence rate, while improving sparsity of the filter kernel; overall, the filter is obtained from the solution to a Linear Program (LP).

Keywords: Biologically-inspired methods, Linear parameter-varying systems, Stability of linear systems
Abstract: This paper presents a feedback control design that stabilizes the position of a drifting vortex in a freestream over a deformable Joukowski foil using camber control. We derive the dynamics of a point vortex in flow around a Joukowski foil using a potential flow model and provide numerical analysis of the number, stability, and controllability of open-loop equilibrium points of the vortex-foil system. We show that the position of a point vortex can effectively be stabilized using a full-state feedback camber control law while maintaining the validity of the dynamics model. We present sample stable and unstable trajectories found using closed-loop control along with a visualization of the region of convergence.

Keywords: Modeling
Abstract: Neural networks have been widely applied in system dynamics modeling. One particular type of networks, hybrid neural networks, combine a neural network model with a physical model which can increase rate of convergence in training. However, most existing hybrid neural network methods require an explicit physical model constructed, which sometimes might not be feasible in practice or could weaken the capability of capturing complex and hidden physical phenomena. In this paper, we propose a novel approach to construct a hybrid neural network. The new method incorporates the physical information to the structure of network construction, but does not need an explicit physical model constructed. The method is then applied to modeling of bit-rock interaction in the down-hole drilling system as a case study, to demonstrate its effectiveness in modeling complex process and efficiency of convergence in training.

Keywords: Modeling, Large-scale systems, Observers for Linear systems
Abstract: This paper discusses a Bond Graph (BG) Structural Analysis Toolbox developed in MATLAB (MATSAT) that performs causal analysis on the BG and assists the user in the sensor selection process for a multi-domain physical system. MATSAT contains modules for performing the Sequential Causality Assignment Procedure (SCAP) and Causal Path Search (CaPS). The modules can be combined to check for structural properties such as structural observability (SO) for any sensor set. The working of MATSAT is shown for standard systems. Verification of SCAP, CaPS, and necessary and sufficient SO conditions is shown.

Keywords: Modeling, Machine learning
Abstract: This manuscript addresses the problem of the data driven modeling of a dynamical system in the presence of partially known dynamics using an operator theoretic dynamic mode decomposition (DMD) approach. The method relies on the linearity of the Liouville operator with respect to the dynamics together with established relations between Liouville operators and occupation kernels, which embed trajectory data as a function within a reproducing kernel Hilbert space. The linearity allows for the known portion of the dynamics to be subtracted from the overall dynamics, and the Liouville operator corresponding to the unknown dynamics may thus be isolated. A model for the unknown portion of the dynamical systems may then be obtained from observed trajectory data, and this model may then be utilized for predicting future states.

Keywords: Modeling, Neural networks, Stability of nonlinear systems
Abstract: This paper presents a Koopman lifting linearization method that is applicable to nonlinear dynamical systems having both stable and unstable regions. It is known that DMD and other standard data-driven methods face a fundamental difficulty in constructing a Koopman model when applied to unstable systems. Here we solve the problem by incorporating knowledge about a nonlinear state equation with a learning method for finding an effective set of observables. In a lifted space, stable and unstable regions are separated into independent subspaces. Based on this property, we propose to find effective observables through neural net training where training data are separated into stable and unstable trajectories. The resultant learned observables are used for constructing a linear state transition matrix using method known as Direct Encoding, which transforms the nonlinear state equation to a state transition matrix through inner product computations with the observables. The proposed method shows a dramatic improvement over existing DMD and data-driven methods.

Keywords: Modeling, Simulation, Nonlinear output feedback
Abstract: An experiment where a 3D printer attempts to repair itself by printing a sequence of increasing-in-quality parts is presented and analyzed. Perturbations are added to some parts of the mechanical structures in the printer to simulate damaged or worn-out parts. Mathematical modeling and simulations are used to predict the asymptotic behavior of the self-repair process after many repair attempts. We show that---in most cases---the system converges to a non-ideal state and validations are presented. Finally, a controller is designed and added to the system, and its benefits to the self-repair process are studied.

Keywords: Modeling, Simulation, Optimization
Abstract: In this work, the implementation and test of a tool for the definition of air pollution optimal short term control to support the definition of policies by Local Authorities is presented. The methodology is based on a receding horizon approach where an autoregressive model provides information about the air quality dynamic in the selected time horizon. The model has been identified starting from measured data (concentration and meteorological variables) and estimated information(emission levels) over the area under study. Every time step, the resulting optimization problem has been solved through a genetic algorithm. The system has been tested for the control of NO2 concentrations in the municipality of Milan. The results show that the control system can be a valuable asset to aid Local Authorities in the selection of suitable air quality plans.

Keywords: Network analysis and control, Control of networks
Abstract: A notion of disturbance propagation stability is defined for dynamical network processes, in terms of decrescence of an input-output energy metric along cutsets away from the disturbance source. A characterization of the disturbance propagation notion is developed for a canonical model for synchronization of linearly-coupled homogeneous subsystems. Specifically, propagation stability is equivalenced with the frequency response of a certain local closed-loop model, which is defined from the subsystem model and local network connections, being sub-unity gain. For the case where the subsystem is single-input single-output (SISO), a further simplification in terms of the subsystem's open loop Nyquist plot is obtained. An extension of the disturbance propagation stability concept toward imperviousness of subnetworks to disturbances is briefly developed, and an example focused on networks with planar subsystems is considered.

Keywords: Network analysis and control, Cooperative control, Agents-based systems
Abstract: This paper studies the problem of designing networks that are strong structurally controllable, and robust simultaneously. For given network specifications, including the number of nodes N, the number of leaders N_L, and diameter D, where 2 le D le N/N_L, we propose graph constructions generating strong structurally controllable networks. We also compute the number of edges in graphs, which are maximal for improved robustness measured by the algebraic connectivity and Kirchhoff index. For the controllability analysis, we utilize the notion of zero forcing sets in graphs. Additionally, we present graph grammars, which are sets of rules that agents apply in a distributed manner to construct the graphs mentioned above. We also numerically evaluate our methods. This work exploits the trade-off between network controllability and robustness and generates networks satisfying multiple design criteria.

Keywords: Network analysis and control, Large-scale systems, Decentralized control
Abstract: We consider networked systems comprised of interconnected sets of non-linear subsystems and develop linear matrix inequality (LMI) techniques for their analysis and interconnection topology synthesis using only the dissipativity properties of the involved subsystems. In particular, we consider four networked system configurations (NSCs) and show that the emph{analysis} of their stability/dissipativity can be formulated as corresponding LMI problems. Using some matrix identities and mild assumptions, we also show that the emph{synthesis} of interconnection typologies for these NSCs can also be formulated as LMI problems. This enables synthesizing the interconnection topology among subsystems to enforce/optimize specific stability/dissipativity properties over the networked system. The formulated LMI problems can be solved efficiently and scalably using standard convex optimization toolboxes. We also provide several numerical examples to illustrate our theoretical results.

Keywords: Network analysis and control, Model/Controller reduction, Power systems
Abstract: We propose a novel model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix that models the network feedback. Then, a reduced network is built, where each node represents the aggregate dynamics of each coherent group, and the reduced network captures the dynamic coupling between the groups. Our approach is theoretically justified under a random graph setting. Finally, numerical experiments align with and validate our theoretical findings.

Keywords: Network analysis and control, Stability of nonlinear systems
Abstract: We consider the problem of synchronization of coupled oscillators in a Kuramoto-type model with lossy couplings. Kuramoto models have been used to gain insight on the stability of power networks which are usually nonlinear and involve large scale interconnections. Such models commonly assume lossless couplings and Lyapunov functions have predominantly been employed to prove stability. However, coupling conductances can impact synchronization. We therefore consider a more advanced Kuramoto model that also includes coupling conductances. Lyapunov analysis once such coupling conductances are included becomes nontrivial and more conventional energy-like Lyapunov functions are not applicable or are conservative. Even though small-signal analysis has been performed for such models, there has not been a formal analysis that the stability result for the linearized system also applies to the nonlinear case. In particular, since the system converges to a manifold a small-signal analysis is on its own inconclusive. In this paper, we provide a formal derivation using centre manifold theory that if a particular condition on the equilibrium point associated with the coupling conductances and susceptances holds, then the synchronization manifold for the system considered is asymptotically stable. A result on the structure of the Laplacian associated with the lossy model is also presented. Our analysis is demonstrated with simulations.

Keywords: Adaptive control, Lyapunov methods, Constrained control
Abstract: This paper presents an adaptive control approach for uncertain nonlinear systems subject to safety constraints that allows for modularity in the selection of the parameter estimation algorithm. Such modularity is achieved by unifying the concepts of input-to-state stability (ISS) and input-to-state safety (ISSf) via control Lyapunov functions (CLFs) and control barrier functions (CBFs), respectively. In particular, we propose a class of exponential ISS-CLFs and ISSf high order CBFs that can be combined with a general class of parameter estimation algorithms akin to those found in the literature on concurrent learning adaptive control. We demonstrate that the unification of ISS and ISSf in an adaptive control setting allows for maintaining a single set of parameter estimates for both the CLF and CBF that can be generated by a class of update laws satisfying a few general properties. The modularity of our approach is demonstrated via numerical examples by comparing performance in terms of stability and safety across different parameter estimation algorithms.

Keywords: Adaptive control, Machine learning
Abstract: Real-time control of highly nonlinear systems is a challenging task in many industrial processes. Here, we propose a learning-based adaptation law for adapting the controller parameters of nonlinear systems. The method applies model-free reinforcement learning to learn an effective parameter adaptation law while maintaining a safe system operation by including a safety layer. The efficacy of the proposed algorithm is demonstrated by controlling thermoacoustic combustion instability, which is a critical issue in developing high-efficiency, low-emission gas turbine technologies. We show that the learning-based mechanism is able to attenuate combustion instabilities in a time-variant system with the presence of process noise. The proposed algorithm outperforms the adaptation performance of other model-free and model-based methods, such as extremum seeking controllers and self-tuning regulators, respectively.

Keywords: Adaptive control, Flight control, Robotics
Abstract: This paper presents an adaptive autopilot for fixed-wing aircraft and compares its performance with a fixed-gain autopilot. The adaptive autopilot is constructed by augmenting the autopilot architecture with adaptive control laws that are updated using retrospective cost adaptive control. In order to investigate the performance of the adaptive autopilot, the default gains of the fixed-gain autopilot are scaled to degrade its performance. This scenario provides a venue for determining the ability of the adaptive autopilot to compensate for the degraded fixed-gain autopilot. Next, the performance of the adaptive autopilot is examined under failure conditions by simulating a scenario where one of the control surfaces is assumed to be stuck at an unknown angle. The adaptive autopilot is also tested in physical flight experiments under degraded-nominal conditions, and the resulting performance improvement is examined.

Keywords: Adaptive control, Learning, Machine learning
Abstract: In this paper, we propose a data-driven adaptive control method for trajectory tracking problems with unmatched uncertainty. The method is characterized by a basis augmentation rule triggered by an expressiveness-based event, which provides extra adaptivity to the controller to overcome unmatched uncertainty. The augmented basis functions take the form of kernel basis functions whose centers are located along the trajectory. The triggering event is defined by setting an upper threshold for the value of power function associated to the dictionary of basis functions. The event-triggered basis augmentation (ETBA) rule can be viewed as a realization of the nonparametric adaptive controller embedded in reproducing kernel Hilbert spaces (RKHS). By leveraging the properties of RKHS, we show that 1) the tracking error asymptotically converges to zero, and 2) the inter-event time of basis augmentation is bounded below by a positive value when the reference trajectory is a set point. A numerical example is presented to illustrate performance of the proposed method and verify the theoretical results.

Keywords: Adaptive control, Estimation, Identification
Abstract: We propose a new discrete-time online parameter estimation algorithm that combines two different aspects, one that adds momentum, and another that includes a time-varying learning rate. It is well known that recursive least squares based approaches that include a time-varying gain can lead to exponential convergence of parameter errors under persistent excitation, while momentum-based approaches have demonstrated a fast convergence of tracking error towards zero with constant regressors. The question is when combined, will the filter from the momentum method come in the way of exponential convergence. This paper proves that exponential convergence of parameter is still possible with persistent excitation. Simulation results demonstrated competitive properties of the proposed algorithm compared to the recursive least squares algorithm with forgetting.

Keywords: Adaptive control, Estimation
Abstract: Lightly damped modes that lie within or outside the controller bandwidth of an attitude control system are challenging. As an active control strategy for harmonic disturbances, the present paper applies predictive cost adaptive control (PCAC) to a system with a rigid-body mode and a lightly damped mode that is unmodeled and possibly aliased. PCAC is applied to the specific case of resonance, where the frequency of the exogenous harmonic disturbance coincides with the peak-amplification frequency of the system. LQG control with and without an internal model and with known and uncertain modal frequency provides a baseline for comparison with PCAC, which uses online identification and requires no prior knowledge of the system dynamics or disturbance spectrum. The numerical comparison accounts for the intersample behavior of the lightly damped mode.

Keywords: Stability of nonlinear systems, Biological systems, Lyapunov methods
Abstract: The presented work addresses the motion control problem for a class of musculoskeletal systems, composed of the combination of a rigid multibody system (i.e. the skeletal part) subjected to efforts produced by a set of muscle-tendon complexes. A control law, prescribing the rate of change of muscle fiber activation, is proposed and shown to guarantee exponential convergence of skeletal joint angles to user-defined desired trajectories. Results of numerical simulations, for a simple two degree of freedom skeletal system actuated by five muscle-tendon complexes, illustrate efficacy of the approach.

Keywords: Stability of nonlinear systems, Lyapunov methods, Constrained control
Abstract: The safe stabilization problem is studied via a graphical approach in this paper. Firstly, the compatibility condition for the control Lyapunov function (CLF) and control barrier function (CBF) is provided by visualizing and analyzing the geometry of safe stabilization. Related graphical interpretations are provided to show the proposed condition's connections with the current results. Next, the analytical solution of the CLF and CBF-based quadratic program (CLF-CBF-QP) is obtained with a graphical interpretation. Because Sontag's universal formula for nonlinear stabilization is a special solution of the pointwise minimal norm (PMN) controller, generalized universal formulas for both compatible and incompatible safe stabilization are derived. Afterward, some essential properties of the two proposed universal formulas are discussed, such as Lipschitz continuity, continuity at origin, locally asymptotic stability, safety, etc. Finally, we use the proposed generalized universal formulas to address the safe stabilization problem in adaptive cruise control (ACC) systems. The efficacy of the generalized universal formulas is exhibited with numerical results.

Keywords: Stability of nonlinear systems, Lyapunov methods, Large-scale systems
Abstract: Many compartmental models in biology, chemistry, ecology, sociology, and related sciences have positive variables, for which equilibrium points of interest are in the interior of the positive orthant. Reactions are often modeled as a bilinearity, which renders a boundary of the positive orthant a separatrix. In such situations, the capability of Lyapunov functions defined on symmetric domains is very limited, and logarithmic functions are sometimes used in mathematical biology. The domain of a logarithm function is a ray, which is asymmetric with respect to the equilibrium of interest. This paper aims to add a useful tool to dissipativity theory for analyzing networks via storage functions defined on asymmetric spaces. This paper focuses on an asymmetric supply rate and discusses its properties and utilities which standard symmetric supply rates do not offer. The power of the asymmetric supply rate is illustrated briefly by establishing asymptotic stability of the endemic equilibrium of the SIQRS model of infectious diseases in an arbitrarily large domain.

Keywords: Stability of nonlinear systems, Lyapunov methods, Nonlinear output feedback
Abstract: Partially stable systems involve dynamical systems whose motion lie in a subspace of the state space resulting in system stability with respect to part of the system’s states. In this paper, we develop partial stability theorems for non-linear dissipative feedback systems. Specifically, by invoking additional structural constraints on the forward loop and feedback loop system storage functions, we develop feedback interconnection partial stability results for dissipative nonlinear dynamical systems. Our results provide extensions of the positivity and small gain theorems for guaranteeing partial stability of feedback interconnected systems

Keywords: Stability of nonlinear systems, Lyapunov methods
Abstract: This paper presents the analysis and stabilization of a hybrid-linear inverted pendulum (H-LIP) model that describes the essential robot dynamics associated with legged locomotion on a dynamic rigid surface (DRS) with a general vertical motion. The H-LIP model is analytically derived by explicitly capturing the discrete-time foot placement and the continuous-phase dynamics associated with DRS locomotion, and by considering aperiodic DRS motions and variable HLIP continuous-phase durations. The closed-loop tracking error dynamics of the H-LIP model is then established under a discrete-time feedback footstep control law. The stability of the closed-loop H-LIP error dynamics is analyzed to construct sufficient conditions on the control gains for ensuring the asymptotic error convergence. Simulation results of the proposed H-LIP walking on a vertically moving DRS confirm the proposed control law stabilizes the H-LIP model under various vertical, aperiodic DRS motion profiles and variable H-LIP step durations.

Keywords: Stability of nonlinear systems, Machine learning, Chemical process control
Abstract: Dissipativity, as a behavioral characterization of nonlinear dynamic systems, contains sufficient information for designing controllers. Such dissipativity information, if learned from data instead of being derived from the model, can be used for model-free data-driven control. The learning of dissipativity for general multi-input-multi-output nonlinear systems, however, is difficult and typically demands large trajectory datasets. In this work, a method for inferring the dissipativity information from online data is proposed, which yields a conservative estimation of the set of supply rate functions, thus guaranteeing the stabilizing model-free control performance. The approach is applied to a two-phase reactor case study.

Keywords: Observers for nonlinear systems, Estimation, Delay systems
Abstract: We provide new observer designs to simultaneously identify parameters and states of systems whose non- linearities have order two near the origin, which include cubic terms arising in the study of jump phenomena, process control, and bistable models of aerospace systems. This yields local exponential convergence of the state estimation error to zero, basin of attraction estimates, and fixed time parameter identification. We illustrate our result using Duffing’s equation, whose cubic term puts it outside the scope of prior methods.

Keywords: Observers for nonlinear systems, Learning, Estimation
Abstract: Designing Luenberger observers for nonlinear systems involves the challenging task of transforming the state to an alternate coordinate system, possibly of higher dimensions, where the system is asymptotically stable and linear up to output injection. The observer then estimates the system's state in the original coordinates by inverting the transformation map. However, finding a suitable injective transformation whose inverse can be derived remains a primary challenge for general nonlinear systems. We propose a novel approach that uses supervised physics-informed neural networks to approximate both the transformation and its inverse. Our method exhibits superior generalization capabilities to contemporary methods and demonstrates robustness to both neural network's approximation errors and system uncertainties.

Keywords: Observers for nonlinear systems, Learning, Estimation
Abstract: The presented paper tackles the problem of modeling an unknown function, and its first r-1 derivatives, out of scattered and poor-quality data. The considered setting embraces a large number of use cases addressed in the literature and fits especially well in the context of control barrier functions, where high-order derivatives of the safe set are required to preserve the safety of the controlled system. The approach builds on a cascade of high-gain observers and a set of Gaussian process regressors trained on the observers' data. The proposed structure allows for high robustness against measurement noise and flexibility with respect to the employed sampling law. Unlike previous approaches in the field, where a large number of samples are required to fit correctly the unknown function derivatives, here we suppose to have access only to a small window of samples, sliding in time. The paper presents performance bounds on the attained regression error and numerical simulations showing how the proposed method outperforms previous approaches.

Keywords: Observers for nonlinear systems, Neural networks
Abstract: Model disturbances result from model uncertainties or external factors acting on the system. They usually affect the closed-loop performance in a control loop system. However, they are often unknown and cannot be then compensated. Therefore, it is crucial to develop estimation methods for the effective estimation of the disturbances which can be then considered appropriately in the control design. This paper proposes a hybrid method for the joint estimation of the state and the disturbance for a class of nonlinear systems in two steps. The approach consists in a neural network with time-varying weights used to approximate the disturbance term and a modulating function method for the finite-time estimation of the state and the weights. The modulating functions approach simplifies the estimation problem into solving an algebraic systems of equations. Both offline and online frameworks are presented and discussed. An example is presented to demonstrate the performance of the proposed algorithm.

Keywords: Observers for nonlinear systems, Optimization algorithms
Abstract: The previously proposed Newton observer for nonlinear systems has fast exponential convergence and applies to a wide class of problems. However, the Newton observer lacks robustness against measurement noise due to the computation of a matrix inverse. In this paper, we propose a novel observer for discrete-time system with sampled measurements to alleviate the impact of measurement noise. The key to the proposed observer is an iterative pre-conditioning technique for the gradient-descent method, used previously for solving general optimization problems. The proposed observer utilizes a non-symmetric pre-conditioner to approximate the observability mapping's inverse Jacobian so that it asymptotically replicates the Newton observer with an additional benefit of enhanced robustness against measurement noise. Our observer applies to a wide class of nonlinear systems, as it is not contingent upon linearization or any specific structure in the plant nonlinearity. Its improved robustness compared to the prominent nonlinear observers is demonstrated through empirical results.

Keywords: Estimation, Observers for nonlinear systems, Lyapunov methods
Abstract: Accurate, real-time state of charge (SoC) and state of health (SoH) estimation is essential for lithium-ion battery management systems to ensure safe and extended life of battery packs. For the large battery packs associated with battery electric locomotives and grid applications, computational efficiency is critical, especially for onboard implementation. This paper presents real-time SoC and batch least square SoH and current sensor bias estimation using measured cell voltage and current from large battery packs. An online gradient-based SoH estimator, coupled with the online SoC estimator, provides real-time onboard health monitoring. The online and offline SoC-SoH algorithms are tested using data from a battery electric locomotive. The SoC-SoH estimation results show tightly clustered capacity, resistance, and current sensor bias estimates for an 11-cell module. The batch and online capacity estimates match to within 5% after the startup transients decay.

Keywords: Energy systems, Reduced order modeling, Simulation
Abstract: Lithium-ion batteries (LIBs) have complex electrochemical behaviors, which result in nonlinear and high-dimensional dynamics. The modeling of this complex system often requires models involving PDEs, which are costly to develop and require invasive experiments to identify battery parameters. Here, we propose a data-driven technique to discover nonlinear reduced-order models that govern state-of-charge (SOC) dynamics from non-invasive input/output data. Accurate SOC estimation is paramount for increased performance, improved operational safety, and extended longevity of LIBs. The SOC model is developed from a library of candidate terms via a sparsity-promoting algorithm and data generated by the Doyle-Fuller-Newman (P2D) model with a thermal model to characterize the cell's thermal effects. We tuned the model's performance and sparsity by exploring different combinations of candidate terms (basis functions) and data sampling rates. Using current, voltage, and SOC, the model was trained and validated on the UDDS city driving cycle. It achieved a predictive performance (RMSE) of 3e-5% and 0.22% for training and model validation, respectively. The generalizability of the model was assessed via cross-validation on the US06 highway driving cycle, where an RMSE of 0.47% was achieved. The modeling technique includes explicit physics-inspired terms, which allows for interpretable and generalizable models. Furthermore, the procedures and methods developed in this research are generic and can guide machine learning modeling of other dynamical systems.

Keywords: Energy systems, Reduced order modeling, Modeling
Abstract: Accurate modeling of Lithium-ion batteries (LiBs) allows for more efficient utilization of their potential without compromising their safety or useful life. Accurate physics-based models require in-situ measurements and proprietary information unavailable for each cell. Data-driven models offer a solution to identify governing equations of individual cells using only the excitation inputs and measured outputs. However, the main drawback of such models is their performance in unseen scenarios, as they tend to overfit the training data and perform poorly in other scenarios. We seek physics-informed reduced-order nonlinear models of LiBs from measured data. The model was trained using a high-fidelity model of a Li-ion cell. We used Sequentially Thresholded Ridge regression (STRidge) optimization to determine the optimal reduced-order model. Using a validation set, we proposed an algorithm to tune hyperparameters (threshold and regularization parameters). A stochastic electrical current signal up to 2C/4C-rates charge/discharge was used in the training set, and the US highway profile (US06 drive cycle) was used for the validation. The model was validated with EPA Urban Dynamometer Driving Schedule (UDDS) as the test set. The test errors (normalized root mean square error (NRMSE)) were 6.3e-3 for SOC and Voltage predictions.

Keywords: Energy systems, Estimation, Learning
Abstract: Accurate parameter estimation has been a long-pursued objective in battery modeling and control practice. To this end, optimization of excitation to improve the estimation accuracy has been an emerging topic, since the quality of data critically determines the accuracy of estimation. However, there are several major drawbacks with existing approaches. First, the commonly used criterion for optimization, e.g., Fisher information, is limited in performance due to not considering the estimation bias caused by inevitable system uncertainties. In addition, alternative existing methods rely on a good a priori knowledge of the parameter to be estimated, which is intrinsically contradictory to the goal of estimation. To address these issues, we propose a reinforcement learning (RL) framework to learn the optimal policy for excitation generation that is robust to system uncertainties. In particular, the framework involves a non-additive objective/reward associated with the newly established optimization criterion, and a state augmentation technique is applied to address the ensuing challenge. It is shown that, when applied to estimate a key health-related battery electrochemical parameter, the RL-based approach achieves significantly higher objective value under nominal conditions, and reduces the estimation error by one-order-of-magnitude in the presence of uncertainties compared with the baseline in existing approaches.

Keywords: Energy systems, Estimation, Identification
Abstract: Lithium-ion battery parameter estimation is a dynamic research field in which creative and novel algorithms are being developed to tune high-fidelity models for advanced control of energy systems. Amidst these efforts, little focus has been placed on the fundamental mechanisms associated with estimation accuracy, giving rise to the question, why is an estimate accurate or inaccurate? In response, we derive a generalized multivariate estimation error equation for the least-squares algorithm, which reveals that the error can be represented as the product of system uncertainties (i.e., in model, measurement, and parameter) and uncertainty-propagating sensitivity structures. We then relate the error equation to conventional error analysis criteria, such as parameter sensitivity, the Fisher information matrix, and the Cramer-Rao bound, to assess the benefits and limitations of each. Broadly, these criteria share the principal deficiency of neglecting estimation bias and system uncertainties, which are inevitable in practice. The error equation is validated through a series of experimental uni- and bivariate estimations of lithium-ion battery electrochemical parameters. These results are also analyzed using the error equation to study the composition of errors under various data sets. Finally, the bivariate analysis indicates that adding an additional target parameter to the estimation without increasing the amount of data intrinsically reduces the error robustness to the influence of system uncertainties.

Keywords: Energy systems, Optimal control, Distributed control
Abstract: Optimal power management (OPM) is critical for large-scale battery energy storage systems. Today's methods often require formidable computational effort due to the design based on centralized numerical optimization. Thus, this paper investigates computationally distributed OPM where the agents based on the cells communicate over a network to cooperatively solve the OPM problem. We propose an accelerated tracking alternating direction method of multipliers (ADMM) algorithm to solve the distributed OPM. The proposed algorithm embeds dynamic average consensus and Nesterov's acceleration technique in the ADMM algorithm. Not only is the proposed algorithm fully distributed without a need for fusion or aggregating nodes, but it also accelerates the convergence. The paper formulates the OPM in a model predictive control framework where it seeks to regulate the charging/discharging power of each battery cell to minimize the total power losses and promote balanced use of the constituent cells while complying with the safety constraints. The paper provides ample simulation results to demonstrate the effectiveness and advantages of the proposed distributed OPM in terms of computation and convergence.

Keywords: Distributed control, Optimization algorithms, Optimal control
Abstract: Large-scale systems comprising of components with complex interactions and nonlinear physics are ubiquitous in modern engineering systems, including integrated and intensified chemical processes and supply chains. Mathematical optimization provides a means of automated decision making for problems of, for example, process control, design, production and maintenance scheduling, and supply chain management, which has formed the backbone of process systems research over the past several decades. Unfortunately, for large-scale and complex systems, it is often the case that the off-the-shelf solution methods (i.e. CPLEX, Ipopt, BARON, …) cannot directly return an optimal decision in an amount of time relevant for the problem (i.e. on the order of seconds for process control). In these instances, it is a natural but also profound idea to decompose the decision-making problem into a set of easier to solve subproblems, often corresponding to subsystems that can be controlled or optimized in a distributed architecture. Historically, this has been done by a systems expert who uses their intuition and knowledge of the underlying process to develop the subproblem structure; however, recent advances in network theory allow for the automatic identification of structure amenable to solution via decomposition approaches.

Keywords: Predictive control for nonlinear systems
Abstract: Integrated energy systems (IESs) play an important role in absorbing renewable energy and improving overall fuel efficiency in distributed energy systems. An IES typically consists of a few energy generation and storage units (e.g., solar panels, wind turbines, battery banks, water tanks) that are closely interconnected. Given the distinct dynamics of the different energy generation and storage units, a centralized control scheme in general does not work well. In this work, we show how an IES can be decomposed into smaller subsystems and how distributed economic model predictive control (EMPC) can be designed based on the decomposed subsystems to optimize the operation of the IES. In the decomposition of the IES, we explore both decomposing the entire system vertically based on the time-scale multiplicity exhibited in the IES dynamics and horizontally based on the closeness of the interconnection between the various operating units. The impact of the order of applying the vertical and horizontal decomposition is also discussed. Based on the decomposed subsystems, a distributed EMPC scheme is designed. We illustrate how the features of the decomposed subsystem models can be used in the design of the local EMPCs to reduce the computational complexity and information exchange between the controllers.