Keywords: Machine learning, Cooperative control, Optimal control
Abstract: We survey a comprehensive theory on the application of the Banach contraction principle to control and dynamical systems. We start with some historical highlights. Next, we generalize the basic contraction property from discrete to continuous time, from Euclidean to non-Euclidean norms, from closed to open systems, and, finally, from single to interconnected systems. We then apply these theoretical tools to modern problems involving machine learning, multi-agent coordination, and optimal control. Finally, we conclude with strengths and weaknesses of the theory as well as open directions of research.

Keywords: Switched systems, Hybrid systems, Kalman filtering
Abstract: Asynchronously switched sampled-data systems can help model power systems and vehicles that evolve in continuous-time with switching behavior and discrete time measurements. We address the problem of jointly estimating a switching signal, with uncertainty in the exact switching times, as well as the continuous states of the system. We prove stability of the standard Kalman filter under uncertainty in the switching time, with statistical bounds relating to the sampling period. We then propose a method for estimation of switching times as well as a method for efficient joint estimation of the state and switching signal inspired by the interacting multiple-model extended-Viterbi algorithm. We validate our algorithms in simulation for a power converter and maneuvering vehicle.

Keywords: Switched systems, Sampled-data control, Adaptive control
Abstract: This work studies data-driven switched controller design for discrete-time switched linear systems. Instead of having access to the full system dynamics, an initialization phase is performed, during which noiseless measurements of the state and the input are collected for each mode. Under certain conditions on these measurements, we develop a stabilizing switched controller for the switched system. To be precise, the controller switches between identifying the active mode of the system and applying a predetermined stabilizing feedback. We prove that if the system switches according to certain specifications, this controller stabilizes the closed-loop system. Simulations on a network example illustrate our approach.

Keywords: Switched systems, Linear systems, Stochastic optimal control
Abstract: Sustained research efforts have been devoted to learning optimal controllers for linear stochastic dynamical systems with unknown parameters, but due to the corruption of noise, learned controllers are usually uncertified in the sense that they may destabilize the system. To address this potential instability, we propose a "plug-and-play" modification to the uncertified controller which falls back to a known stabilizing controller when the norm of the state exceeds a certain threshold. We show that the switching strategy enhances the safety of the uncertified controller by making the linear-quadratic cost bounded even if the underlying linear feedback gain is destabilizing. We also prove the near-optimality of the proposed strategy by quantifying the maximum performance loss caused by switching as asymptotically negligible. Finally, we demonstrate the effectiveness of the proposed switching strategy using simulation on an industrial process example.

Keywords: Switched systems, Identification, Adaptive control
Abstract: This work proposes an online adaptive identification method for multi-input multi-output (MIMO) switched affine systems with guaranteed parameter convergence. A family of online parameter estimators is used that is equipped with a dual-layer low pass filter architecture to facilitate parameter learning and identification of each subsystem. The filters capture information about the unknown parameters in the form of a prediction error which is used in the parameter estimation algorithm. A salient feature of the proposed method that distinguishes it from most previous results is the use of a memory bank that stores filter values and promotes parameter learning during both active and inactive phases of a subsystem. Specifically, the learnt experience from the previous active phase of a subsystem is retained in the memory and leveraged for parameter learning in its subsequent active and inactive phases. Further, a new notion of intermittent initial excitation (IIE) is introduced that extends the previously established initial excitation (IE) condition to the switched system framework. IIE is shown to be sufficient to ensure exponential convergence of the switched system parameters.

Keywords: Switched systems, LMIs, Robust control
Abstract: This paper proposes an algorithm based on LMIs to simultaneously design a switching control law and state-feedback gains that robustly stabilize a continuous-time switched linear system. The method is based on the computation of a stable convex combination of a polytope of matrices. First, the problem is reformulated as a relaxed LMI condition where the scalar parameters appear affinely. Differently from the majority of existing approaches, that resort to the use of gridding, a stable convex combination is determined through an iterative procedure. The algorithm is then extended to provide at the same time a switching strategy and the gains that stabilize the closed-loop system, also including the maximization of a bound to the decay rate. Numerical examples illustrate the results.

Keywords: Switched systems, Lyapunov methods, Subspace methods
Abstract: We present an algorithmic framework for the identification of candidate invariant subspaces for switched linear systems. Namely, the framework allows to compute an orthonormal basis in which the matrices of the system are close to block-triangular matrices, based on a finite set of observed one-step trajectories and with a priori confidence level. The link between the existence of an invariant subspace and a common block-triangularization of the system matrices is well known. Under some assumptions on the system, one can also infer the existence of an invariant subspace when the matrices are close to be block-triangular. Our approach relies on quadratic Lyapunov analysis and recent tools in scenario optimization. We present two applications of our results for problems of consensus and opinion dynamics; the first one allows to identify the disconnected components in a switching hidden network, while the second one identifies the stationary opinion vector of a switching gossip process with antagonistic interactions.

Keywords: Adaptive control, Adaptive systems, Human-in-the-loop control
Abstract: Practical adaptive control implementations where human pilots coexist in the loop are still uncommon, despite their success in handling uncertain dynamical systems. This is owing to their special nonlinear characteristics which lead to unfavorable interactions between pilots and adaptive controllers. To pave the way for the implementation of adaptive controllers in piloted applications, we propose an adaptive human pilot model that takes into account the time delay in the pilot's response while operating on an adaptive control system. The model can be utilized in the evaluation of adaptive controllers through the simulation environment and guide in their design.

Keywords: Adaptive control, Adaptive systems, Lyapunov methods
Abstract: In this paper, a novel proportional integral (PI)-like estimator-based adaptive extremum seeking control (AdESC) algorithm is proposed for online optimization, where parameter convergence is achieved under a relaxed mathematical condition called initial excitation (IE). The proposed AdESC algorithm utilizes a new set of low-pass filter dynamics, which omits the requirement of switching mechanism in past literature for rank-checking while still ensuring parameter convergence. A detailed Lyapunov analysis is carried out using singular-perturbation like principle to establish closed-loop stability of the AdESC algorithm.

Keywords: Adaptive control, Autonomous robots, Visual servo control
Abstract: This paper investigates the trajectory tracking problem of nonholonomic mobile robot in the environment where localization cannot be obtained. An adaptive visual servoing velocity controller without direct position measurement is presented in the paper. The proposed dynamic controller is based on a position estimation algorithm using feedback from encoders, inertial measurement unit (IMU) and a visual system. It is shown that the controlled mobile robot is able to track the desired trajectory. Simulation example illustrates the effectiveness of the proposed approach.

Keywords: Adaptive control, Autonomous vehicles, Cooperative control
Abstract: In longitudinal platooning, ‘disturbance decoupling’ refers to the problem of making the inter-vehicle spacing independent of the disturbance input from the preceding vehicle, while ‘adaptive’ refers to handling vehicle parametric uncertainty such as engine time constant. This work constructs a platooning architecture to achieve disturbance decoupling and adaptive goals without absolute position and relative velocity feedback, required in the state of the art. The interest in targeting disturbance decoupling is to have string stability (attenuation of disturbances along the platoon) as a by-product, as well as a decentralized design that helps handling parametric uncertainty. Stability analysis is provided along with numerical simulations.

Keywords: Adaptive control, Constrained control, Robust adaptive control
Abstract: This paper proposes an anti-windup mechanism for a model reference adaptive control (MRAC) scheme subject to actuator saturation constraints. The proposed compensator has the same architecture as well known non-adaptive schemes, which rely on the assumption that the system model is known fairly accurately. This is in contrast to the adaptive nature of the controller, which assumes that the system (or parts of it) is unknown. The approach proposed here uses of an “estimate” of the system matrices for the anti-windup com- pensator formulation and modifies the adaptation laws that update the controller gains. It will be observed that if the (unknown) ideal control gain is reached, a type of “model recovery anti-windup” formulation is obtained. In addition, it is shown that if the control signal eventually lies within the control constraints, then, under certain conditions, the system states will converge to those of the reference model as desired. The paper highlights the main challenges involved in the design of anti-windup compensators for model-reference adaptive control systems and demonstrates its success via a simulation of a flight control application.

Keywords: Adaptive control, Constrained control, Linear systems
Abstract: Satisfaction of state and input constraints is one of the most critical requirements in control engineering applications. In classical model reference adaptive control (MRAC) formulation, although the states and the input remain bounded, the bound is neither user-defined nor known a-priori. In this paper, an MRAC is developed for multivariable linear time-invariant (LTI) plant with user-defined state and input constraints using a simple saturated control design coupled with a barrier Lyapunov function (BLF). Without any restrictive assumptions that may limit practical implementation, the proposed controller guarantees that both the plant state and the control input remain within a user-defined safe set for all time while simultaneously ensuring that the plant state trajectory tracks the reference model trajectory. The controller ensures that all the closed-loop signals remain bounded and the trajectory tracking error converges to zero asymptotically. Simulation results validate the efficacy of the proposed constrained MRAC in terms of better tracking performance and limited control effort compared to the standard MRAC algorithm.

Keywords: Robotics, Robust control, Optimization
Abstract: A common way to implement navigation in mobile robots is through the use of landmarks. In this case, the main goal of the controller is to make progress toward a goal location (stability), while avoiding the boundary of the environment (safety). In our previous work, we proposed a method to synthesize global controllers for environments with a polyhedral decomposition; our solution uses a Quadratically Constrained Quadratic Program with Chance Constraints to take into account the uncertainty in landmark measurements. Building upon this work, we introduce the concept of virtual landmarks, which are defined as linear combinations of actual landmark measurements that minimize the uncertainty in the resulting control actions. Interestingly, our results show that the first minimum-variance landmark is independent of the feedback control matrix, thus decoupling the design of the landmark from the one of the controller; attempting to derive additional, statistically independent landmarks, however, requires solving non-convex problems that involve also the controller. Numerical experiments demonstrate that, by minimizing the variance of the inputs, the resulting controller will be less conservative, and the robot is able to complete navigation tasks more effectively (faster and with less jitter in the trajectory).

Keywords: Robotics, Optimization, Control applications
Abstract: In this paper, we consider the problem of protecting a high-value unit from inadvertent attack by a group of agents using defending robots. Specifically, we develop a control strategy for the defending agents that we call ``dog robots" to prevent a flock of ``sheep agents" from breaching a protected zone. We take recourse to control barrier functions to pose this problem and exploit the interaction dynamics between the sheep and dogs to find dogs' velocities that result in the sheep getting repelled from the zone. We solve a QP reactively that incorporates the defending constraints to compute the desired velocities for all dogs. Owing to this, our proposed framework is composable textit{i.e.} it allows for simultaneous inclusion of multiple protected zones in the constraints on dog robots' velocities. We provide a theoretical proof of feasibility of our strategy for the one dog/one sheep case. Additionally, we provide empirical results of two dogs herding upto ten sheep averaged over a hundred simulations and report high success rates. We also demonstrate this algorithm experimentally on non-holonomic robots. Videos of these results are available at url{https://tinyurl.com/4dj2kjwx}.

Keywords: Robotics, Optimization, Estimation
Abstract: This paper presents a new numerical method to solve the forward kinematics (FK) of a parallel manipulator with a three-limb spherical-prismatic-revolute (3SPR) structure. Unlike the existing numerical approaches that require the manipulator’s Jacobian matrix and its inverse at each iteration, the proposed algorithm requires much less complex computations to estimate the FK parameters. A cost function is introduced that measures the difference between actual FK values and its estimates. At each iteration, the problem is handled in two steps. First, the estimates of the platform orientation from the heave estimates are obtained. Then, the heave estimates are updated along the gradient direction of the proposed cost function. To evaluate the performance of the proposed algorithm, we compare results with those of a Jacobian-based (JB) approach for a 3SPR parallel manipulator.

Keywords: Robotics
Abstract: Performing highly agile dynamic motions, such as jumping or running on uneven stepping stones has remained a challenging problem in legged robot locomotion. This paper presents a framework that combines trajectory optimization and model predictive control to perform robust and consecutive jumping on stepping stones. In our approach, we first utilize trajectory optimization based on full-nonlinear dynamics of the robot to generate periodic jumping trajectories for various jumping distances. A jumping controller based on a model predictive control is then designed for realizing smooth jumping transitions, enabling the robot to achieve continuous jumps on stepping stones. Thanks to the incorporation of MPC as a real-time feedback controller, the proposed framework is also validated to be robust to uneven platforms with unknown height perturbations and model uncertainty on the robot dynamics.

Keywords: Robotics, Cooperative control, Adaptive control
Abstract: The success of a cooperative manipulation process depends on the level of disturbance rejection between the cooperating agents. However, this attribute may be jeopardized due to unexpected behaviors, such as joint saturation or internal collisions. This leads to deterioration in the performance of the manipulation task. In this paper, we present an adaptive distributed control framework that directly mitigates these internal disturbances, both in the joint (and task) spaces. With our approach, we show that including the manipulator-load coupling in the definition of the task error yields improved performance and robustness. To validate this statement, we provide stability guarantees and simulation results for two implementation cases.

Keywords: Robotics, Cooperative control, Adaptive control
Abstract: This paper addresses the problem of admittance control for bimanual and cooperative manipulators. First, a novel admittance controller is devised to be consistent with the geometry of the cooperative task space and exploits the dual quaternion logarithmic mapping of wrenches and corresponding elastic displacements. By describing the coupled motion exploiting the geometric features of dual quaternions, the desired compliant behaviour is enforced on the whole dual-arm system and not on the single manipulator separately. The solution is thereafter extended by means of an adaptive modulation of the impedance gains along the logarithmic space of the dual quaternion algebra for cooperative dual task-space variables. The overall scheme consists of a stiffness adapter, cooperative admittance controller, and wrench adapter complete with an inner motion controller along with the cooperative system. Stability proofs and conditions for the stiffness and damping adaptation of the cooperative variables is provided. Finally, we present a use case depicting a cooperative variable stiffness adaptation policy with respect to the relative elastic behaviour between arms to reduce internal stress whilst satisfying grasp feasibility under shear forces and varying load conditions. Our formulation is validated by thorough simulation studies on two Franka Emika Panda robots carrying a shared object under varying loading conditions. The experimental investigations reinforce our claim of robust performance when compared with fixed stiffness and standard width-adaptation solutions.

Keywords: Machine learning, Autonomous vehicles, Identification for control
Abstract: Choosing an appropriate parameter set for the designed controller is critical for the final performance but usually requires a tedious and careful tuning process, which implies a strong need for automatic tuning methods. However, among existing methods, derivative-free ones suffer from poor scalability or low efficiency, while gradient-based ones are often unavailable due to possibly non-differentiable controller structure. To resolve the issues, we tackle the controller tuning problem using a novel derivative-free reinforcement learning (RL) framework, which performs timestep-wise perturbation in parameter space during experience collection and integrates derivative-free policy updates into the advanced actor-critic RL architecture to achieve high versatility and efficiency. To demonstrate the framework’s efficacy, we conduct numerical experiments on two concrete examples from autonomous driving, namely, adaptive cruise control with PID controller and trajectory tracking with MPC controller. Experimental results show that the proposed method outperforms popular baselines and highlight its strong potential for controller tuning.

Keywords: Machine learning, Computational methods, Optimization algorithms
Abstract: Bayesian optimization (BO) is a data-efficient approach for optimizing expensive-to-evaluate black-box functions that suffer from noisy evaluations. Traditional BO algorithms ignore the relationship between consecutive input values, which is known to lead to significant "jumps" in the search space that cannot be implemented in practice, especially in online experimental systems. For example, in performance-driven control applications, large changes in the chosen setpoint parameters may trigger fail-safe mechanisms and/or lead to violation of critical safety constraints. In such applications, it is necessary to limit the allowable search space at each BO iteration, which can be done by incorporating local search constraints into the original problem setting. In this paper, we show how this novel BO setting can be cast as a Markov decision process (MDP) for which the optimal policy is characterized by an intractable dynamic programming (DP) problem. To overcome this challenge, we take advantage of approximate DP methods, particularly rollout with fast policy search, to derive an efficient multi-step lookahead BO policy. We also propose a novel base policy needed for the rollout algorithm, which explicitly incorporates the local search restrictions in an efficient and intuitive manner. Lastly, we empirically show that our proposed multi-step lookahead BO policy outperforms existing methods on a well-known benchmark problem.

Keywords: Machine learning, Computational methods, Simulation
Abstract: Bayesian optimization (BO) has demonstrated potential for optimizing control performance in data-limited settings, especially for systems with unknown dynamics or unmodeled performance objectives. The BO algorithm efficiently trades-off exploration and exploitation by leveraging uncertainty estimates using surrogate models. These surrogates are usually learned using data collected from the target dynamical system to be optimized. Intuitively, the convergence rate of BO is better for surrogate models that can accurately predict the target system performance. In classical BO, initial surrogate models are constructed using very limited data points, and therefore rarely yield accurate predictions of system performance. In this paper, we propose the use of meta-learning to generate an initial surrogate model based on data collected from performance optimization tasks performed on a variety of systems that are different to the target system. To this end, we employ deep kernel networks (DKNs) which are simple to train and which comprise encoded Gaussian process models that integrate seamlessly with classical BO. The effectiveness of our proposed DKN-BO approach for speeding up control system performance optimization is demonstrated using a well-studied nonlinear system with unknown dynamics and an unmodeled performance function.

Keywords: Machine learning, Filtering, Estimation
Abstract: We consider the filtering and prediction problem for a diffusion process. The signal and observation are modeled by stochastic differential equations (SDEs) driven by correlated Wiener processes. In classical estimation theory, measure-valued stochastic partial differential equations (SPDEs) are derived for the filtering and prediction measures. These equations can be hard to solve numerically. We provide an approximation algorithm using conditional generative adversarial networks (GANs) in combination with signatures, an object from rough path theory. The signature of a sufficiently smooth path determines the path completely. As a result, in some cases, GANs based on signatures have been shown to efficiently approximate the law of a stochastic process. For our algorithm we extend this method to sample from the conditional law, given noisy, partial observation. Our generator is constructed using neural differential equations (NDEs), relying on their universal approximator property. We show well-posedness in providing a rigorous mathematical framework. Numerical results show the efficiency of our algorithm.

Keywords: Machine learning, Healthcare and medical systems, Optimization
Abstract: In this paper, we consider a risk-averse multi-armed bandit (MAB) problem where the goal is to learn a policy that minimizes the risk of low expected return, as opposed to maximizing the expected return itself, which is the objective in the usual approach to risk-neutral MAB. Specifically, we formulate this problem as a transfer learning problem between an expert and a learner agent in the presence of contexts that are only observable by the expert but not by the learner. Thus, such contexts are unobserved confounders (UCs) from the learner's perspective. Given a dataset generated by the expert that excludes the UCs, the goal for the learner is to identify the true minimum-risk arm with fewer online learning steps, while avoiding possible biased decisions due to the presence of UCs in the expert's data. To achieve this, we first formulate a mixed-integer linear program that uses the expert data to obtain causal bounds on the Conditional Value at Risk (CVaR) of the true return for all possible UCs. We then transfer these causal bounds to the learner by formulating a causal bound constrained Upper Confidence Bound (UCB) algorithm to reduce the variance of online exploration and, as a result, identify the true minimum-risk arm faster, with fewer new samples. We provide a regret analysis of our proposed method and show that it can achieve zero or constant regret. Finally, we use an emotion regulation in mobile health example to show that our proposed method outperforms risk-averse MAB methods without causal bounds.

Keywords: Machine learning, Identification, Observers for nonlinear systems
Abstract: The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the state and the nonlinear system model. To cope with this challenge, we investigate the effectiveness of deep learning in the modeling of dynamic systems with nonlinear behavior by advocating an approach which relies on three main ingredients: (i) we show that under some structural conditions on the to-be-identified model, the state can be expressed in function of a sequence of the past inputs and outputs; (ii) this relation which we call the state map can be modelled by resorting to the well-documented approximation power of deep neural networks; (iii) taking then advantage of existing learning schemes, a state-space model can be finally identified. After the formulation and analysis of the approach, we show its ability to identify three different nonlinear systems. The performances are evaluated in terms of open-loop prediction on test data generated in simulation as well as a real world data-set of unmanned aerial vehicle flight measurements.

Keywords: Stochastic optimal control, Predictive control for linear systems, Stochastic systems
Abstract: This paper studies the problem of distributionally robust model predictive control (MPC) using total variation distance ambiguity sets. For a discrete-time linear system with additive disturbances, we provide a conditional value-at-risk reformulation of the MPC optimization problem that is distributionally robust in the expected cost and chance constraints. The distributionally robust chance constraint is over-approximated as a simpler, tightened chance constraint that reduces the computational burden. Numerical experiments support our results on probabilistic guarantees and computational efficiency.

Keywords: Uncertain systems, Stochastic systems, Stability of nonlinear systems
Abstract: Guaranteeing safety for robotic and autonomous systems in real-world environments is a challenging task that requires the mitigation of stochastic uncertainties. Control barrier functions have, in recent years, been widely used for enforcing safety related set-theoretic properties, such as forward invariance and reachability, of nonlinear dynamical systems. In this paper, we extend this rich framework to nonlinear discrete-time systems subject to stochastic uncertainty and propose a framework for assuring risk-sensitive safety in terms of coherent risk measures. To this end, we introduce risk control barrier functions (RCBFs), which are compositions of barrier functions and dynamic, coherent risk measures. We show that the existence of such barrier functions implies invariance in a coherent risk sense. Furthermore, we formulate conditions based on finite-time RCBFs to guarantee finite-time reachability to a desired set in the coherent risk. Conditions for risk-sensitive safety and finite-time reachability of sets composed of Boolean compositions of multiple RCBF are also formulated. We show the efficacy of the proposed method through its application to a cart-pole system in a safety-critical scenario.

Keywords: Statistical learning, Learning, Networked control systems
Abstract: We prove that the governing dynamics of a class of stochastic networks can be learned through their coupling functions. It is shown that the dynamics of such networks can generate geometrically ergodic trajectories under some reasonable assumptions. We show that a general class of coupling functions can be learned using only one sample trajectory from the network. This approach is plausible in numerous applications when one prefers to run an experiment only once but for a more extended period rather than repeating the same experiment multiple times under different initial conditions. Building upon ideas from the concentration inequalities for geometrically ergodic Markov chains, we formulate several results about the convergence of the empirical estimator to the actual coupling function. Extensive simulation results support our theoretical findings.

Keywords: Lyapunov methods, Nonlinear systems, Uncertain systems
Abstract: This paper studies the design of controllers that guarantee stability and safety of nonlinear control affine systems with parametric uncertainty in both the drift and control vector fields. To this end, we introduce novel classes of robust control barrier functions (RCBF) and robust control Lyapunov functions (RCLF) that facilitate the synthesis of safety-critical controllers in the presence of parametric uncertainty using quadratic programming. Since the initial bounds on the system uncertainty may be highly conservative, we present a data-driven approach to reducing such bounds using input-output data collected online. In particular, we leverage an integral set-membership identification algorithm that iteratively shrinks the set of possible system parameters online and guarantees stability and safety during learning. The efficacy of the developed approach is illustrated via numerical examples.

Keywords: Autonomous robots, Cooperative control, Stochastic optimal control
Abstract: We study a chance-constrained variant of the cooperative aerial-ground vehicle routing problem, in which an Unmanned Aerial Vehicle (UAV) with limited battery capacity and an Unmanned Ground Vehicle (UGV) that can also act as a mobile recharging station need to jointly accomplish a mission such as monitoring a set of points. Due to the limited battery capacity of the UAV, two vehicles sometimes have to deviate from their task to rendezvous and recharge the UAV@. Unlike prior work that has focused on the deterministic case, we address the challenge of stochastic energy consumption of the UAV@. We are interested in finding the optimal policy that decides when and where to rendezvous such that the expected travel time of the UAV is minimized and the probability of running out of charge is less than a user-defined tolerance. We formulate this problem as a Chance Constrained Markov Decision Process (CCMDP). To the best knowledge of the authors, this is the first CMDP-based formulation for the UAV-UGV routing problems under power consumption uncertainty. We adopt a Linear Programming (LP) based approach to solve the problem optimally. We demonstrate the effectiveness of our formulation in the context of an Intelligence Surveillance and Reconnaissance (ISR) mission.

Keywords: Stochastic optimal control, Stochastic systems, Optimization
Abstract: We propose a methodology for performing risk-averse quadratic regulation of partially observed Linear Time-Invariant (LTI) systems, disturbed by process and output noise. To compensate against the induced variability due to both types of noises, state regulation is subject to two risk constraints. The latter renders the resulting controller to be cautious of stochastic disturbances, by restricting the statistical variability, namely, a simplified version of the cumulative expected predictive variance, of both the state and the output. It turns out that our proposed formulation results in an optimal risk-averse policy that preserves favorable characteristics of the classical Linear Quadratic (LQ) control. In particular, the optimal policy has an affine structure with respect to the minimum mean square error (mmse) estimates. The linear component of the policy regulates the state more strictly in riskier directions, where the process and output noise covariance, cross-covariance, and the corresponding penalties are simultaneously large. This is achieved by ``inflating" the state penalty in a systematic way. The additional affine terms force the state against pure and cross third-order statistics of the process and output disturbances. Another favorable characteristic of our optimal policy is that it can be pre-computed off-line, thus, avoiding limitations of prior work. Stability analysis shows that the derived controller is always internally stable regardless of parameter tuning. The functionality of the proposed risk-averse policy is illustrated through a working example via extensive numerical simulations.

Keywords: Identification, Statistical learning, Large-scale systems
Abstract: We consider the identification of large-scale linear and stable dynamic systems whose outputs may be the result of many correlated inputs. Hence, severe ill-conditioning may affect the estimation problem. This is a scenario often arising when modeling complex physical systems given by the interconnection of many sub-units where feedback and algebraic loops can be encountered. We develop a strategy based on Bayesian regularization where any impulse response is modeled as the realization of a zero-mean Gaussian process. The stable spline covariance is used to include information on smooth exponential decay of the impulse responses. We then design a new Markov chain Monte Carlo scheme that deals with collinearity and is able to efficiently reconstruct the posterior of the impulse responses. It is based on a variation of Gibbs sampling which updates possibly overlapping blocks of the parameter space on the basis of the level of collinearity affecting the different inputs. Numerical experiments are included to test the goodness of the approach where hundreds of impulse responses form the system and inputs correlation may be very high.

Keywords: Identification, Identification for control, Stochastic systems
Abstract: This paper provides a Bayesian analysis of the total least-squares problem with independent Gaussian noise of known variance. It introduces a derivation of the likelihood density function, conjugate prior probability-density function, and the posterior probability-density function. All in the shape of the Bingham distribution, introducing an unrecognized connection between orthogonal least-squares methods and directional analysis. The resulting Bayesian inference expands on available methods with statistical results. A recursive statistical identification algorithm of errors-in-variables models is laid-out. An application of the introduced inference is presented using a simulation example, emulating part of the identification process of linear permanent magnet synchronous motor drive parameters. The paper represents a crucial step towards enabling Bayesian statistical methods for problems with errors in variables.

Keywords: Identification, Closed-loop identification
Abstract: Recent applications have proven the effectiveness of kernel-based regularization approach in system identification. Most of the existing kernel-based regularization methods design the regularization term based on the exponential convergence of impulse response, thus enforcing stability of the system. Therefore, it is difficult to identify unstable systems with existing methods. This paper employs the coefficients of Laurent series expansion defined on the unit circle as a model structure, and proposes a way to use kernels for stable systems in identifying the coefficients. Since the coefficients show exponential convergence even when the system is unstable, the proposed method is applicable for unstable systems. The effectiveness of the proposed method is demonstrated by a numerical example.

Keywords: Nonlinear systems identification, Kalman filtering, Predictive control for nonlinear systems
Abstract: In this paper, we extend the State-Space Kriging (SSK) modelling technique presented in a previous work by the authors so that non autonomous systems can be considered. The SSK method computes predictions as linear combinations of past outputs. In order to model nonlinearity, we develop here a new version of the SSK where kernel functions are used to model nonlinear dynamics instead of resorting on considerations about local data, which in practice is akin to a linearization. Also, a Kalman filter is used to improve the obtained predictions at each time step in the case of noisy measurements. A constrained Nonlinear Model Predictive Control (NMPC) scheme is built upon the black-box input-output system obtained by means of the SSK prediction method. Finally, a numerical example of a continuously stirred tank reactor (CSTR) is provided in order to assess the performance of the proposed controller.

Keywords: Nonlinear systems identification, Linear parameter-varying systems, Modeling
Abstract: Limit cycle oscillations are phenomena arising in nonlinear dynamical systems and characterized by periodic, locally-stable, and self-sustained state trajectories. Systems controlled in a closed loop along a periodic trajectory can also be modelled as systems experiencing limit cycle behavior. The goal of this work is to identify from data, the local dynamics around the limit cycle using linear periodically parameter-varying models. Using a coordinate transformation onto transversal surfaces, the dynamics are decomposed into two parts: one along the limit cycle, and one on the transversal surfaces. Then, the model is identified from trajectory data using kernel-based methods with a periodic kernel design. The kernel-based model is extended to also account for variations in system parameters associated with different operating conditions. The performance of the proposed identification method is demonstrated on a benchmark nonlinear system and on a simplified airborne wind energy model. The method provides accurate model parameter estimation, compared to the analytical linearization, and good prediction capability.

Keywords: Estimation, Identification, Optimization
Abstract: Accurate identification of stochastic systems with fast-varying parameters is a challenging task which cannot be accomplished using model-free estimation methods, such as weighted least squares, which assume only that system coefficients can be regarded as locally constant. The current state of the art solutions are based on the assumption that system parameters can be locally approximated by a linear combination of appropriately chosen basis functions. The paper shows that when the internal correlation structure of estimated parameters is known, the tracking performance of the local basis function estimation algorithms can be further improved by means of regularization. The optimal form of the regularization matrix is derived analytically and it is shown that the best settings of the regularized algorithm can be determined in the computationally efficient way using cross-validation.

Keywords: Estimation, Delay systems
Abstract: This paper proposes a high-gain observer design for nonlinear systems with delayed output measurements using time-varying gains. The proposed observer is endowed with an exponential stability guarantee and relies on the generalization of the Halanay-type inequalities. We establish that the estimated state and the adapted gain are exponentially bounded and prevent the oscillatory response of the estimates. The time-varying gain feature limits the constant high-gain values of the standard high-gain observer design to the minimum gain required to achieve stability. Furthermore, we derive an explicit relation between the maximum bound of the delay and the maximum gain parameter by using a Lyapunov-Krasovskii functional jointly with the time-varying Halanay inequality. Finally, a comparison with the standard high-gain observer is provided through numerical simulations to demonstrate the superiority of the proposed high-gain observer in rejecting the noise and reducing the peaking phenomena.

Keywords: Estimation, Filtering, Networked control systems
Abstract: This paper investigates the stochastic event-triggered remote state estimation problem with intermittent measurements over a Gaussian communication channel. Because of the channel noises, the remote estimator does not know whether the measurements are received and transmitted by the sensor. Assuming the prior distribution of the estimation process is Gaussian, an approximate minimum mean squared error estimator with adaptive weights is derived by the Bayesian inference method. The proposed estimate convexly combines the estimates for three arrival and transmission cases. Then the proposed estimator is shown to be conventional forms under three extreme situations. Numerical results demonstrate that our estimator has comparable performance to the Kalman filtering with intermittent measurements without the knowledge of the arrival variables and the triggering decisions.

Keywords: Estimation, Game theory, Autonomous robots
Abstract: Robots operating in multi-player settings must simultaneously model the environment and the behavior of human or robotic agents who share that environment. This modeling is often approached using Simultaneous Localization and Mapping (SLAM); however, SLAM algorithms usually neglect multi-player interactions. In contrast, the motion planning literature often uses dynamic game theory to explicitly model noncooperative interactions of multiple agents in a known environment with perfect localization. Here, we present GTP-SLAM, a novel, iterative best response-based SLAM algorithm that accurately performs state localization and map reconstruction, while using emph{game theoretic priors} to capture the inherent non-cooperative interactions among multiple agents in an uncharted scene. By formulating the underlying SLAM problem as a potential game, we inherit a strong convergence guarantee. Empirical results indicate that, when deployed in a realistic traffic simulation, our approach performs localization and mapping more accurately than a standard bundle adjustment algorithm across a wide range of noise levels.

Keywords: Estimation, Optimization algorithms, Variational methods
Abstract: In this paper, we propose the concept of accelerated convergence that has originally been developed to speed up the convergence of numerical methods for extremum seeking (ES) loops. We demonstrate how the dynamics of ES loops may be analyzed to extract structural information about the generated output of the loop. This information is then used to distil the limit of the loop without having to wait for the system to converge to it.

Keywords: Stochastic systems, Estimation
Abstract: We aim to analyze the behaviour of a finite-time stochastic system, whose model is not available, in the context of more rare and harmful outcomes. Standard estimators are not effective in making predictions about such outcomes due to their rarity. Instead, we use Extreme Value Theory (EVT), the theory of the long-term behaviour of normalized maxima of random variables. We quantify risk using the upper-semideviation rho(Y) := E(max{Y - mu,0}) of an integrable random variable Y with mean mu := E(Y). rho(Y) is the risk-aware part of the common mean-upper-semideviation functional, mu + lambda rho(Y) with lambda in [0,1]. To assess more rare and harmful outcomes, we propose an EVT-based estimator for rho(Y) in a given fraction of the worst cases. We show that our estimator enjoys a closed-form representation in terms of the popular conditional value-at-risk functional. In experiments, we illustrate the extrapolation power of our estimator using a small number of i.i.d. samples (<50). Our approach is useful for estimating the risk of finite-time systems when models are inaccessible and data collection is expensive. The numerical complexity does not grow with the size of the state space.

Keywords: Estimation, Identification for control, Optimization
Abstract: We consider the problem of on-line evaluation of critical characteristic parameters such as the L_2-gain, input feedforward passivity index and output feedback passivity index of non-linear systems using their input-output data. Typically, having an accurate measure of such emph{system indices} enables the application of systematic control design techniques. Moreover, if such system indices can efficiently be evaluated on-line, they can be exploited to design intelligent control solutions. However, the existing off-line estimation methods of such system indices are computationally inefficient and require a large amount of input-output data. On the other hand, the existing on-line estimation methods take an averaging-based approach, which may be sub-optimal, computationally inefficient and susceptible to estimate saturation. To overcome these challenges in the on-line estimation of system indices, we establish and exploit several interesting theoretical results on a particular class of fractional function optimization problems. Finally, we provide several numerical examples to highlight our contributions.

Keywords: Optimization algorithms, Distributed control
Abstract: Decentralized non-convex optimization is important in many problems of practical relevance. Existing decentralized methods, however, typically either lack convergence guarantees for general non-convex problems, or they suffer from a high subproblem complexity. We present a novel bi-level SQP method, where the inner quadratic problems are solved via ADMM. A decentralized stopping criterion from inexact Newton methods allows the early termination of ADMM as an inner algorithm to improve computational efficiency. The method has local convergence guarantees for non-convex problems. Moreover, it only solves sequences of Quadratic Programs, whereas many existing algorithms solve sequences of Nonlinear Programs. The method shows competitive numerical performance for an optimal power flow problem.

Keywords: Optimization algorithms, Machine learning, Distributed control
Abstract: This paper introduces a new method to efficiently solve distributed mixed-integer programs (MIP) as arising in problems of distributed machine learning or distributed control. The method is based on the alternating direction method of multipliers (ADMM), and it determines an exact penalty weight in order to close the duality gap of the MIP. The weight, which can be computed with low effort, allows one to formulate and solve a two-stage ADMM procedure for determining an optimum (or a sub-optimum) of the MIP. Numeric examples confirm the efficiency of the proposed method.

Keywords: Optimization algorithms, Machine learning, Optimization
Abstract: Federated learning is a framework for distributed optimization that places emphasis on communication efficiency. In particular, it follows a client-server broadcast model and is particularly appealing because of its ability to accommodate heterogeneity in client compute and storage resources, non-i.i.d. data assumptions, and data privacy. Our contribution is to offer a new federated learning algorithm, FedADMM, for solving non-convex composite optimization problems with non-smooth regularizers. We prove converges of FedADMM for the case when not all clients are able to participate in a given communication round under a very general sampling model.

Keywords: Optimization algorithms, Distributed control, Large-scale systems
Abstract: Alternating Directions Method of Multipliers (ADMM) is a form of decomposition-coordination method that typically requires several iterations/communication rounds between the subproblems and the master problem to converge. Repeatedly solving the subproblems over several iterations add to the total computation time. Noting that the subproblems solved from one iteration to the next differs only by a few variables, this paper proposes a novel sensitivity-assisted ADMM framework for nonlinear programming (NLP) problems, where the subproblems are cheaply approximated using the parametric sensitivities. By exploiting the parametric sensitivities, the computation of the subproblems can be reduced to a single linear solve instead of solving the full NLP problem, thereby reducing the overall computation cost. Different algorithmic variations are discussed and demonstrated using two numerical examples.

Keywords: Optimization algorithms, Distributed control
Abstract: Design of optimal distributed linear feedback controllers to achieve a desired aggregate behavior, while simultaneously satisfying state and input constraints, is a challenging but important problem in many applications. System level synthesis is a recent technique which has been used to reparametrize the optimal control problem as a convex program. Prior work on system level synthesis with state and input constraints has included closed-loop finite impulse response and locality constraints or, in the case where these constraints were lifted using a simple pole approximation, only a centralized design was considered. However, closed-loop finite impulse response and locality constraints cannot be satisfied in many applications. Furthermore, the centralized design using the simple pole approximation lacks robustness to communication failures and disturbances, has high computational cost and does not preserve data privacy of local controllers. The main contribution of this work is to develop a distributed solution to system level synthesis with the simple pole approximation in order to incorporate state and input constraints without closed-loop finite impulse response or locality constraints, and in a distributed implementation. To achieve this, it is first shown that the dual of this problem is a distributed consensus problem. Then, an algorithm is developed based on the alternating direction method of multipliers to solve the dual while recovering a primal solution, and a convergence certificate is provided. Finally, the method's performance is demonstrated on a test case of control design for distributed energy resources that collectively provide stability services to the power grid.

Keywords: Optimization algorithms, Networked control systems, Energy systems
Abstract: Latency is inherent in almost all real-world networked applications. In this paper, we propose a distributed resource allocation strategy over multi-agent networks with delayed communications. The state of each agent (or node) represents its share of assigned resources out of a fixed amount (equal to the overall demand). Every node locally updates its state towards optimizing a global allocation cost function via received information of its neighboring nodes even when the data exchange over the network is heterogeneously delayed at different links. The update is based on the alternating direction method of multipliers (ADMM) formulation subject to both sum-preserving coupling-constraint and local box-constraints. The solution is derivative-free and holds for general (not necessarily differentiable) convex cost models. We use the notion of augmented consensus over undirected networks to model delayed information-exchange for convergence analysis. We simulate our delay-tolerant algorithm for optimal energy reservation-production scheduling.

Keywords: Linear systems, Agents-based systems, Decentralized control
Abstract: In this paper, we consider a network of homogeneous LTI hybrid dynamics under time-driven aperiodic jumps and exchanging information over a fixed communication graph. Based on the notion of almost equitable partitions, we explicitly characterize the clusters induced by the network over the nodes and, consequently, the corresponding multi-consensus trajectories. Then, we design a decentralized control ensuring convergence of all agents to the corresponding multi-consensus trajectory. Simulations over an academic example illustrate the results.

Keywords: Linear systems, Autonomous systems
Abstract: We study dynamic consensus for general networked (homogeneous) linear autonomous systems, that is, it is only assumed that they are stabilizable. Dynamic consensus pertains to a general form of consensus in which, as a result of the systems' interactions, they exhibit a rich collective dynamic behavior. This generalizes the classical consensus paradigm in which case all systems stabilize to a common equilibrium point. Our main statements apply to systems interconnected over generic directed connected graphs and, most significantly, the proofs are constructive. Indeed, even though our controllers are reminiscent of others previously used in the literature, to the best of our knowledge, we provide for the first time in the literature strict Lyapunov functions for fully distributed consensus over generic directed graphs.

Keywords: Linear systems, Delay systems, Agents-based systems
Abstract: In this paper, we investigate the consensus problem of linear time-invariant systems with respect to stochastic noises and deterministic disturbances. We consider first-order dynamic agents interconnected by a directed communication graph with time delay, and we seek to determine the best achievable performance that measures the error in achieving consensus under the influence of noises and disturbances. Our results consist of analytical expressions of the minimal error achievable, measured under both mathcal{H}_2 and mathcal{H}_infty criteria. The expressions show explicitly how agent and network dynamics may interact to cast fundamentally dispersion effects on the consensus among the agents.

Keywords: Decentralized control, Distributed control, Robotics
Abstract: This work addresses the problem of distributed formation tracking for a group of follower holonomic mobile robots around a reference signal. The reference signal is comprised of the geometric center of the positions of multiple leaders. This work's main contribution is a novel Modulated Distributed Virtual Observer (MDVO) for the reference signal. Moreover, the proposed MDVO is based on an exact dynamic consensus algorithm with a prescribed convergence time. In addition, we provide simulation examples showcasing two different application scenarios for the proposal.

Keywords: Cooperative control, Distributed control, Networked control systems
Abstract: This paper deals with the output-feedback consensus problem for homogeneous linear multi-input multi-output multi-agent systems on directed graphs. A novel output-feedback protocol is proposed. A main merit of the protocol is that it only requires relative output measurement of neighboring agents, but does not need to exchange protocol state information through communication. Necessary and sufficient conditions are proposed for the existence of the protocol, which are shown to be feasible if the graph has a spanning tree and some easy-to-verify assumptions are imposed on agent dynamics. Consensus under the designed protocol is proved and consensus states are explicitly derived. Different from most of the existing related results, the proposed protocol still meets the separation principle-like property and thus the protocol gains are easy to compute. A numerical example is finally provided to demonstrate the effectiveness of the proposed protocol.

Keywords: Agents-based systems, Networked control systems, Cooperative control
Abstract: This paper proposes matrix-scaled consensus algorithm, which generalizes the scaled consensus algorithm in [1]. In (scalar) scaled consensus algorithms, the agents' states do not converge to a common value, but to different points along a straight line in the state space, which depends on the scaling factors and the initial states of the agents. In the matrix-scaled consensus algorithm, a positive/negative definite matrix weight is assigned to each agent. Each agent updates its state based on the product of the sum of relative matrix scaled states and the sign of the matrix weight. Under the proposed algorithm, each agent asymptotically converges to a final point differing with a common consensus point by the inverse of its own scaling matrix. Thus, the final states of the agents are not restricted to a straight line but can be extended to almost the whole state-space. Convergence analysis of matrix-scaled consensus for single and double-integrator agents are studied in detail. Simulation results are given to support the analysis.

Keywords: Stochastic systems, Agents-based systems, Randomized algorithms
Abstract: The objective of the paper is to establish a computable upper bound for the almost sure convergence rate for a class of ratio consensus algorithms defined via column-stochastic matrices. Our result extends the works of Iutzeler et al. from 2013 on similar bounds that have been obtained in a more restrictive setup with limited conclusions. The present paper complements the results by Gerencsér and Gerencsér from 2022, identifying the exact almost sure convergence rate of a wide class of ratio consensus algorithms in terms of a spectral gap, which is, however, not computable in general. The upper bound provided in the paper will be compared to the actual rate of almost sure convergence experimentally on a range of modulated random geographic graphs with random local interactions.

Keywords: Stochastic systems, Estimation, Identification
Abstract: The influence model (IM) is a discrete-time stochastic model that captures the spatiotemporal dynamics of networked Markov chains. Partially-observed IM (POIM) is an IM in which the statuses for some sites are unobserved. Identifiability and estimation of POIMs from incomplete state information are critical for POIM applications. In this paper, we develop a new estimation algorithm for both homogeneous and heterogeneous POIMs. The method, called EM-JMPE, integrates expectation maximization (EM) and joint-margin probability estimation (JMPE) to achieve reduced computation. In addition, we study the identifiability of POIMs by exploring the reduced-size joint-margin matrix, based on which necessary conditions for both homogeneous and heterogeneous POIMs are provided. The simulation studies verify the developed results.

Keywords: Stochastic systems, Game theory, Variational methods
Abstract: The study of complex political phenomena such as parties' polarization calls for mathematical models of political systems. In this paper, we aim at modeling the time evolution of a political system whereby various parties selfishly interact to maximize their political success (e.g., number of votes). More specifically, we identify the ideology of a party as a probability distribution over a one-dimensional real-valued ideology space, and we formulate a gradient flow in the probability space (also called a Wasserstein gradient flow) to study its temporal evolution. We characterize the equilibria of the arising dynamic system, and establish local convergence under mild assumptions. We calibrate and validate our model with real-world time-series data of the time evolution of the ideologies of the Republican and Democratic parties in the US Congress. Our framework allows to rigorously reason about various political effects such as parties' polarization and homogeneity. Among others, our mechanistic model can explain why political parties become more polarized and less inclusive with time (their distributions get "tighter"), until all candidates in a party converge asymptotically to the same ideological position.

Keywords: Stochastic systems, Markov processes, Constrained control
Abstract: The privacy issue has become one of the most critical concerns in cyber-physical systems (CPSs) as CPSs are vulnerable to information leakage. In particular, a passive intruder could infer the secret information of the system through observations, and the system may be critically compromised or damaged once the intruder has high confidence on certain secret states. In this paper, we investigate the planning problem of a stochastic system in the presence of a passive eavesdropping intruder. In this system, the planner is modeled as a Markov decision process (MDP) who can access the state information and control the system transition. The intruder, who has a partial observation of the system state, is modeled as a hidden Markov model. The goal of the intruder is to infer the secrets of the system in terms of whether the current system is in some sensitive states, and the goal of the defender is to maximize the reward while preventing the intruder from inferring the secret. Distinct from existing work that embedded privacy as a part of the reward or utility function, we quantify privacy as a constraint for the planning. The problem is formulated as a constrained partially observable MDP (POMDP) planning problem and a belief state partition approach is proposed to solve the privacy-preserving planning problem via value iteration. Our observation is that the defender could prevent the intruder from inferring sensitive information via belief manipulation. However, the introduction of the privacy concern may sacrifice the system performance or even cause the problem to be infeasible. A necessary and sufficient condition is given to check the feasibility of the planning problem and examples are shown to illustrate our proposed algorithm.

Keywords: Stochastic systems, Markov processes, Delay systems
Abstract: We introduce a finite memory interacting Polya urn process over a connected network which models consensus dynamics for interacting individuals. More specifically, each urn (individual) in the network is initially equipped with some red and black balls, with the fraction corresponding to the individual's opinion (or belief) on a certain color. At each time instant and for each urn, a ball is drawn from a ``super-urn", which consists of all balls present in that urn and its neighboring urns; then reinforcing balls of the color just drawn are added to the urn for a limited period of M future time instants, where M denotes the memory parameter. Additionally, and important for our objective, as of time t=M+1, we remove the balls which were present in the urns initially. By examining the structure of the resulting underlying reducible Markov process, we show that individuals eventually reach consensus in the sense that they all achieve identical probabilities of drawing a red ball. Moreover, when the network has homogeneous reinforcement parameters, we construct a class of linear dynamical systems with time delay whose trajectory gives the probability of drawing a red ball for each node i at a time instant t. We examine the asymptotic behavior of such a network and exactly determine its consensus value. Our simulation confirms our theoretical findings by demonstrating the asymptotic behavior of draw variables of the network in some case studies.

Keywords: Stochastic systems, Markov processes, Modeling
Abstract: Interesting posts are continually forwarded by the users of the online social network (OSN). Such propagation leads to re-forwarding of the post to some of the previous recipients, which increases as the post reaches a large number of users. Consequently, the effective forwards (after deleting the re-forwards) reduce, eventually leading to the saturation of the total number of copies. We model this process as a new variant of the branching process, the `saturated total-population-dependent branching process', and analyse it using the stochastic approximation technique. Notably, we obtain deterministic trajectories which approximate the total and unread copies of the post `asymptotically and almost surely' over any finite time window; this trajectory depends only on four parameters related to the network characteristics. Further, we provide expressions for the peak unread copies, maximum outreach and the life span of the post. We observe known exponential growth but with time-varying rates. We also validate our theory through detailed simulations on the SNAP Twitter dataset.

Keywords: Distributed parameter systems, Flexible structures, Kalman filtering
Abstract: Working from an observability characterization based on output energy sensitivity to changes in initial conditions, we derive both analytical and empirical observability Gramian tools for a class of continuum material systems. Using these results, optimal sensor placement is calculated for an Euler-Bernoulli cantilever beam for the following cases: analytical observability for the continuum system and analytical observability for a finite number of modes. Error covariance of an Unscented Kalman Filter is determined for both cases and compared to randomly placed sensors to demonstrate effectiveness of the techniques.

Keywords: Distributed parameter systems, Nonlinear systems
Abstract: In this article we show the existence and uniqueness of classical and generalized solutions of a class of nonlinear infinite dimensional systems. Such systems are obtained by modifying the second order differential equation that is part of the description of conservative linear systems "out of thin air" introduced by M. Tucsnak and G. Weiss in 2003. The modified system contains a new nonlinear damping term, that is maximal monotone and possibly set-valued and hence state trajectories obey a differential inclusion. We show that this new class of nonlinear infinite dimensional systems is incrementally scattering passive (hence well-posed). The proof is based on the Crandall-Pazy theorem which shows that the Lax-Phillips type nonlinear semigroup (that represents the entire system) is a contraction.

Keywords: Distributed parameter systems, Output regulation, Lyapunov methods
Abstract: The input-output stability (IOS) of a reaction-diffusion equation by means of a finite-dimensional linear time-invariant control system is studied. The reaction-diffusion plant admits a finite number of unstable poles and is open-loop unstable. The infinite-dimensional plant is put in feedback with a dynamic controller to achieve output stability via a Dirichlet boundary measurement and regulated output. The control design problem consists of deriving sufficient conditions in the form of matrix inequalities which allows us to show that the order of the finite-dimensional controller can be selected large enough to achieve IOS even when the control design is not optimal.

Keywords: Stability of linear systems, Distributed parameter systems, Linear systems
Abstract: Distributed port-Hamiltonian systems with boundary damping and possible internal dissipation are considered. The multiplier method is used to show exponential decay Me^{-alpha t} with an expression for M and alpha in terms of the system parameters. The exponential stability of port-Hamiltonian systems has been studied in the literature, but previous results did not provide an explicit bound on the decay rate. This result is illustrated by the boundary stabilization of a Timoshenko beam.

Keywords: Distributed parameter systems, Sampled-data control, Lyapunov methods
Abstract: The Stefan problem models a liquid-solid phase change phenomena as time evolution of a temperature profile in a liquid-solid material and its moving interface. This paper develops an event-triggered boundary control strategy for the one-phase Stefan problem. The proposed method consists of a full-state feedback backstepping boundary control law developed to drive the liquid-solid interface position to a desired setpoint and a dynamic event triggering mechanism which determines the time instants at which the control input requires to be updated. The existence of a minimal-dwell time between two consecutive events is proved, which eliminates the occurrence of the so-called textit{Zeno phenomenon} in the closed-loop system. The control input is updated at event times and applied in a textit{Zero-Order-Hold (ZOH)} fashion. The well-posedness of the closed-loop system along with certain model validity conditions is proved. Furthermore, using the Lyapunov approach, it is shown that the proposed control approach globally exponentially converges the temperature profile to the melting temperature of the material in L_2-norm and the moving interface to the desired setpoint. Finally, a simulation example is provided to validate the theoretical developments.

Keywords: Distributed parameter systems, Stability of linear systems, Lyapunov methods
Abstract: In this paper, we consider the exponential stabilisation of a distributed parameter port-Hamiltonian system interconnected with an unstable finite-dimensional linear system at its free end and control input at the opposite one. The infinite-dimensional system can also have in-domain anti- damping. The control design passes through the definition of a finite-dimensional linear system that “embeds” the response of the distributed parameter model, and that can be stabilised by acting on the available control input. The conditions that link the exponential stability of the latter system with the exponential stability of the original one are obtained thanks to a Lyapunov analysis. Simulations are presented to show the pros and cons of the proposed synthesis methodology.

Keywords: Hybrid systems, Networked control systems, Distributed control
Abstract: This paper explores the consensus problem for a homogeneous multi-agent system composed of agents with second-order dynamics. To promote scalability and efficient resource utilization, the agents communicate intermittently and asynchronously using an event-triggered control strategy. The approximate consensus problem is recast as a set stabilization problem, and sufficient conditions for stability are obtained through a Lyapunov-based analysis. Unlike previous results that only provide a stability analysis, we formulate a well-posed hybrid system that admits non-Zeno complete maximal solutions, renders the approximate consensus attractor robust to vanishing perturbations, employs triggers that have a positive minimum inter-event time, and achieves approximate consensus. Moreover, if the drift matrix is invertible and only has eigenvalues with non-positive real parts, then the average of the agent states is bounded and solutions of the hybrid system are bounded. In addition, the average consensus problem may be handled as a special case of the proposed formulation. Specifically, it is shown that, if the initial velocity of all agents is zero, then the MAS converges to the average of the initial conditions. Simulation results are provided to validate the development.

Keywords: Networked control systems, Lyapunov methods
Abstract: In this paper, we propose a new event-triggering approach to schedule control data transmissions in state feedback control of linear time-invariant dynamical systems. Specifically, an energy function-based and norm-free event-triggering condition is presented, where the embedded processor broadcasts a sampled data of its control signal value through a zero-order-hold operator to the dynamical system when the left side of the event-triggering condition equals to its right side. Here, the energy function-based feature implies that the right side of this event-triggering condition involves an energy function as well as its time-derivative for making the selection of its right side user-adjustable. Moreover, the norm-free feature implies that the left side of this event-triggering condition does not depend on signal norms to yield better control data transmission reduction. We also present illustrative numerical examples in order to demonstrate the efficacy of the proposed event-triggering approach in scheduling state feedback control data transmissions.

Keywords: Agents-based systems, Networked control systems, Control of networks
Abstract: It is well known that the employed triggering scheme has great impact on the control performance when control loops operate under scarce communication resources. Various practical and simulative works have demonstrated the potential of event-triggered control to reduce communication while providing a similar performance level when compared to time-triggered control. For non-cooperative networked control systems, analytical performance comparisons of time- and event-triggered control support this finding under certain assumptions. While being well-studied in the non-cooperative setting, it remains unclear if and how the performance relationship of the triggering schemes is altered in a multi-agent system setup. To close this gap, in this paper, we consider a homogeneous single-integrator multi-agent consensus problem for which we compare the performance of time- and event-triggered control schemes analytically. Under the assumption of equal average triggering rates, we use the long-term average of the quadratic deviation from consensus as a performance measure to contrast the triggering schemes. Contrary to the non-cooperative setting, we prove that event-triggered control performs worse than time-triggered control beyond a certain number of agents in this setup. In addition, we derive the asymptotic order of the performance measure as a function of the number of agents under both triggering schemes.

Keywords: Stability of linear systems, Robust control
Abstract: We provide a new event-triggered delay compensation approach for linear systems with arbitrarily long constant input delays. Our prediction map is expressible as a solution of a discrete time system. Our method ensures input-to-state stability. We also provide an analog under measurement delays, where the prediction map is expressible as a solution of a continuous-discrete system. Significant novel features are our combined use of matrices of absolute values and our prediction based event triggers, instead of Euclidean norms, and the fact that the predictor dynamics always has the same dimension as that of the original system. Our marine robotic example illustrates an advantage of using our new methods.

Keywords: Discrete event systems, Stability of nonlinear systems, Stability of hybrid systems
Abstract: In systems where the ability to actuate is a scarce resource, e.g., spacecrafts, it is desirable to only apply a given controller in an intermittent manner---with periods where the controller is on and periods where it is off. Motivated by the event-triggered control paradigm, where state-dependent triggers are utilized in a sample-and-hold context, we generalize this concept to include state triggers where the controller is off thereby creating a framework for intermittent control. Our approach utilizes certificates---either Lyapunov or barrier functions---to design intermittent trigger laws that guarantee stability or safety; the controller is turned on for the period for which is beneficial with regard to the certificate, and turned off until a performance threshold is reached. The main result of this paper is that the intermittent controller scheme guarantees (set) stability when Lyapunov functions are utilized, and safety (forward set invariance) in the setting of barrier functions. As a result, our trigger designs can leverage the intermittent nature of the actuator, and at the same time, achieve the task of stabilization or safety. We further demonstrate the application and benefits of intermittent control in the context of the spacecraft orbit stabilization problem.

Keywords: Networked control systems, Constrained control, Nonlinear systems
Abstract: This paper addresses the practical master-slave synchronization of nonlinear discrete-time Lur’e systems subject to saturation using event-triggered control. Considering an emulation approach, the aim is to design an event generator that features a relaxed triggering criterion to reduce the number of control updates. Constructive conditions for generic slope-restricted nonlinearities are derived to ensure the regional practical stabilization of the synchronization error, i.e., to guarantee that it converges to a specified vicinity of the origin. In order to tune the event generator parameters, an optimization problem is proposed aiming at reducing the number of events when compared to triggering functions without relaxations. An illustrative example shows the advantages of our approach.

Keywords: Predictive control for linear systems, Closed-loop identification, Adaptive control
Abstract: In this paper we develop a recursive linear predictive control algorithm with integral action and plug-and-play capabilities. Typically, adaptive model predictive control requires a recursive estimation step for updating the prediction model and then builds prediction matrices on-line. In contrast to this approach, we develop a least-squares algorithm for recursively estimating the prediction matrices directly. We then exploit an analytic relation between standard and integral prediction matrices to recursively estimate the latter. Furthermore, to assess the convergence of the closed-loop estimation, we discuss various methods that generate a persistently exciting input. The efficiency of the recursive integral predictive controller is demonstrated on a motion control application.

Keywords: Predictive control for linear systems, Emerging control applications, Machine learning
Abstract: This paper presents a robust finite-horizon control scheme based on data that produces feasible control sequences. The scheme makes use of a database that includes information from prior experiences of the same and others controllers handling similar systems. By the convex combination of feasible histories plus an auxiliary control law that deals with uncertainties, this scheme can be used as a robust historian-based predictive controller. Further application could include a cooperative learning-based strategy in which multiple controllers share their previous executions to gain collective benefits in terms of performance. The validity of the proposed controller is tested in a simulated case study.

Keywords: Predictive control for linear systems, Linear systems
Abstract: Linear-quadratic-Gaussian (LQG) control is a classical optimal control problem where the disturbance in the system dynamics is traditionally treated as random noise. Motivated by the possibility of forecasting future disturbance in some relevant works for linear-quadratic regulator (LQR) systems where the disturbance distribution is arbitrary, we introduce a time-varying disturbance forecast model in the LQG problem. Our model characterizes the Gaussianity of the disturbances and thus enables us to give theoretical results including optimal average cost even though the forecast error can be unbounded. Numerical examples are provided to illustrate the theoretical results.

Keywords: Predictive control for linear systems, Neural networks, Randomized algorithms
Abstract: Stochastic Model Predictive Control (MPC) gained popularity thanks to its capability of overcoming the conservativeness of robust approaches, at the expense of a higher computational demand. This represents a critical issue especially for sampling-based methods. In this work we propose a policy learning MPC approach, which aims at reducing the cost of solving stochastic optimization problems. The presented scheme relies upon the use of neural networks for identifying a mapping between the current state of the system and the probabilistic constraints. This allows to reduce the sample complexity to be less than or equal to the dimension of the decision variable, significantly scaling down the computational burden of stochastic MPC approaches, while preserving the same probabilistic guarantees. The efficacy of the proposed policy-learning MPC is proved by means of a numerical example.

Keywords: Predictive control for linear systems, Identification for control
Abstract: This paper contrasts recursive state space models and direct multi-step predictors for linear predictive control. We provide a tutorial exposition for both model structures to solve the following problems: 1. stochastic optimal control; 2. system identification; 3. stochastic optimal control based on the estimated model. Throughout the paper, we provide detailed discussions of the benefits and limitations of these two model parametrizations for predictive control and highlight the relation to existing works. Additionally, we derive a novel (partially tight) constraint tightening for stochastic predictive control with parametric uncertainty in the multi-step predictor.

Keywords: Predictive control for linear systems, Optimal control, Machine learning
Abstract: We show that the explicit realization of data-driven predictive control (DPC) for linear deterministic systems is more tractable than previously thought. To this end, we compare the optimal control problems (OCP) corresponding to deterministic DPC and classical model predictive control (MPC), specify its close relation, and systematically eliminate ambiguity inherent in DPC. As a central result, we find that the explicit solutions to these types of DPC and MPC are of exactly the same complexity. We illustrate our results with two numerical examples highlighting features of our approach.

Keywords: Emerging control applications, Information technology systems, Optimization
Abstract: Online advertising is mostly served through real-time bidding, and advertising campaigns are often defined as optimization problems. Historically, these problems consider only the advertiser return on investment subject to constraints specified by the advertiser. The operational cost of the optimization platform is typically not accounted for explicitly. This paper addresses this limitation of previous work by including a cost per bid constraint to an otherwise advertiser-centric optimization problem. Maintaining the constraint prevents the operational cost of the platform to exceed what the platform provider charges the advertiser for the service. The optimal bidding mechanism is derived and it is shown how the solution can be implemented as four separate subsystems. Feedback control plays an important role to make this optimization scalable and adaptive. A proof of concept campaign control system is proposed and evaluated in simulations.

Keywords: Emerging control applications, Lyapunov methods, Nonlinear output feedback
Abstract: One of the critical technologies in plasma etching in semiconductor wafers is radio frequency impedance matching control. An impedance matching network is essential to ensure the maximum power transfer in any system, and its application is ubiquitous. Many researches have been proposed control strategies to get a robust performances, reduce convergence speed, and more accurate. However, these proposal present a non-monotonic decreasing behavior of the reflected power, thus affecting the overall matching control performance. In this paper, we propose a controller technique, based on a Control Lyapunov Function (CLF), which ensures global asymptotic stability of the system. This takes place under a safe space of capacitor values defined by a control barrier function (CBF). Numerical simulations on a benchmark setup show the novelty of the proposed control scheme. Concerning others in the literature, it presents lower convergence time and robustness under several non-ideal conditions. Also, our study includes analysis of other indexes like the mean and maximum value of the reflection coefficient integral and reflected power.

Keywords: Emerging control applications, Quantized systems, Large-scale systems
Abstract: In this paper, we present a distributed version of the k-means algorithm for multi-agent systems with directed communication links. The goal of k-means is to partition the network's agents in mutually exclusive sets (groups) such that agents in the same set have (and possibly share) similar information and are able to calculate a representative value for their group. Our distributed algorithm allows each node to transmit quantized values in an event-driven fashion, and exhibits distributed stopping capabilities. Transmitting quantized values leads to more efficient usage of the available bandwidth and reduces the communication bottleneck, whereas distributed stopping preserves available resources. We characterize the properties of the proposed distributed algorithm and show that its execution (on any static and strongly connected digraph) will partition all agents in mutually exclusive clusters in finite time. We conclude with examples that illustrate the operation, performance, and potential advantages of the proposed algorithm.

Keywords: Variable-structure/sliding-mode control
Abstract: In this manuscript a robust stabilization controller for the Furuta's pendulum in presence of parametric uncertainties is proposed. We used a normal form transformation and partial feedback linearisation to tackle the problem with a cascade system approach, then a continuous sliding mode algorithm stabilize the cascade system. A closed-loop stability analysis is presented to proof asymptotic stability of the Furuta's pendulum equilibrium point. Also, experiments over a real Furuta's pendulum are presented to corroborate the theoretical results shown.

Keywords: Transportation networks, Emerging control applications
Abstract: Last-mile delivery services have become ubiquitous in the recent past. Delivery services for food (eg., DoorDash, Grubhub, Uber Eats) and groceries (eg., Instacart, Cornershop) earned a combined revenue of 25B in 2020, and are expected to exceed 72B in revenues by 2025. The COVID-19 pandemic accelerated the growth of such services by making their value proposition even more attractive. The lower risk of contact coupled with the convenience of ordering from the comfort of their homes led to widespread customer adoption. Even so, most last-mile delivery services are not profitable. The high cost of delivery is cited as the major cause of losses. Thus, analyzing the factors influencing delivery costs is crucial for understanding the long-term viability of these services. The pooling of orders is a critical source of efficiency in last-mile delivery. We propose a queuing-based spatial model for the delivery process to analyze the value created by pooling. We demonstrate how the trade-off between delivery times and the cost of delivery, mediated by the extent of pooling, dictates which services will be economically viable. Our simulation study of a typical grocery delivery service in Los Angeles, California suggests that delivery times of less than 1 hour are unprofitable for most regions in the US. We find that driver wages account for 90% of the delivery cost. We also discuss the potential impact of technological innovations such as automated delivery and labor regulations on the profitability of last-mile delivery services.

Keywords: Building and facility automation, Control applications, Process Control
Abstract: Active latent heat storage (ALHS) involving phase-change materials constitutes a promising energy-efficient solution for building energy management (BEM). Current BEM systems based on conventional reactive control lack the level of control delicacy required to exploit the full potential of ALHS for BEM. This study proposes a smart model predictive control (MPC) approach for BEM to minimize energy costs while maintaining indoor climate by fully applying ALHS. An MPC framework considering ALHS dynamics and dynamic electricity prices is proposed. A case study entailing a set of simulations is designed based on a single-family house with a space heating system integrated with ALHS. The proposed MPC approach, compared to conventional reactive control, enables more than 70% of reductions in electricity costs. Further analysis reveals that coupling ALHS with MPC is critical to exploiting the ALHS potential for BEM: while conventional reactive control of an ALHS-equipped building increases the electricity cost, an MPC-enabled building could reduce the electricity cost by 45.1% due to ALHS adoption.

Keywords: Nonlinear systems, Optimal control, Stability of nonlinear systems
Abstract: This paper considers an approximate solution of the event-triggered Hamilton-Jacobi-Bellman (ET-HJB) equation to derive a finite-time suboptimal event-triggered control law for a class of nonlinear systems. To reduce the communication and computation overhead, the control law is computed and actuated after violating a predefined state-dependent event triggering condition. To obtain the controller gain, the ET-HJB equation is approximated as a state-dependent differential Riccati equation (SDRE). After converting the ET-HJB into an SDRE, a frozen time concept is used to eliminate the issues related to state dependency in the system and input matrices between two consecutive events. This helps reframe the SDRE into a simple differential Riccati equation (DRE), where the state-dependent system and input matrices remain fixed until the next event occurs. Using the solution of a differential Lyapunov equation, the solution of the DRE is computed forward in time. The designed event-triggered control law is readily amenable to an online implementation, and also it ensures the input-to-state stability of closed-loop systems. Simulation results are reported to prove the efficacy of the proposed control approach.

Keywords: Optimal control, Nonlinear systems, Constrained control
Abstract: A conventional optimal control problem subject to state constraints is investigated. The controllability matrix is presented and the normality condition is formulated as the condition of full rank for this matrix. As an application of the obtained result, the normality of solution to calculus of variation problem with state constraints and fixed endpoints is justified. The approach is employed which also ensures the property of controllability of the constrained control system in question.

Keywords: Optimal control, Predictive control for nonlinear systems, Optimization algorithms
Abstract: We propose an approximate algorithm for Nonlinear Model Predictive Control (NMPC) which is based on a reformulation of the inequality constrained optimal control problem using barrier terms and squashing functions. Within an SQP framework, the particular structure of the reformulated problem can be leveraged by using a Generalized Gauss-Newton Hessian approximation. Moreover, the quadratic subproblems can be efficiently solved using a single backward and forward sweep of the Ricatti recursion. We show locally linear convergence of the proposed algorithm, as well as locally quadratic convergence in the case of linear system dynamics. The computational speed-up, which can be achieved with the proposed method, is illustrate in a simulation study.

Keywords: Optimal control, Nonlinear systems, Robotics
Abstract: Drifters are energy-efficient sampling platforms for waterways and other water bodies with pronounced flows. The motion of passive drifters is determined by the underlying flow and thus limited. To overcome this limitation and enhance maneuverability, we consider an active drifter, which has a variable control surface for modulating the hydrodynamic drag force, and a thruster for propulsion or braking. In order to maintain the active drifter as an energy-efficient platform, the use of the thruster must be sparing and carefully considered. In this paper we present an optimal control problem for a one-degree-of-freedom active drifter system, where the cost function aims to balance the objectives of shortest time and minimal thruster use. Despite the complex, realistic nonlinear dynamics of the active drifter, an analytical solution to the optimal control is found by exploiting Pontryagin's Minimum Principle. In particular, for a given desired final state, each candidate optimal control solution is propagated backward in time, to compute the points in the state space where the optimal control switches; such points are parameterized by the co-state variables, linked implicitly to the system's initial conditions. The proposed approach naturally results in a final-state-dependent partition of the state space, where each region corresponds to a given optimal control value. A feedback control law is readily derived from the aforementioned map. The efficacy of the proposed approach is supported with a numerical example, where the trade-off between time-optimality and fuel-efficiency is illustrated.

Keywords: Optimal control, Optimization, Cooperative control
Abstract: This paper investigates the problem of cooperative tuning of multi-agent optimal control systems, where a network of agents (i.e. multiple coupled optimal control systems) adjusts parameters in their dynamics, objective functions, or controllers in a coordinated way to minimize the sum of their loss functions. Different from classical techniques for tuning parameters in a controller, we allow tunable parameters appearing in both the system dynamics and the objective functions of each agent. A framework is developed to allow all agents to reach a consensus on the tunable parameter, which minimizes team loss. The key idea of the proposed algorithm rests on the integration of consensus-based distributed optimization for a multi-agent system and a gradient generator capturing the optimal performance as a function of the parameter in the feedback loop tuning the parameter for each agent. Both theoretical results and simulations for a synchronous multi-agent rendezvous problem are provided to validate the proposed method for cooperative tuning of multi-agent optimal control.

Keywords: Numerical algorithms, Optimal control, Sampled-data control
Abstract: In this paper, we introduce an approximation method to solve an optimal control problem via the Lagrange dual of its weak formulation, which applies to problems with an unknown, non-necessarily polynomial, dynamics accessed through samples, akin to model-free reinforcement learning. It is based on a sum-of-squares representation of the Hamiltonian, and extends a previous method from polynomial optimization to the generic case of smooth problems. Such a representation is infinite-dimensional and relies on a particular space of functions – a reproducing kernel Hilbert space – chosen to fit the structure of the control problem. After subsampling, it leads to a practical method that amounts to solving a semi-definite program. We illustrate our approach numerically on a low-dimensional control problem.

Keywords: Observers for nonlinear systems, Hybrid systems, Nonlinear systems
Abstract: Various methods are nowadays available to design observers for broad classes of systems. Nevertheless, the question of the tuning of the observer to achieve satisfactory estimation performance remains largely open. This paper presents a general supervisory design framework for online tuning of the observer gains with the aim of achieving various trade-offs between robustness and speed of convergence. We assume that a robust nominal observer has been designed for a general nonlinear system and the goal is to improve its performance. We present for this purpose a novel hybrid multi-observer, which consists of the nominal one and a bank of additional observer-like systems, that are collectively referred to as modes and that differ from the nominal observer only in their output injection gains. We then evaluate on-line the estimation cost of each mode of the multi-observer and, based on these costs, we select one of them at each time instant. Two different strategies are proposed. In the first one, initial conditions of the modes are reset each time the algorithm switches between different modes. In the second one, the initial conditions are not reset. We prove a convergence property for the hybrid estimation scheme and we illustrate the efficiency of the approach in improving the performance of a given nominal high-gain observer on a numerical example.

Keywords: Observers for nonlinear systems, Hybrid systems, Stability of hybrid systems
Abstract: We propose a hybrid sensorless observer for permanent magnet synchronous machines with global asymptotic stability guarantees. Exploiting the constraint of the rotor flux on a circle of unknown radius, we design an integrator system with periodic jumps triggered by a clock to generate a linear regression containing the flux estimation error. Then, a normalized projected gradient descent identifier provides the observer estimates. For the closed-loop system, it is shown that there is a robustly globally asymptotically stable compact attractor, which, additionally, ensures zero estimation error if appropriate Persistency of Excitation (PE) conditions are satisfied. In this respect, sufficient conditions ensuring PE are provided for the angular speed and the clock period.

Keywords: Observers for nonlinear systems, Distributed parameter systems, Estimation
Abstract: An adaptive observer is designed for online estimation of Hilbert-Schmidt operators from online measurement of part of the state for some class of nonlinear infinite-dimensional dynamical systems. Convergence is ensured under detectability and persistency of excitation assumptions. The class of systems considered is motivated by an application to kernel reconstruction of neural fields, commonly used to model spatiotemporal activity of neuronal populations. Numerical simulations confirm the relevance of the approach.

Keywords: Observers for nonlinear systems, Uncertain systems
Abstract: This paper presents a novel interval observer design for uncertain locally Lipschitz continuous-time (CT) and discrete-time (DT) systems with noisy nonlinear observations that is input-to-state stable (ISS) and minimizes the L1-gain of the observer error system with respect to the uncertainties. Using mixed-monotone decompositions, the proposed observer is correct and positive by construction without the need for additional constraints/assumptions. This, in turn, allows us to directly leverage techniques for positive systems to design an ISS and L1-robust interval observer via (mixed-integer) linear programs instead of semi-definite programs with linear matrix inequalities. Further, our observer design offers additional degrees of freedom that may serve as a surrogate for coordinate transformations. Finally, we demonstrate the effectiveness of our proposed observer on some CT and DT systems.

Keywords: Observers for nonlinear systems, LMIs, Estimation
Abstract: This paper deals with observer design for a class of Lipschitz nonlinear systems. Specifically, we propose a mathematically rigorous technique to handle systems having non-globally Lipschitz properties on the whole set mathbb{R}^{n}. The unique assumption made on the nonlinearity is for it to be Lipschitz on a compact convex set Omega subset mathbb{R}^{n}, in which lives the system state. The idea consists in extending the nonlinear function to become globally Lipschitz on the whole space mathbb{R}^{n}. Such an extension is performed by using the famous Hilbert projection theorem, which generalizes some existing results in the literature. The projection is then involved in the observer structure to overcome the non-satisfaction of the global property by the original nonlinear function. More importantly, to overcome the conservatism related to the boundedness of the system states, an extension to systems having only some bounded states is proposed under different but less conservative assumptions. It is shown that all the previous observer design methods in the literature that rely on a global Lipschitz property can be applied straightforwardly without changing their synthesis conditions.

Keywords: Observers for nonlinear systems, Observers for Linear systems
Abstract: This work establishes a new approach for a linearization based non-asymptotic state observer design. To receive a linear input-output relation of the nonlinear system for the state observer and to avoid the necessity of time-derivatives of the measurement and actuator signals, a combination of linearization with the modulating function technique is applied. The estimates are obtained non-asymptotically using a sliding time window of finite length. This procedure allows a continuous-time and recursive update of the state estimates and extends the possible applications of the modulating function technique to a wider range of nonlinear systems. The class of unitary modulating functions is introduced to ensure the solvability of the estimation problem when subject to time-varying coefficients generated from the linearized state trajectory. Two examples illustrate the real-time capability of the algorithm.

Keywords: Stability of nonlinear systems, Machine learning, Network analysis and control
Abstract: Motivated by advances in neuroscience and machine learning, this paper is concerned with the modeling and analysis of Hopfield neural networks with dynamic recurrent connections undergoing Hebbian learning. To capture the synaptic sparsity of neural circuits, we propose a low dimensional formulation for the model and then characterize its key dynamical properties. First, we give a biologically-inspired forward invariance result. Then, we give sufficient conditions for the non-Euclidean contractivity of the model. Our contraction analysis leads to stability and robustness of time-varying trajectories -- for networks with both excitatory and inhibitory synapses governed by both Hebbian and anti-Hebbian rules. Our proposed contractivity test is based upon biologically meaningful quantities, e.g., neural and synaptic decay rate, maximum out-degree, and the maximum synaptic strength. Finally, we show that the model satisfies Dale's principle. The effectiveness of our results is illustrated via a numerical example.

Keywords: Neural networks, Estimation, Distributed parameter systems
Abstract: In this work, we propose a distributed adaptive observer for a class of nonlinear networked systems inspired by biophysical neural network models. Neural systems learn by adjusting intrinsic and synaptic weights in a distributed fashion, with neuronal membrane voltages carrying information from neighbouring neurons in the network. We show that this learning principle can be used to design an adaptive observer based on a decentralized learning rule that greatly reduces the number of observer states required for exponential convergence of parameter estimates. This novel design is relevant for biological, biomedical and neuromorphic applications.

Keywords: Stochastic systems, Hybrid systems, Biological systems
Abstract: Action potential (AP)-triggered neurotransmitter release forms the key basis of inter-neuronal communication. We present a stochastic hybrid system model that captures the release of neurotransmitter-filled vesicles from a presynaptic neuron. More specifically, vesicles arrive as a Poisson process to attach to a given number of docking sites, and each docked vesicle has a certain probability of release when an AP is generated in the presynaptic neuron. The released neurotransmitters enhance the membrane potential of the postsynaptic neuron, and this increase is coupled to the continuous exponential decay of the membrane potential. The buildup of potential to a critical threshold level results in an AP firing in the postsynaptic neuron, with the potential subsequently resetting back to its resting level. Our model analysis develops formulas that quantify the fluctuations in the number of released vesicles and mechanistically connects them to fluctuations in both the postsynaptic membrane potential and the AP firing times. Increasing the frequency of APs in the presynaptic neuron leads to saturation effects on the postsynaptic side, resulting in a limiting frequency range of neurotransmission. Interestingly, AP firing in the postsynaptic neuron becomes more precise with increasing AP frequency in the presynaptic neuron. We also investigate how noise in the AP timing varies with different parameters, such as the probability of releases, the number of docking sites, the voltage threshold for AP firing, and the timescale of voltage decay. In summary, our results systematically explain how stochastic mechanisms in neurotransmission enhance or impinge the precision of AP fringing times.

Keywords: Linear systems, Nonlinear systems, Stochastic systems
Abstract: Understanding the dynamics resulting from large-scale populations of systems poses one of the greatest challenges ahead of modern science. While it is often expected that the emerging dynamics from such populations compound in complexity, we here show that, on the contrary, the aggregation of complex individual dynamics can in fact lead to simpler behavior overall. In particular, mounting empirical evidence from neuroscience and beyond has pointed out the linearity of macroscopic dynamics that result from the interaction of large populations of microscopic subsystems, despite the highly nonlinear dynamics possessed by the individual subsystems. Rigorous analyses and theoretical grounds for such observations, however, have remained lacking. In this paper, we develop a general theoretical framework showing that the average dynamics of a broad family of populations of nonlinear stochastic subsystems converge to linear time-varying (LTV) dynamics transiently and to linear time-invariant (LTI) dynamics in steady state. Simulations are provided to illustrate this effect in populations of static (feedforward) nonlinear maps as well as a wide range of nonlinear systems exhibiting bistable, limit cycle, and chaotic dynamics.

Keywords: Nonlinear systems, Biological systems, Network analysis and control
Abstract: In the human brain, highly recurrent cortical circuitry supports information processing, coordinates learning episodes, and regulates healthy and diseased states. A key outstanding challenge of neural engineering is to ultimately control the collective dynamics of distinct neural populations, so as to promote the emergence or recovery of desired activity patterns. In this paper, we investigate the control of a general rate model of neural activity with rectified activation function. We first show that any target state in the open positive orthant can be reached in finite time. Furthermore, we present an array of results to perform (feedback and feedforward) efficient control in prototypical classes of networks with distinct connection types and in the case of sparse control inputs. Due to the relevance of rate models in both biological and artificial neural networks, our results lay the groundwork to enhance the dynamical behavior of in vivo and synthetic neural circuitry.

Keywords: Biological systems, Networked control systems, Nonlinear systems
Abstract: Cluster synchronization underlies various functions in the brain. Abnormal patterns of cluster synchronization are often associated with neurological disorders. Deep brain stimulation (DBS) is a neurosurgical technique used to treat several brain diseases, which has been observed to regulate neuronal synchrony patterns. Despite its widespread use, the mechanisms of DBS remain largely unknown. In this paper, we hypothesize that DBS plays a role similar to vibrational control since they both highly rely on high-frequency excitation to function. Under the framework of Kuramoto-oscillator networks, we study how vibrations introduced to network connections can stabilize cluster synchronization. We derive some sufficient conditions and also provide an effective approach to design vibrational control. Also, a numerical example is presented to demonstrate our theoretical findings.

Keywords: Switched systems, Stability of hybrid systems, Lyapunov methods
Abstract: We address the problem of setpoint regulation for cascaded minimum-phase linear systems interconnected through a scalar hysteresis, modeled as a Prandtl-Ishlinskii operator. Employing well-posed constrained differential inclusions to represent the hysteretic dynamics, we formulate the control problem in terms of stabilization of a compact set of equilibria depending on the hysteresis states. For our design, we firstly consider a proportional-integral controller for linear systems with hysteretic input, and provide model-free sufficient conditions based on high-gain arguments for closed-loop stability. Then, the controller is dynamically extended to obtain an inversion-free stabilizer of the overall cascade. For the presented schemes, we prove robust global asymptotic stability of a compact set that ensures setpoint regulation, regardless of the hysteresis states.

Keywords: Switched systems, Markov processes, Stability of hybrid systems
Abstract: This work provides 1-moment stability conditions for discrete-time Markov Jump Linear Systems under time-homogeneous and time-inhomogeneous transition probabilities. For the latter, we further address the polytopic switching case. The analysis is carried out leveraging the comparison principle and the theory of positive systems, without nevertheless limiting the overall analysis to the latter. We provide sufficient stability conditions that only involve non-negative matrices and can be checked via linear programming.

Keywords: Switched systems, Time-varying systems, Stability of linear systems
Abstract: We establish exponential stability for a class of linear systems with slow and fast time variation and switching. We use the averaging method to approximate the original system by the average system which only exhibits slow time variation and switching. We then apply a stability criterion recently developed for such systems to prove stability of the average system and, consequently, of the original system.

Keywords: Switched systems, Uncertain systems, LMIs
Abstract: This paper deals with switched affine systems control ensuring asymptotic stability of an unknown equilibrium point. More specifically, our study is focused on the class of systems with the affine term depending linearly on an uncertain vector, which can be used to model input and load variations of dc-dc power converters. The main goal is to design a switching function that governs the state trajectories towards an unknown equilibrium point containing in one of its components the desired value specified by the designer. The other components are adapted in real time based on the uncertainty estimation. The design conditions are solved by a two-steps procedure expressed in terms of linear matrix inequalities, and they do not require any stability property of the individual subsystems. The control design of a dc-dc flyback converter is used for illustration and comparison together with an academic example composed of two third order unstable subsystems.

Keywords: Switched systems, Large-scale systems, Constrained control
Abstract: Ensuring feasibility in externally switched systems usually requires identifying time-varying, control invariant (CI) sets that ensure state and input constraints can be respected under any possible switching signal. As with traditional, time-invariant CI sets, these time-varying constraints can be very difficult to compute for higher dimensional systems. Furthermore, if multiple switching signals are present, the number of switching sequences that must be considered grows exponentially. Previous works would struggle to account for this growth. Inspired by distributed systems, this work examines a class of high dimensional systems with multiple switching signals. The switching signals are constrained using directed graphs that are significantly more flexible than dwell time based methods. An iterative algorithm is developed that computes the time-varying CI sets for this class of systems. Critically, this algorithm is parallelized over the number of agents, preventing the exponential growth in computation time as agents are added to the system. The scalability of the results is demonstrated on a randomized numerical example.

Keywords: Switched systems, Control over communications
Abstract: This paper studies the security issue of switched systems suffering from disturbance and asynchronous denial of service (DoS) attacks. To this end, an active control strategy is presented to deal with the asynchronous DoS attacks. The switching signal is designed to guarantee the uniformly ultimate boundedness when the mismatched behavior between subsystem mode and controller mode is involved. Moreover, an algorithm calculating the converging bound is suggested. Finally, the effectiveness of the results is verified by a numerical example.

Keywords: Adaptive control, Direct adaptive control, Constrained control
Abstract: The paper addresses the problem of adaptive backstepping control of nonlinear parametrically uncertain plants with constrained input and unknown control gain. The main focus of the paper consists in design of a modular controller with improved parameters tuning achieved by complete compensation of the tuning rate in the closed-loop system and applying a Kreisselmeier-type adaptation algorithm generating high-order time derivatives (HOTD) of the adjustable parameters. It is shown that the transients of the adjustable parameters can be accelerated by increasing the adaptation gain without significant increase of the initial swing of the tracking error.

Keywords: Adaptive control, Decentralized control, Cyber-Physical Security
Abstract: This paper introduces a decentralized adaptive control scheme for networks of cyber-physical systems under sensor and coordinated actuator attacks. First, a simplified model, in which each node system is isolated, is studied. A partially adaptive controller with a non-adaptive linear component and an adaptive nonlinear component is proposed: this guarantees bounded system trajectories and asymptotic regulation of the state. Then, the whole network system under coordinated actuator attacks is studied and a decentralized fully adaptive controller is proposed. By jointly placing the fully adaptive controller and the partially adaptive controller, according to the so-called feedback vertex set of the underlying graph, boundedness and convergence properties of the simplified model can be guaranteed for the entire network. Finally, a simulation example for a multi-stage water distribution system is presented. The results show that the proposed controller guarantees robustness of the closed-loop network system against sensor and coordinated actuator attacks and it is capable of restoring the transient performance to that of the attack-free case.

Keywords: Adaptive control, Direct adaptive control, Automotive control
Abstract: Adaptive control strategies usually are designed based on gradient methods for the sake of simplicity in Lyapunov analysis. However, least squares (LS)-based parameter identifiers, with proper selection of design parameters, exhibit better transient performance than the gradient-based ones, from the aspects of convergence speed and robustness to measurement noise. On the other hand, most of the LS-based adaptive control procedures are designed via the indirect adaptive control approaches, due to the difficulty in integrating an LS-based adaptive law within the direct approaches starting with a certain Lyapunov-like cost function to be driven to (a neighborhood of) zero. In this paper, a formal constructive analysis framework is proposed to integrate the recursive LS-based parameter identification with direct adaptive control. Application of the proposed procedure in adaptive cruise control design is studied through Matlab/Simulink and CarSim simulations, validating the analytical results.

Keywords: Adaptive control, Delay systems, LMIs
Abstract: Recently a new time-delay approach was introduced for extremum seeking (ES), but the results were confined to static maps. In the present paper, the time-delay approach is extended for the 1st time to ES of dynamic maps in the case of scalar plants. We not only provide a precise perturbed system of ES without any approximation, but also suggest a direct Lyapunov-Krasovskii method for the transformed time-delay plant to find efficient stability conditions for the closed-loop ES system in the form of linear matrix inequalities (LMIs). Differently from the approaches based on classical averaging and Lie brackets, we provide the quantitative bounds on the frequency and the resulting extremum seeking error, under assumption that the extremum point, the extremum value and the Hessian are uncertain from some known intervals.

Keywords: Adaptive control, Networked control systems, Machine learning
Abstract: In recent years, there has been considerable interest in reinforcement learning for linear quadratic Gaussian (LQG) systems. In this paper, we consider a generalization of such systems where the controller and the plant are connected over an unreliable packet drop channel. Packet drops cause the system dynamics to switch between controlled and uncontrolled modes. This switching phenomena introduces new challenges in designing learning algorithms. We identify a sufficient condition under which the regret of Thompson sampling-based reinforcement learning algorithm with dynamic episodes (TSDE) at horizon T is bounded by tilde{mathcal{O}}(sqrt{T}), where the tilde{mathcal{O}}(cdot) notation hides logarithmic factors in T. These are the first results to generalize regret bounds of LQG systems to packet-drop networked control models.

Keywords: Adaptive control, Fault tolerant systems, Nonlinear output feedback
Abstract: In this paper, an adaptive output feedback fault-tolerant tracking scheme is proposed for a class of nonlinear systems with system uncertainties, external disturbances and sensor failures, in which redundant sensors are utilized to measure the system output. While a sensor fusion mechanism is designed to fuse sensor outputs and possible external diagnostic data, a coupled controller is designed based on sensor fused output, a new high-gain update law and a state observer. It is shown that the proposed method can ensure the closed-loop system stability and improve the tracking performance.

Keywords: Robotics, Observers for nonlinear systems, Fault detection
Abstract: A nonlinear observer is presented for the estimation of the joint velocities and of the deformation modes and their rates for a two-link flexible robot arm, using only motor encoders and a tip position sensor. The state observer can be used then for trajectory tracking control. By monitoring the mismatch between measured and estimated outputs, we can also detect the occurrence of permanent or intermittent system anomalies such as actuator faults or link collisions.

Keywords: Robotics, Stability of nonlinear systems, Lyapunov methods
Abstract: In the past, several motion and force controls were successfully implemented on rigid-joint robots with constraints. With the invention of mechanically compliant robots, the focus on designing controllers for elastic joint robots with constraints is increasing, especially involving the complexity of the joint elasticity in control. Aiming to bridge the gap between the control schemes of rigid- and elastic-joint robots, this letter presents a controller consisting of a PD+ task-space tracking and integral force control, while the intrinsic inertial and elastic properties of the system are fully preserved. We provide a passivity analysis and prove uniform asymptotic stability of the equilibrium. Simulations on a planar two-armed benchmark system with constraints validate the proposed control law.

Keywords: Observers for nonlinear systems, Estimation, Stability of nonlinear systems
Abstract: In this paper, we present a novel adaptive observer for nonholonomic differential-drive robots to simultaneously estimate the system's angular and linear velocities, along with its external matched disturbances. The proposed method is based on the immersion and invariance technique and makes use of a dynamic scaling factor. The stability and convergence proof of the velocity and disturbance errors are performed using a strict Lyapunov function. We present a detailed simulation study to validate the performance of our approach.

Keywords: Robotics, Biologically-inspired methods
Abstract: While animals easily and seamlessly transition between gaits to overcome challenging environments, current methods to design stable gait transitions often rely on computationally expensive optimization. In this work, we introduce a central pattern generator (CPG) model that allows intuitive gait definition and online, real-time gait transitions while ensuring stability and forward progression. Specifically, we propose to rely on keyframes -- discrete key leg configurations that can be sequenced into a gait -- to define arbitrary legged gaits. We introduce a new task-space CPG, which relies on the well-known Kuramoto model and a new feedforward term to ensure synchronized convergence to these keyframes. We then show how this framework can naturally be extended to allow arbitrary gait transitions by developing two stabilization techniques. First, we reason about the robot's predicted stability to disable specific oscillator updates during transition, while minimizing the resulting effect on forward locomotion. Second, we control the robot's body position within the grounded legs to ensure current and predicted stability based on inexpensive forward prediction of the CPG model. We validate our approach by presenting simulation and experimental results on a hexapod robot following and transitioning among hexapedal and quadrupedal gaits in a number of indoor and outdoor locomotion and mobile manipulation scenarios.

Keywords: Robotics, Simulation, Mechatronics
Abstract: There have been several successful implementations of bio-inspired legged robots that can trot, walk, and hop robustly even in the presence of significant unplanned disturbances. Despite all of these accomplishments, practical control and high-level decision-making algorithms in multi-modal legged systems are overlooked. In nature, animals such as birds impressively showcase multiple modes of mobility including legged and aerial locomotion. They are capable of performing robust locomotion over large walls, tight spaces, and can recover from unpredictable situations such as sudden gusts or slippery surfaces. Inspired by these animals' versatility and ability to combine legged and aerial mobility to negotiate their environment, our main goal is to design and control legged robots that integrate two completely different forms of locomotion, ground and aerial mobility, in a single platform. Our robot, the Husky Carbon, is being developed to integrate aerial and legged locomotion and to transform between legged and aerial mobility. This work utilizes a Reference Governor (RG) based on low-level control of Husky's dynamical model to maintain the efficiency of legged locomotion, uses Probabilistic Road Maps (PRM) and 3D A* algorithms to generate an optimal path based on the energetic cost of transport for legged and aerial mobility.

Keywords: Robotics
Abstract: This paper introduces a novel robotic system, coined as a hybrid rigid-soft (HyRiSo) robot composed of rigid links and soft links serially attached. HyRiSo combines the benefits of the dexterity of a soft manipulator with the support capability of a classical stiff arm. Due to the heterogeneous modes of actuation for the revolute joints and to enable the bending of the soft links, it is challenging to design an integrated controller for this class of robots. We demonstrate in this paper that the well-known passivity-based adaptive and robust controllers can be utilized to address this challenge. Specifically, we use these controllers for task space tracking in the presence of uncertain mass, stiffness, damping and actuation. We demonstrate the effectiveness of the proposed HyRiSo robot by showing task space tracking in the presence of complex obstacles and joint limits. We provide numerical examples using a 2-rigid-2-soft HyRiSo robot and compare the performance of the proposed task space controllers illustrating the efficacy of these frameworks.

Keywords: Learning, Stochastic optimal control, Nonlinear systems
Abstract: In Reinforcement Learning, model-free and model-based methods are known to have both strengths and weaknesses. The most recent literature on these topics focuses on trying to combine them in a way that preserves their advantages: sample-efficiency and good asymptotic behaviour respectively. This paper presents a new approach for directly estimating value-functions from data, which however relies on a particular model of the environment, therefore lying in between the two perspectives. The estimation problem indeed is targeting only the rewards of the transitions. This is achieved through the Koopman operator framework, which allows to describe a generic dynamical system in terms of its action on functions rather than on states, lifting the evolution in a Reproducing Kernel Hilbert Space. By leveraging a Bayesian perspective the latter approach enables also the propagation of estimation error and the definition of confidence intervals.

Keywords: Machine learning, Stochastic optimal control, Iterative learning control
Abstract: In this paper, we develop a novel variant of natural actor-critic algorithm using off-policy sampling and linear function approximation, and establish a sample complexity of mathcal{O}(epsilon^{-3}), outperforming all the previously known convergence bounds of such algorithms. In order to overcome the divergence due to deadly triad in off-policy policy evaluation under function approximation, we develop a critic that employs n-step TD-learning algorithm with a properly chosen n. We present finite-sample convergence bounds on this critic, which are of independent interest. Furthermore, we develop a variant of natural policy gradient under function approximation, with an improved convergence rate of mathcal{O}(1/T) after T iterations. Combining the finite sample bounds of the actor and the critic, we obtain an overall mathcal{O}(epsilon^{-3}) sample complexity. Our results were derived solely based on the assumption that the behavior policy sufficiently explores the state-action space, which is a much lighter assumption compared to the related literature.

Keywords: Machine learning, Nonlinear systems identification, Intelligent systems
Abstract: System representations inspired by the infinite-dimensional Koopman operator (generator) are increasingly considered for predictive modeling. Due to the operator's linearity, a range of nonlinear systems admit linear predictor representations - allowing for simplified prediction, analysis and control. However, finding meaningful finite-dimensional representations for prediction is difficult as it involves determining features that are both Koopman-invariant (evolve linearly under the dynamics) as well as relevant (spanning the original state) - a generally unsupervised problem. In this work, we present Koopmanizing Flows - a novel continuous-time framework for supervised learning of linear predictors for a class of nonlinear dynamics. In our model construction a latent diffeomorphically related linear system unfolds into a linear predictor through the composition with a monomial basis. The lifting, its linear dynamics and state reconstruction are learned simultaneously, while an unconstrained parameterization of Hurwitz matrices ensures asymptotic stability regardless of the operator approximation accuracy. The superior efficacy of Koopmanizing Flows is demonstrated in comparison to a state-of-the-art method on the well-known LASA handwriting benchmark.

Keywords: Machine learning, Neural networks, Optimization algorithms
Abstract: Adaptive gradient algorithms have become the prevalent tool in training complex neural networks; recent examples include AdaBound and MAdam. For a better understanding of such existing optimization algorithms and design ideas for new algorithms, well-known tools from classical control appear to be promising. This area of research is built upon modeling optimization algorithms as closed-loop dynamical systems. Consequently, this paper exploits a control-theoretic methodology in analyzing AdaBound, a recent adaptive gradient algorithm, and proposing a novel optimizer for machine learning. Specifically, inspired by the recently developed state-space perspective in the G-AdaGrad and the Adam algorithm, we present a simple convergence analysis of the AdaBound algorithm for non-convex optimization problems. Next, we propose a new variant of the MAdam algorithm upon applying the concept of transfer functions. Our experimental results demonstrate the efficiency of the proposed algorithm in training CNN models for image classification problems. The findings in this paper suggest further exploration of the existing tools from control theory in complex machine learning problems.

Keywords: Machine learning, Stochastic optimal control
Abstract: We provide performance guarantees for a variant of simulation-based policy iteration for controlling Markov decision processes that involves the use of stochastic approximation algorithms along with state-of-the-art techniques that are useful for very large MDPs, including lookahead, function approximation, and gradient descent. Specifically, we analyze two algorithms; the first algorithm involves a least squares approach where a new set of weights associated with feature vectors is obtained via least squares minimization at each iteration and the second algorithm is a two-time-scale algorithm taking several steps of gradient descent towards the least squares solution before obtaining the next iterate using a stochastic approximation algorithm.

Keywords: Machine learning, Smart grid
Abstract: Wind farms are subject to the so-called "wake effect", where upstream turbines facing the wind create sub-optimal wind conditions for turbines located downstream. One strategy to address this issue is to use yaw actuators to misalign the wind turbines with regard to the incoming wind direction, thus deflecting wakes away from downstream turbines. Tractable models for yaw optimization are however subject to inaccuracies, ignore wake dynamics and lack adaptability. This incentivizes the use of model-free methods. In this paper, we propose a delay-aware decentralized Q-learning algorithm for yaw control on wind farms. We introduce a strategy to handle delayed cost collection, and show that our method significantly increases power production in simulations with realistic wake dynamics. We validate our results for two farm layouts on mid-fidelity wind farm simulator FAST.Farm.

Keywords: Lyapunov methods, Nonlinear systems
Abstract: In this paper, we present two Control Lyapunov Function based families of cruise controllers for the two-dimensional movement of autonomous vehicles on lane-free roads using the bicycle kinematic model. The control Lyapunov functions are based on measures of the energy of the system with the kinetic energy expressed in ways similar to Newtonian or relativistic mechanics. The derived feedback laws (cruise controllers) are decentralized, as each vehicle determines its control input based on its own speed and on the relative speeds and distances from adjacent vehicles and from the boundary of the road. Moreover, the corresponding macroscopic models are derived, obtaining fluid-like models that consist of a conservation equation and a momentum equation with pressure and viscous terms. Finally, we show that, by selecting appropriately the parameters of the feedback laws, we get free hand to create an artificial fluid that approximates the emerging traffic flow.

Keywords: Autonomous vehicles, Traffic control, Delay systems
Abstract: For the predictor-feedback Cooperative Adaptive Cruise Control (CACC) design for homogenous platoons, recently developed by Davis, we establish robustness of string stability to delay mismatch and positivity of spacing and speed states. Each individual vehicle’s dynamics are described by a second-order linear system with delayed desired acceleration, under acceleration information transmitted to the ego vehicle from a single, preceding vehicle. The nominal design (in the delay-free case) is a constant time-headway (CTH) policy and no restriction on the delay size, in relation with the desired time headway, is imposed. The proofs rely on combination of an input-output approach (on the frequency domain) and on deriving estimates on explicit, closed-loop solutions; under specific, sufficient conditions that are derived on initial conditions and parameters of the baseline, CTH controller.

Keywords: Traffic control, Modeling, Constrained control
Abstract: The simultaneous proliferation of electric vehicles and intermittent renewable energy sources promises to expedite decarbonization of two sectors with highest emissions. However, both these developments threaten to endanger power system stability, which may hinder their widespread adoption. To tackle these challenges, there is a need for joint modelling of electric vehicle traffic flows, together with their battery dynamics. We propose a macroscopic electromobility model, augmenting the well-known LWR model, describing the traffic dynamics, with an inhomogeneous advection equation, describing the evolution of vehicles' State of Charge (SoC). The Riemann problem for the joint model is solved for the case of triangular fundamental diagram, and the solutions are used to formulate a Godunov-like scheme for model discretization. Additionally, we propose an advection-based charging station model, discretize it, and link it with the rest of the traffic and SoC model. We demonstrate the capabilities and use of the full coupled model by proposing a pedagogic example where a simple control law regulates the average SoC of all vehicles on a ring road by controlling the traffic flow entering the charging station.

Keywords: Traffic control, Simulation, Machine learning
Abstract: Traffic simulators can capture the complex dynamics of road networks thus are widely used to understand the behavior of the traffic system and predict the effects of transportation technologies, events and new policy changes. To build a traffic simulation model that can accurately capture the real traffic conditions, the Origin-Destination (OD) matrix is needed to be fed into the simulator as an input. In general, it is difficult to acquire information about the real OD matrix of a network. In this paper, we propose a neural network model for estimating the OD matrix that excites the microscopic simulation model for complex traffic networks to reproduce real world traffic flows using only the flow rate information of a small subset of links in the traffic network, which is relatively easy to collect. An optimization method is used to generate the training dataset of the neural network. Combining the OD matrix estimation model, the training dataset generation method, and the microscopic traffic simulator, an integrated traffic simulation-prediction system is developed to predict the behavior of the transportation system. We test the proposed system on the road network of the central terminal area of the Los Angeles International Airport and demonstrate that the integrated traffic simulation-prediction system can reproduce the real world traffic flow with low relative root mean square errors especially for high volume links and can be used to simulate the behavior of real world traffic scenarios.

Keywords: Distributed parameter systems, Constrained control, Traffic control
Abstract: This paper investigates the boundary feedback control for the two-lane traffic flow with lane-changing interactions in the presence of actuator saturations. The macroscopic traffic dynamics are described by the Lighthill-Whitham-Richards (LWR) model for both two lanes. Two variable speed limits (VSLs) are applied at boundaries for controlling the vehicle velocity so as to stabilize the traffic density of each lane. A saturated boundary feedback controller is proposed to drive the traffic densities of both lanes to the steady states. In contrast to the fruitful results in saturated control of ordinary differential equation (ODE) systems, there are few related studies for hyperbolic partial differential equation (PDE) systems. We define the exponential stability for the hyperbolic PDEs under saturated control. Then sufficient conditions for ensuring exponential stability of the two-lane traffic flow system are developed in terms of matrix inequalities under both the linear and nonlinear cases, by employing the Lyapunov function method along with a sector condition in L2-norm and H2-norm, respectively. Finally, the effectiveness of the proposed conditions is validated by numerical simulations.

Keywords: Traffic control, Learning, Optimal control
Abstract: This paper studies the issue of data-driven optimal control design for traffic signals of oversaturated urban road networks. The signal control system based on the store and forward model is generally uncontrollable for which the controllable decomposition is needed. Instead of identifying the unknown parameters like saturation rates and turning ratios, a finite number of measured trajectories can be used to parametrize the system and help directly construct a transformation matrix for Kalman controllable decomposition through the fundamental lemma of J. C. Willems. On top of that, an infinite-horizon linear quadratic regulator (LQR) problem is formulated considering the constraints of green times for traffic signals. The problem can be solved through a two-phase data-driven learning process, where one solves an infinite-horizon unconstrained LQR problem and the other solves a finite-horizon constrained LQR problem. The simulation result shows the theoretical analysis is effective and the proposed data-driven controller can yield desired performance for reducing traffic congestion.

Keywords: Identification, Statistical learning, Optimization algorithms
Abstract: Regularized methods have been widely applied to system identification problems without known model structures. This paper proposes an infinite-dimensional sparse learning algorithm based on atomic norm regularization. Atomic norm regularization decomposes the transfer function into first-order atomic models and solves a group lasso problem that selects a sparse set of poles and identifies the corresponding coefficients. The difficulty in solving the problem lies in the fact that there are an infinite number of possible atomic models. This work proposes a greedy algorithm that generates new candidate atomic models maximizing the violation of the optimality condition of the existing problem. This algorithm is able to solve the infinite-dimensional group lasso problem with high precision. The algorithm is further extended to reduce the bias and reject false positives in pole location estimation by iteratively reweighted adaptive group lasso and complementary pairs stability selection respectively. Numerical results demonstrate that the proposed algorithm performs better than benchmark parameterized and regularized methods in terms of both impulse response fitting and pole location estimation.

Keywords: Identification, Linear systems
Abstract: This paper is concerned with the fundamental limit on the identification of discrete-time SISO (Single Input Single Output) system, where the diagonal canonical form of the system is inferred from a finite number of input/output sample trajectories. Through the analysis of the Fisher information matrix used in Cram ́er-Rao bound, we show that the sample complexity of the identification problem using any unbiased estimator explodes superpolynomially with respect to system dimension in the average sense, assuming that the eigenvalues of the system matrix are uniformly distributed. Furthermore, we extend our result to the widely applied Ho-Kalman algo- rithm and prove that the algorithm is ill-conditioned for high dimensional SISO systems as well. Numerical results further demonstrate the conclusion of this paper.

Keywords: Identification, Manufacturing systems and automation, Linear systems
Abstract: The batch-least squares (BLS) approach to parameter identification is a well-known technique utilized for system identification. In this paper, we adapt the BLS approach to a 2D repetitive process model. Our approach first derives a regression model for the 2D repetitive process, which is then used for implementing the BLS algorithm. Our adapted BLS algorithm then uses the repetitive nature of the system to identify both the parameters associated with the system repetition and inputs applied. We evaluated the adapted BLS algorithm on an additive manufacturing process.

Keywords: Identification, Optimization
Abstract: In this paper, we consider the identification of continuous-time linear-time-invariant systems from sampled input-output data corrupted by unknown but bounded noise. We formulate the problem in the framework of errors-in- variables set-membership identification. First, we derive a mathematical description of the feasible parameter set in terms of polynomial constraints. Such a description accounts for a- priori information on the model structure and the noise bounds, and for the effects of the discretization error. Then, we select the parameter estimate from the feasible parameter set by computing the solution to a suitable polynomial optimization problem. We show the effectiveness of the proposed approach through a numerical example.

Keywords: Identification, Linear systems, Network analysis and control
Abstract: Physical dynamic networks most commonly consist of interconnections of physical components that can be described by diffusive couplings. Diffusive couplings imply symmetric cause-effect relationships in the interconnections and therefore diffusively coupled networks can be represented by undirected graphs. This paper shows how local dynamics of (undirected) diffusively coupled networks can be identified on he bases of local signals only. Sensors and actuators are allocated to guarantee consistent identification. An algorithm is developed for identifying the local dynamics.

Keywords: Identification, Modeling, Biological systems
Abstract: Estimation of brain effective connectivity (EC) faces several issues, among which are computational complexity and estimation accuracy. Here, we focus on increasing estimation accuracy, in particular addressing the bias introduced by the pre-processing pipeline employed on resting-state (rs) fMRI signals, which includes temporal band-pass prefiltering.

In this paper, we propose an alternative model (so-called ``Filtered rs-DCM'') that adapts a stochastic linear rs-DCM model to the filtered input. Filtered rs-DCM is built by augmenting the neuronal rs-DCM with the filter model used in the pre-processing step. The parameter estimation is performed with EM-algorithm with a sparsity inducing prior. The simulation experiments run on band-pass filtered synthetic datasets demonstrate that this approach outperforms classical DCM models in terms of EC estimation accuracy.

Keywords: Mechatronics
Abstract: This paper investigates detecting faults in robotic manipulators with bounded nonlinearities and time-variant parameters using transmissibility operators. Transmissibility operators are mathematical relations between a set of system responses to another set of responses within the same system. Both parameter variation and system nonlinearities are considered to be unknown. Transmissibility operators are shown in the literature to be independent of the system inputs. The bounded nonlinearities are considered as independent excitations on the system, which renders transmissibilities independent of these nonlinearities. To overcome the unknown variant parameters, we propose identifying transmissibilities using recursive least-squares in the structure of noncausal FIR models. While parameter variation can be treated as system nonlinearities, the recursive least squares algorithm is used to optimize what time-variant dynamics to include in the transmissibility operator and what dynamics to push to the system nonlinearities over time. The identified transmissibilities are then used for the purpose of fault detection in an experimental robotic arm with variant picked mass. The experimental results show the proposed approach to be used effectively to detect faults in robotic manipulators.

Keywords: Fault detection, Hybrid systems, Estimation
Abstract: This paper considers a class of fault detection problems for discrete-time piecewise-affine (PWA) systems. Inspired by the state-of-the-art of set-membership methods to estimate the state of PWA systems, a novel detection method based on zonotopes and over-approximation of sets is proposed to overcome high computational complexity caused by unknown discrete states. The efficiency and high accuracy of detection of the new method is confirmed through both theoretical analysis and numerical examples.

Keywords: Fault diagnosis, Fault detection, Optimization algorithms
Abstract: This paper proposes a hybrid stochastic-deterministic approach to realize the observer-based active fault diagnosis (AFD) for linear time-varying systems. A novel conception called hybrid zonotope-Gaussian dispersity for random variables of systems is introduced to establish an online optimization strategy for AFD. The optimal gain of observer and the optimal input are simultaneously designed at each step by solving a non-convex quadratic fractional programming problem, which is proved to be equivalent to a mixed integer quadratic programming problem. The proposed approach avoids the strict set-separation constraint conditions of traditional off-line AFD technology by making full use of the online measured outputs such that the diagnosisability of systems has potential to be further improved. At the end, a quadrotor model is used to verify the effectiveness of our proposed method.

Keywords: Fault detection, Algebraic/geometric methods, Linear systems
Abstract: The problem considered in this paper is dual to the control problem for over-actuated systems found in the literature. We show that, due to a certain notion of weak output redundancy, there always exists an unobservability subspace containing the input subspace, which ensures that the original system can be partitioned into two subsystems, one of which is not affected by actuator faults. We use this fact to estimate the disturbance and the fault in a cascaded fashion: we first design a discrete-time filter on a properly designed residual signal, that can reconstruct the disturbance. The estimated disturbance can then be used to perform fault detection and estimation in a cascaded fashion. A numerical example verifies the efficacy of the proposed strategy.

Keywords: Fault tolerant systems, Formal Verification/Synthesis, Resilient Control Systems
Abstract: Complex, interconnected Cyber-physical Systems (CPS) are increasingly common in applications including smart grids and transportation. Ensuring safety of interconnected systems whose dynamics are coupled is challenging because the effects of faults and attacks in one sub-system can propagate to other sub-systems and lead to safety violations. In this paper, we study the problem of safety-critical control for CPS with coupled dynamics when some sub-systems are subject to failure or attack. We first propose resilient-safety indices (RSIs) for the faulty or compromised sub-systems that bound the worst-case impacts of faulty or compromised sub-systems on a set of specified safety constraints. By incorporating the RSIs, we provide a sufficient condition for the synthesis of control policies in each failure- and attack- free sub-systems. The synthesized control policies compensate for the impacts of the faulty or compromised sub-systems to guarantee safety. We formulate sum-of-square optimization programs to compute the RSIs and the safety-ensuring control policies. We present a case study that applies our proposed approach on the temperature regulation of three coupled rooms. The case study demonstrates that control policies obtained using our algorithm guarantee system's safety constraints.

Keywords: Fault diagnosis, Nonlinear systems, Optimization
Abstract: In this paper, we present a methodology for actuator and sensor fault estimation in nonlinear systems. The method consists of augmenting the system dynamics with an approximated ultra-local model (a finite chain of integrators) for the fault vector and constructing a Nonlinear Unknown Input Observer (NUIO) for the augmented dynamics. Then, fault reconstruction is reformulated as a robust state estimation problem in the augmented state (true state plus fault-related state). We provide sufficient conditions that guarantee the existence of the observer and stability of the estimation error dynamics (asymptotic stability of the origin in the absence of faults and ISS guarantees in the faulty case). Then, we cast the synthesis of observer gains as a semidefinite program where we minimize the L2-gain from the model mismatch induced by the approximated fault model to the fault estimation error. Finally, simulations are given to illustrate the performance of the proposed methodology.

Keywords: Constrained control, Predictive control for nonlinear systems, Autonomous systems
Abstract: This paper presents a methodology for constructing Control Barrier Functions (CBFs) that proactively consider the future safety of a system along a nominal trajectory, and effect corrective action before the trajectory leaves a designated safe set. Specifically, this paper presents a systematic approach for propagating a nominal trajectory on a receding horizon, and then encoding the future safety of this trajectory into a CBF. If the propagated trajectory is unsafe, then a controller satisfying the CBF condition will modify the nominal trajectory before the trajectory becomes unsafe. Compared to existing CBF techniques, this strategy is proactive rather than reactive and thus potentially results in smaller modifications to the nominal trajectory. The proposed strategy is shown to be provably safe, and then is demonstrated in simulated scenarios where it would otherwise be difficult to construct a traditional CBF. In simulation, the predictive CBF results in less modification to the nominal trajectory and smaller control inputs than a traditional CBF, and faster computations than a nonlinear model predictive control approach.

Keywords: Constrained control, Learning, Sampled-data control
Abstract: We develop a novel form of differentiable predictive control (DPC) with safety and robustness guarantees based on control barrier functions. DPC is an unsupervised learning-based method for obtaining approximate solutions to explicit model predictive control (MPC) problems. In DPC, the predictive control policy parametrized by a neural network is optimized offline via direct policy gradients obtained by automatic differentiation of the MPC problem. The proposed approach exploits a new form of sampled-data barrier function to enforce offline and online safety requirements in DPC settings while only interrupting the neural network-based controller near the boundary of the safe set. The effectiveness of the proposed approach is demonstrated in simulation.

Keywords: Constrained control, Nonlinear systems, Computational methods
Abstract: State and input constraints are ubiquitous in control system design. One recently developed tool to deal with these constraints is control barrier functions (CBF) which transform state constraints into conditions in the input space. CBF-based controller design thus incorporates both the CBF conditions and input constraints in a quadratic program. However, the CBF-based controller is well-defined only if the CBF conditions are compatible. In the case of perturbed systems, robust compatibility is of relevance. In this work, we propose an algorithmic solution to verify or falsify the (robust) compatibility of given CBFs a priori. Leveraging the Lipschitz properties of the CBF conditions, a grid sampling and refinement method with theoretical analysis and guarantees is proposed.

Keywords: Constrained control, Learning, Optimal control
Abstract: Control barrier functions (CBFs) are widely used in safety-critical controllers. However, constructing a valid CBF is challenging, especially under nonlinear or non-convex constraints and for high relative degree systems. Meanwhile, finding a conservative CBF that only recovers a portion of the true safe set is usually possible. In this work, starting from a ``conservative" handcrafted CBF (HCBF), we develop a method to find a CBF that recovers a reasonably larger portion of the safe set. Since the learned CBF controller is not guaranteed to be safe during training iterations, we use a model predictive controller (MPC) to ensure safety during training. Using the collected trajectory data containing safe and unsafe interactions, we train a neural network to estimate the difference between the HCBF and a CBF that recovers a closer solution to the true safe set. With our proposed approach, we can generate safe controllers that are less conservative and computationally more efficient. We validate our approach on two systems: a second-order integrator and a ball-on-beam.

Keywords: Constrained control, Nonlinear systems, Healthcare and medical systems
Abstract: Control barrier functions (CBFs) have commonly been used to encode the safety requirements of a dynamical system and to constrain the control input to guarantee forward invariance of a safe set. High-order control barrier functions (HOCBFs) are a method of ensuring the safety of a system of high relative degree. The method developed in this paper can be applied to a variety of nonlinear systems with more general dynamics than previous works, and is demonstrated on a motorized rehabilitative cycle of relative degree two. A motor controller is designed to constrain the crank position to a time-varying user-defined safe range. Because of the uncertain and nonlinear dynamics of the system, robust control methods are borrowed from Lyapunov theory to develop worst-case controllers that render the intersection of a series of sets forward invariant. The controller is designed so that it provides minimal assistance within the safe range, maximizing the efforts of the rider and facilitating more effective therapy.

Keywords: Constrained control, Observers for nonlinear systems, Robust control
Abstract: This paper addresses the synthesis of safety-critical controllers using estimate feedback. We propose an observer-controller interconnection to ensure that the nonlinear system remains safe despite bounded disturbances on the system dynamics and measurements that correspond to partial state information. The co-design of observers and controllers is critical, since even in undisturbed cases, observers and controllers designed independently may not render the system safe.

We propose two approaches to synthesize observer-controller interconnections. The first approach utilizes Input-to-State Stable observers, and the second uses Bounded Error observers. Using these stability and boundedness properties of the observation error, we construct novel Control Barrier Functions that impose inequality constraints on the control inputs which, when satisfied, certifies safety. We propose quadratic program-based controllers to satisfy these constraints, and prove Lipschitz continuity of the derived controllers. Simulations and experiments on a quadrotor demonstrate the efficacy of the proposed methods.

Keywords: Network analysis and control, Distributed control, Cooperative control
Abstract: The separation principle in a centralized estimation and control problem gives us the flexibility to design a feedback controller independent of the state estimator. However, the same principle does not hold when the estimation and control are distributed over a network of agents. In this case, the estimator may need to be redesigned when the controller is revised, which can be computationally expensive. We investigate a weaker notion of the separation principle in the distributed estimation and control of linear time-invariant (LTI) systems. As a main contribution, applying the small-gain theorem, we characterize the notion using matrix inequalities and compute a set of feedback controllers that agents in the network can adopt without redesigning the estimator. We also analyze how the frequency of information exchange between neighboring agents affects the characterization. We illustrate our analytical results through simulations of a multi-vehicle system problem.

Keywords: Networked control systems, Communication networks, Control of networks
Abstract: In this paper we propose algorithms to connect and disconnect nodes to/from an existing graph, which are able to maintain the regularity of a graph while requiring minimal reconfiguration of the network. Further, simulations suggest that the algorithms maintain a minimum bound on the algebraic connectivity of the graph. These properties of the algorithms suit their use in plug-and-play networks.

Keywords: Cooperative control, Distributed control, Networked control systems
Abstract: This paper studies the relation between node deletion and algebraic connectivity for graphs with a hierarchical structure represented by layers. To capture this structure, the concepts of layered path graph and its (sub)graph cone are introduced. The problem is motivated by a mobile robot formation control guided by a leader. In particular, we consider a scenario in which robots may leave the network resulting in the removal of the nodes and the associated edges. We show that the existence of at least one neighbor in the upper layer is crucial for the algebraic connectivity not to deteriorate by node deletion.

Keywords: Agents-based systems, Network analysis and control, Autonomous systems
Abstract: Topology inference for networked dynamical systems (NDSs) has received considerable attention in recent years. The majority of pioneering works have dealt with inferring the topology from abundant observations of NDSs, so as to approximate the real one asymptotically. Leveraging the characteristic that NDSs will react to various disturbances and the disturbance’s influence will consistently spread, this paper focuses on inferring the topology by a few active excitations. The key challenge is to distinguish different influences of system noises and excitations from the exhibited state deviations, where the influences will decay with time and the exciatation cannot be arbitrarily large. To practice, we propose a one-shot excitation based inference method to infer h-hop neighbors of a node. The excitation conditions for accurate one-hop neighbor inference are first derived with probability guarantees. Then, we extend the results to h-hop neighbor inference and multiple excitations cases, providing the explicit relationships between the inference accuracy and excitation magnitude. Specifically, the excitation based inference method is not only suitable for scenarios where abundant observations are unavailable, but also can be leveraged as auxiliary means to improve the accuracy of existing methods. Simulations are conducted to verify the analytical results.

Keywords: Agents-based systems, Decentralized control, Linear systems
Abstract: Dynamics evolving on different time scales appear naturally in networks of clusters. In this paper, we emphasize that the synchronization of interconnected agents partitioned in clusters involves three time-scales. Using a coordinate transformation, we reformulate the overall closed-loop clustered network dynamics in new coordinates describing the mean-field dynamics, the intra-cluster and the inter-cluster synchronization error dynamics. Then, under realistic assumptions, we show that the network dynamics can be represented in a two-parameter standard singular perturbation form in the new coordinate. The mean-field dynamics, which is the network’s long-term behavior, evolve on the slowest time-scale. The intra-cluster error dynamics, which characterizes the synchronization inside clusters, evolve on the fastest time scale. Finally, the inter-cluster error dynamics, which characterizes the synchronization between clusters, is fast with respect to the mean-field one and slow with respect to the intra-cluster one. Using the two-parameter singular perturbation form, we establish approximations of the variables using standards techniques based on Tychonoff’s theorem. Numerical simulations validate our theoretical results.

Keywords: Networked control systems, Network analysis and control
Abstract: We consider the identifiability and identification problem of a dynamical network modeled by a switched linear dynamical system governed by a sequence of switchings. We aim at exactly reconstructing the network sequence along with the switching signal from the state trajectories of all nodes. The identification of a switching dynamical network is more challenging than that of a time-invariant dynamical network in that the data is generated by a number of different subsystems at different periods. By observability conditions, we first establish a necessary and sufficient condition for the identifiability of switching dynamical networks. Building on this, a sufficient identification condition is developed leveraging coupled Lyapunov-transpose matrix equations, which allows us to design a new algorithm that can exactly recover the whole network sequence, even if the switching signal is completely unknown a prior. Finally, a numerical example is provided to verify the effectiveness of the theoretical results.

Keywords: Stochastic systems, Agents-based systems, Network analysis and control
Abstract: In this work, we study an instance of continuous time voter model over directed graphs on social networks with a specific refinement: the agents can break or create new links in the graph. The edges of the graph thus coevolve with the agents’ spin. Specifically, the agents may break their links with neighbours of different spin, and create links with the neighbours of their neighbours (2-hop neighbours), provided they have same spin. We characterize the absorbing configurations and present a particular case that corresponds to a single agent facing two antagonistic ideologies. By asymptotic analysis, we observe two regimes depending on the parameters: in one regime, hesitation disappears rapidly, while when the link creation rate is high enough, slow extinction or metastability occurs. We compute the threshold value and illustrate these results with numerical simulations.

Keywords: Stochastic systems, Identification, Estimation
Abstract: A relevant problem in many areas of science is to determine the structure of a network by observing its nodes. A desirable property of any network reconstruction techniques is consistency, namely the convergence of the reconstructed network to the actual structure when the time horizon of the observations goes to infinity. Unfortunately, when feedthrough components are present in the network, multiple structures could give rise to the same observations. Hence, in these situations, the best theoretical result that can be achieved is the determination of all the possible structures compatible with what is being observed. There are some results offering such theoretical guarantees, but these methods rely on a large number of statistical tests making their sample complexity relatively large. This article proposes the adoption of reconstruction techniques where, given the observed data, each structure is evaluated according to a score representing the likelihood that such structure is the actual one. Such a technique is proven to have the same consistency properties of state-of-the-art methods based on statistical tests, while numerical experiments show it to have a lower sample complexity.

Keywords: Predictive control for linear systems, Constrained control, Stochastic optimal control
Abstract: In this work, recursively feasible model predictive control (MPC) is considered for systems under additive disturbances. Combining a nonparametric Gaussian Process (GP) prior for modeling the additive disturbance with the model of the undisturbed system results in a model structure referred to as latent force model (LFM). Using spectral factorization, the whole LFM can be represented by an equivalent/approximate stochastic state-space model used as the predictor in the MPC formulation. Chance constraints are incorporated by constraint tightening using so-called probabilistic reachable sets of the LFM state and recursive feasibility is guaranteed by optimizing the initial value of the MPC predicted trajectory. The LFM formulation allows leveraging the disturbance information to all components of the MPC, which can significantly enhance its performance. The proposed LFM-based MPC approach is demonstrated on a simulated quadcopter under additive disturbances. The performance of the closed-loop controller using the LFM-state-space reformulation is compared to standard MPC.

Keywords: Stochastic systems, Switched systems, Automata
Abstract: In this paper, we develop tools to establish almost sure stability of stochastic switched systems whose switching signal is constrained by an automaton. After having provided the necessary generalizations of existing results in the setting of stochastic graphs, we provide a characterization of almost sure stability in terms of multiple Lyapunov functions. We introduce the concept of lifts, providing formal expansions of stochastic graphs, together with the guarantee of conserving the underlying probability framework. We show how these techniques, firstly introduced in the deterministic setting, provide hierarchical methods in order to compute tight upper bounds for the almost sure decay rate. The theoretical developments are finally illustrated via a numerical example.

Keywords: Stochastic systems, Identification, Lyapunov methods
Abstract: In this letter, we consider the parameter estimation problem of continuous-time linear stochastic regression models described by stochastic differential equations using the sampling data. An online least squares (LS) algorithm is proposed by minimizing the accumulative prediction error at discrete sampling time instants. By employing both the stochastic Lyapunov function and martingale estimate methods, we establish the convergence analysis of the proposed algorithm under conditions of the excitation of the sampling data and the sampling time interval. We also provide the upper bound of the accumulative regret for the adaptive predictor. A simulation example is given to verify our theoretical results.

Keywords: Stochastic systems, Observers for Linear systems, Stability of hybrid systems
Abstract: This paper focuses on the problem of observability and observer design for linear stochastic systems. To introduce our idea, we first construct an idealistic observer. This idealistic observer is not causal as it requires perfect knowledge of the Brownian motion. However, after introducing an a posteriori method to reconstruct the variations of the Brownian motion in discrete time, we propose a realistic hybrid observer which approximates the idealistic observer. The performance of this hybrid observer can be made arbitrarily close to that of the idealistic observer. Numerical simulations illustrate the results of the paper.

Keywords: Optimal control, Time-varying systems, Machine learning
Abstract: The Linear Quadratic Regulator (LQR), which is arguably the most classical problem in control theory, was recently related to kernel methods in cite{aubin2020hard_control} for finite dimensional systems. We show the result extends to infinite dimensional systems, i.e. control of linear partial differential equations. The quadratic objective paired with the linear dynamics encode the relevant kernel, defining a Hilbert space of controlled trajectories, for which we obtain a concise formula based on the solution of the differential Riccati equation. This paves the way to applying representer theorems from kernel methods to solve infinite dimensional optimal control problems.

Keywords: Distributed parameter systems, Stochastic systems, LMIs
Abstract: Recently, finite-dimensional controllers were introduced for 1D stochastic parabolic PDEs via the modal decomposition method. In the present paper, we suggest a sampled-data implementation of a finite-dimensional observer-based boundary controller for 1D stochastic parabolic PDEs under discrete-time non-local measurement, where both the considered system and the measurement are subject to nonlinear multiplicative noise. We provide mean-square L² exponential stability analysis of the full-order closed-loop system, where we employ It^{o}'s formula. We consider sampled-data control that employs zero-order hold device and use the time-delay approach to the sampled-data system. We construct Lyapunov functional V, and further combine it with Halanay's inequality with respect to expected value of V to compensate sampling in the infinite-dimensional tail. We provide linear matrix inequalities (LMIs) for finding the observer dimension N and upper bounds on sampling intervals and noise intensities that preserve the exponential stability. We prove that the LMIs are always feasible for large enough N and small enough sampling intervals and noise intensities. A numerical example demonstrates the efficiency of our method.

Keywords: Traffic control, Formal Verification/Synthesis, Predictive control for nonlinear systems
Abstract: This work investigates traffic signal optimization to improve mobility and safety of traffic flow at signalized intersections. The existing pre-timed and actuated control techniques are incapable of optimally using traffic data in achieving congestion-free traffic flow. To overcome this limitation, we propose a model predictive control (MPC) with the signal spatio-temporal logic (SSTL) from formal methods to utilize traffic data. For this, we construct a cell transmission traffic model and describe traffic mobility and safety specifications using SSTL. Then to optimize traffic signal timings in this setting, we formulate an optimization problem with an objective to minimize traffic congestion subject to constraints given as SSTL specifications. A numerical example is provided to illustrate the traffic flow control using MPC with SSTL.

Keywords: Biological systems, Nonlinear systems, Nonlinear output feedback
Abstract: The main contribution of this paper is a novel sensory feedback control law for an octopus arm. The control law is inspired by, and helps integrate, several observations made by biologists. The proposed control law is distinct from prior work which has mainly focused on open-loop control strategies. Several analytical results are described including characterization of the equilibrium and its stability analysis. Numerical simulations demonstrate life-like motion of the soft octopus arm, qualitatively matching behavioral experiments. Quantitative comparison with bend propagation experiments helps provide the first explanation of such canonical motion using a sensory feedback control law. Several remarks are included that help draw parallels with natural pursuit strategies such as motion camouflage or classical pursuit.

Keywords: Fluid flow systems, Optimization, Robust control
Abstract: In this paper, we propose a method to learn linear controllers that completely suppress the vortex-shedding regime past a cylinder at Reynolds number 100, using a single actuator and sensor pair in a feedback configuration. The method is based on the Youla parametrization for guaranteeing closed-loop stability in a neighbourhood of the fixed point. Among the set of controllers stabilizing the fixed point, a derivative-free optimization algorithm searches for a controller suppressing the natural limit cycle oscillation. We show existence of simple single input, single output LTI controllers driving the full vortex shedding regime to the natural unstable base flow for infinite dimension, highly nonlinear Navier-Stokes dynamics.

Keywords: Distributed parameter systems
Abstract: This paper deals with the stabilization of a linear hyperbolic system subject to a boundary disturbance. Our feedback design relies on a super-twisting control algorithm, which leads to a feedback that is continuous with respect to the state, in contrast with the classical sliding mode design. Our first result is the existence of solutions of the closed-loop system. Moreover, the global asymptotic stability, that is our second result, is proved together with the guarantee that the disturbance is rejected

Keywords: Identification for control, Statistical learning, Adaptive control
Abstract: Classical control theory deals with input-output descriptions of plants and controllers, a.k.a. kernel representations. A consistent Data-Driven control theory has been developed for linear systems using these representations. This theory is centered around the model reference design paradigm and is founded upon the classical tools of system identification - i.e. prediction error and correlation based identification. Data-driven design of state feedback controllers and of implicit control laws, on the other hand, has found a perfect fit in the behavioral description of plants and controllers. Subspace identification and predictive control became the foundations of design and analysis methodologies arising in this context. In this paper we will summarize the fundamentals of the `classical' data-driven control theory, describe some of the applications that it has encountered and point to the challenges still ahead in this approach. Next we'll motivate the behavioral approach to Data-Driven control, and highlight an important result that has been proven both for kernels and for behaviors: the conceptual conditions under which `direct' data-driven design outperforms `indirect' design - i.e. data-driven identification plus model-based design.

Keywords: Identification for control, Robust control, Behavioural systems
Abstract: The purpose of this paper is to provide a tutorial on the so-called informativity framework for direct data-driven control. This framework views data-driven analysis and design through the lens of robust control, and aims at assessing system properties and determining controllers for sets of systems unfalsified by the data. We will first introduce the informativity approach at an abstract level. Thereafter, we will study several case studies where we highlight the strength of the approach in the context of stabilizability analysis and stabilizing feedback design in different setups involving exact and noisy data, and for both input-state and input-output measurements. Finally, we provide an account of other applications of the data informativity framework.

Keywords: Optimal control, Identification for control, Behavioural systems
Abstract: The linear quadratic regulator (LQR) problem is a cornerstone of control theory and a widely studied benchmark problem. When a system model is not available, the conventional approach to LQR design is indirect, i.e., based on a model identified from data. Recently a suite of direct data- driven LQR design approaches has surfaced by-passing explicit system identification (SysID) and based on ideas from subspace methods and behavioral systems theory. In either approach, the data underlying the design can be taken at face value (certainty- equivalence) or the design is robustified to account for noise. An emerging topic in direct data-driven LQR design is to regularize the optimal control objective to account for implicit SysID (in a least-square or low-rank sense) or to promote robust stability. These regularized formulations are flexible, computationally attractive, and theoretically certifiable; they can interpolate between direct vs. indirect and certainty-equivalent vs. robust approaches; and they can be blended resulting in remarkable empirical performance. This manuscript reviews and compares different approaches to regularized direct data-driven LQR.

Keywords: Predictive control for linear systems, Robust control, Control software
Abstract: This paper presents a tutorial overview of model predictive control (MPC), subspace predictive control (SPC) and data-enabled predictive control (DeePC), with emphasis on offset-free design. Based on recent results on offset-free SPC design and on the relation between SPC and DeePC, we show that when incremental inputs are used in the identification step (SPC) or in the Hankel matrix (DeePC), the resulting data-driven predictive controllers are offset-free. Moreover, they are equivalent with offset-free MPC in the deterministic case. For noisy data the equivalence does not hold and a regularized version of the DeePC algorithm is necessary. We show that regularized DeePC can be formulated as a Tikhonov regularized least squares problem. This enables systematic tuning of the regularization parameter. We compare the performance of the offset-free data-driven predictive controllers in an application example from high-precision mechatronics.

Keywords: Predictive control for linear systems, Uncertain systems, Optimal control
Abstract: Data-driven model predictive control (DD-MPC) based on Willems' Fundamental Lemma has received much attention in recent years, allowing to control systems directly based on an implicit data-dependent system description. The literature contains many successful practical applications as well as theoretical results on closed-loop stability and robustness. In this paper, we provide a tutorial introduction to DD-MPC for unknown linear time-invariant (LTI) systems with focus on (robust) closed-loop stability. We first address the scenario of noise-free data, for which we present a DD-MPC scheme with terminal equality constraints and derive closed-loop properties. In case of noisy data, we introduce a simple yet powerful approach to analyze robust stability of DD-MPC by combining continuity of DD-MPC w.r.t. noise with inherent robustness of model-based MPC, i.e., robustness of nominal MPC w.r.t. small disturbances. Moreover, we discuss how the presented proof technique allows to show closed-loop stability of a variety of DD-MPC schemes with noisy data, as long as the corresponding model-based MPC is inherently robust.

Keywords: Building and facility automation, Learning, Smart cities/houses
Abstract: This manuscript offers the perspective of experimentalists on a number of modern data-driven techniques: model predictive control relying on Gaussian processes, adaptive data-driven control based on behavioral theory, and deep reinforcement learning. These techniques are compared in terms of data requirements, ease of use, computational burden, and robustness in the context of real-world applications. Our remarks and observations stem from a number of experimental investigations carried out in the field of building control in diverse environments, from lecture halls and apartment spaces to a hospital surgery center. The final goal is to support others in identifying what technique is best suited to tackle their own problems.

Keywords: Predictive control for linear systems, Distributed control
Abstract: This paper proposes a parallelizable algorithm for linear-quadratic model predictive control (MPC) problems with state and input constraints. The algorithm itself is based on a parallel MPC scheme that has originally been designed for systems with input constraints. In this context, one contribution of this paper is the construction of time-varying yet separable constraint margins ensuring recursive feasibility and asymptotic stability of sub-optimal parallel MPC in a general setting, which also includes state constraints. Moreover, it is shown how to tradeoff online run-time guarantees versus the conservatism that is introduced by the tightened state constraints. The corresponding performance of the proposed method as well as the cost of the recursive feasibility guarantees is analyzed in the context of controlling a large-scale mechatronic system. This is illustrated by numerical experiments for a large-scale control system with more than 100 states and 60 control inputs leading to run-times in the millisecond range.

Keywords: Predictive control for linear systems, Cyber-Physical Security, Resilient Control Systems
Abstract: Software rejuvenation is a cyberdefense mechanism that periodically resets the mission control software of a system to limit the impact of cyberattacks, activating in case it is necessary a safety controller to guarantee that the system returns to a target safe set. Unlike other works that consider feedback gains as mission controllers, here we propose a tree-based model predictive control scheme to explicitly account for the software refresh events and the possibility of cyberattacks. The benefits of the proposed method are illustrated using a simulated microgrid as a case study.

Keywords: Predictive control for linear systems, Distributed control
Abstract: A plug-and-play model predictive control (PnP MPC) scheme is proposed for varying-topology networks to track piecewise constant references. The proposed scheme allows subsystems to occasionally join and leave the network while preserving asymptotic stability and recursive feasibility and comprises two main phases. In the redesign phase, passivity-based control is used to ensure that asymptotic stability of the network is preserved. In the transition phase, reconfigurable terminal ingredients are used to ensure that the distributed MPC problem is initially feasible after the PnP operation. The efficacy of the proposed scheme is evaluated by applying it to a network of mass-spring-damper systems and comparing it to a benchmark scheme. It is found that the novel redesign phase results in faster PnP operations, whereas the novel transition phase increases flexibility by accepting more requests.

Keywords: Predictive control for linear systems, Model/Controller reduction, Large-scale systems
Abstract: In model predictive control (MPC) for large-scale applications, the computational limitations for on-line optimization often lead to the use of (relatively) short prediction horizons. In this paper, we show that as a result, the controller optimizes over only a fraction of the dynamics of the large-scale system. Based on this observation, which we will formalize, we propose a method to construct reduced-order models of minimal order, by exploiting the system-theoretic concept of finite-horizon observability, that exactly match the response of the large-scale system within a finite horizon. These so-called finite-horizon minimal realizations are used to implement equivalent MPC schemes with reduced computational effort (or the same computational effort but with a larger prediction horizon) without sacrificing accuracy/performance (as the equivalent optimization problem has the same optimizers as the original MPC problem). By computing finite-horizon minimal realizations, we can determine the dynamics as “seen” by the MPC, which can provide useful design insights, in particular, when tuning the prediction horizon. We demonstrate the strengths of our results in a numerical case study.

Keywords: Predictive control for linear systems, Neural networks, Constrained control
Abstract: Model predictive control (MPC) provides a useful means for controlling systems with constraints, but suffers from the computational burden of repeatedly solving an optimization problem in real time. Offline (explicit) solutions for MPC attempt to alleviate real time computational challenges using either multiparametric programming or machine learning. The multiparametric approaches are typically applied to linear or quadratic MPC problems, while learning-based approaches can be more flexible and are less memory-intensive. Existing learning-based approaches offer significant speedups, but the challenge becomes ensuring constraint satisfaction while maintaining good performance. In this paper, we provide a neural network parameterization of MPC policies that explicitly encodes the constraints of the problem. By exploring the interior of the MPC feasible set in an unsupervised learning paradigm, the neural network finds better policies faster than projection-based methods and exhibits substantially shorter solve times. We use the proposed policy to solve a robust MPC problem, and demonstrate the performance and computational gains on a standard test system.

Keywords: Predictive control for linear systems, Robust control, Optimization
Abstract: We propose a robust risk-aware model predictive control (MPC) algorithm for linear discrete-time systems with bounded disturbances. The MPC problem is formulated to maximize the size of the predicted disturbance sets (which are subsets of the maximal disturbance sets) at each time step, under state and control constraints and a reachability specification. It is shown that the proposed scheme has the following properties: i) its feasible state set (i.e., the set of states starting from which the MPC problem is feasible) is as large as that of the MPC problem for the corresponding undisturbed system; ii) it maintains recursive feasibility if the conventional robust MPC problem is feasible. The proposed controller enlarges the feasible state set, at the expense of the risk of possible constraint violation that is quantified by the optimal solution of the problem. When the sets are represented as zonotopes, we further provide a computationally tractable reformulation and design an online implementation algorithm with adaptive prediction horizon. We illustrate the effectiveness of the proposed methods using a simulated example.

Keywords: Traffic control, Robust control
Abstract: In this paper, a mixed platoon on an open-road is studied, that includes one connected and automated vehicle (CAV) and multiple human-driven vehicles (HDVs). We represent the car-following behavior of HDVs by the optimal velocity model (OVM), while considering the driver reaction time as a delay in their dynamics. Also, we assume that the changes of traffic conditions result in a time-varying desired velocity. Considering a varying desired speed, reaction time delay, and parametric uncertainties in the HDV dynamics, a gain-scheduled robust H_{infty} control strategy is developed, that can stabilize the traffic flow in the presence of undesired perturbations. We indicate the efficiency of the proposed static output-feedback controller through simulation results.

Keywords: Transportation networks, Traffic control, Estimation
Abstract: This letter focuses on the problem of traffic state estimation for highway networks with junctions in the form of on- and off-ramps while maintaining differential privacy of traffic data. Two types of sensors are considered, fixed sensors such as inductive loop detectors and connected vehicles which provide traffic density and speed data. The celebrated nonlinear second-order Aw-Rascle-Zhang (ARZ) model is utilized to model the traffic dynamics. The model is formulated as a nonlinear state-space difference equation. Sensitivity relations are derived for the given data which are then used to formulate a differentially private mechanism which adds a Gaussian noise to the data to make it differentially private. A Moving Horizon Estimation (MHE) approach is implemented for traffic state estimation using a linearized ARZ model. MHE is compared with Kalman Filter variants namely Extended Kalman Filter, Ensemble Kalman Filter and Unscented Kalman Filter. Several research and engineering questions are formulated and analysis is performed to find corresponding answers.

Keywords: Optimal control, Automotive control, Optimization
Abstract: The conventional wisdom is that the minimum-time trajectory of road vehicles on straights is `straight'. Actually, this is not always the case, at least for two-wheeled vehicles. Indeed, on four-wheeled vehicles the maximum accelerations are mainly limited by tyre-road friction and engine power. On the contrary, on two-wheeled vehicles the maximum accelerations are also limited by wheelie (front tyre lift) and stoppie (rear tyre lift). As a consequence, the maximum performance is not always obtained by going `straight' on straights. The issue is investigated within a nonlinear optimal control framework, where the objective is to minimize the manoeuvre time of the vehicle. A recently introduced free-trajectory method based on g-g diagrams is employed, and extended with refinement on the vehicle and road models. A direct solution method is employed, i.e. the optimal control problem (OCP) is transcribed into a nonlinear programming problem (NLP).

Keywords: Hierarchical control, Optimization, Robotics
Abstract: This paper describes a hierarchical solution consisting of a multi-phase planner and a low-level safe controller to jointly solve the safe navigation problem in crowded, dynamic, and uncertain environments. The planner employs dynamic gap analysis and trajectory optimization to achieve collision avoidance with respect to the predicted trajectories of dynamic agents within the sensing and planning horizon and with robustness to agent uncertainty. To address uncertainty over the planning horizon and real-time safety, a fast reactive safe set algorithm (SSA) is adopted, which monitors and modifies the unsafe control during trajectory tracking. Compared to other existing methods, our approach offers theoretical guarantees of safety and achieves collision-free navigation with higher probability in uncertain environments, as demonstrated in scenarios with 20 and 50 dynamic agents.

Keywords: Modeling, Networked control systems, Energy systems
Abstract: In this paper, we use elements of graph theory and port-Hamiltonian systems to develop a modular dynamic model describing the hydraulic behavior of 4th generation district heating networks. In contrast with earlier generation networks with a single or few heat sources and pumps, newer installations will prominently feature distributed heat generation units, bringing about a number of challenges for the control and stable operation of these systems, e.g., flow reversals and interactions among pumps controllers, which may lead to severe oscillations. We focus thus on flexible system setups with an arbitrary number of distributed heat sources and end-users interconnected through a meshed, multi-layer distribution network of pipes. Moreover, differently from related works on the topic, we incorporate dynamic models for the pumps in the system and explicitly account for the presence of pressure holding units. By inferring suitable (power-preserving) interconnection ports, we provide a number of claims about the passivity properties of the overall, interconnected system, which can prove to be highly beneficial in the design of decentralized control schemes and stability analyses.

Keywords: Information theory and control, Control over communications, Distributed control
Abstract: In this letter, we consider a Linear Quadratic Gaussian (LQG) control system where feedback occurs over a noiseless binary channel and derive lower bounds on the minimum communication cost (quantified via the channel bitrate) required to attain a given control performance. We assume that at every time step an encoder can convey a packet containing a variable number of bits over the channel to a decoder at the controller. Our system model provides for the possibility that the encoder and decoder have shared randomness, as is the case in systems using dithered quantizers. We define two extremal prefix-free requirements that may be imposed on the message packets; such constraints are useful in that they allow the decoder, and potentially other agents to uniquely identify the end of a transmission in an online fashion. We then derive a lower bound on the rate of prefix-free coding in terms of directed information; in particular we show that a previously known bound still holds in the case with shared randomness. We generalize the bound for when prefix constraints are relaxed, and conclude with a rate-distortion formulation.

Keywords: Optimization algorithms, Optimization, Optimal control
Abstract: In this paper, we propose a Feasible Sequential Linear Programming (FSLP) algorithm applied to timeoptimal control problems (TOCP) obtained through direct multiple shooting discretization. This method is motivated by TOCP with nonlinear constraints which arise in motion planning of mechatronic systems. The algorithm applies a trust-region globalization strategy ensuring global convergence. For fully determined problems our algorithm provides locally quadratic convergence. Moreover, the algorithm keeps all iterates feasible enabling early termination at suboptimal, feasible solutions. This additional feasibility is achieved by an efficient iterative strategy using evaluations of constraints, i.e., zeroorder information. Convergence of the feasibility iterations can be enforced by reduction of the trust-region radius. These feasibility iterations maintain feasibility for general Nonlinear Programs (NLP). Therefore, the algorithm is applicable to general NLP. We demonstrate our algorithm’s efficiency and the feasibility updates for a TOCP of an overhead crane motion planning simulation case.

Keywords: Numerical algorithms, Optimal control, Constrained control
Abstract: In this study, we propose a non-interior-point method to solve the optimal control problem with equilibrium constraints (OCPEC). OCPEC is an intractable problem owing to its inherently unstable constraint system, resulting in the numerical difficulties such as a feasible region without strict interior. Compared to interior-point methods, the proposed method does not require all iterates to remain in the feasible region, and therefore has more freedom to select the stepsize to mitigate the numerical difficulties. This stepsize freedom is achieved by introducing a smoothing-equation reformulation for the complementary conditions of inequality constraints in the Karush--Kuhn--Tucker conditions. We solve the discretized OCPEC in the framework of the continuation method that solves a sequence of nonlinear programming problems. A sparsity exploitation technique is introduced to efficiently solve the linear system, and a line search strategy with a dedicated merit function is introduced to guarantee the convergence. We demonstrate the effectiveness of the proposed algorithm using several numerical examples and make a comparison with an interior-point method solver.

Keywords: Optimal control, Numerical algorithms, Computational methods
Abstract: Solutions to optimal control problems can be discontinuous, even if all the functionals defining the problem are smooth. This can cause difficulties when numerically computing solutions to these problems. While conventional numerical methods assume state and input trajectories are continuous and differentiable or smooth, our method is able to capture discontinuities in the solution by introducing time-mesh nodes as decision variables. This allows one to obtain a higher accuracy solution for the same number of mesh nodes compared to a fixed time-mesh approach. Furthermore, we propose to first solve a sequence of suitably-defined least-squares problems to ensure that the error in the dynamic equation is below a given tolerance. The cost functional is then minimized subject to an inequality constraint on the dynamic equation residual. We demonstrate our implementation on an optimal control problem that has a chattering solution. Solving such a problem is difficult, since the solution involves infinitely many switches of decreasing duration. This simulation shows how the flexible mesh is able to capture discontinuities present in the solution and achieve superlinear convergence as the number of mesh intervals is increased.

Keywords: Numerical algorithms, Optimal control, Switched systems
Abstract: This letter introduces the NOnSmooth Numerical Optimal Control (NOSNOC) open-source software package. It is a modular MATLAB tool based on CasADi and IPOPT for numerically solving Optimal Control Problems (OCP) with piecewise smooth systems (PSS). The tool supports: 1) automatic reformulation of systems with state jumps into PSS (via the time-freezing reformulation [Nurkanovic et al., 2021]) and of PSS into computationally more convenient forms, 2) automatic discretization of the OCP via, e.g., the recently introduced Finite Elements with Switch Detection [Nurkanovic et al., 2022] which enables high accuracy optimal control and simulation of PSS, 3) solution methods for the resulting discrete-time OCP. The nonsmooth discrete-time OCP are solved with techniques of continuous optimization in a homotopy procedure, without the use of integer variables. This enables the treatment of a broad class of nonsmooth systems in a unified way. Two tutorial examples are given. A benchmark shows that NOSNOC provides both faster and more accurate solutions than conventional approaches, including mixed-integer formulations.