This paper introduces an add-on, supervisory scheme, referred to as Action Governor (AG), for discrete-time linear systems to enforce exclusion-zone avoidance requirements. It does so by monitoring, and minimally modifying when necessary, the nominal control signal to a constraint-admissible one. The AG operates based on set-theoretic techniques and online optimization. This paper establishes its theoretical foundation, discusses its computational realization, and uses two simulation examples to illustrate its effectiveness.
The paper considers the application of reference governors to linear discrete-time systems with constraints given by polynomial inequalities. We propose a novel algorithm to compute the maximal output admissible invariant set in the case of polynomial constraints. The reference governor solves a constrained nonlinear minimization problem at initialization and then uses a bisection algorithm at the subsequent time steps. The effectiveness of the method is demonstrated by two numerical examples.
This note describes a reference governor design for a continuous-time nonlinear system with an additive disturbance. The design is based on predicting the response of the nonlinear system by the response of a linear model with a set-bounded prediction error, where a state-and-input dependent bound on the prediction error is explicitly characterized using logarithmic norms. The online optimization is reduced to a convex quadratic program with linear inequality constraints. Two numerical examples are reported.
The action governor is an add-on scheme to a nominal control loop that monitors and adjusts the control actions to enforce safety specifications expressed as pointwise-in-time state and control constraints. In this paper, we introduce the Robust Action Governor (RAG) for systems the dynamics of which can be represented using discrete-time Piecewise Affine (PWA) models with both parametric and additive uncertainties and subject to non-convex constraints. We develop the theoretical properties and computational approaches for the RAG. After that, we introduce the use of the RAG for realizing safe…
Reference governors are add-on schemes that are used to modify trajectories to prevent controlled dynamical systems from violating constraints and so are playing an increasingly important role in aerospace, robotic, and other engineering applications. Here we present a novel reference governor design for systems whose polynomial constraints depend on unknown bounded parameters. This is a significant departure from earlier treatments of reference governors, where the constraints were linear or known, because here we transfer the uncertainties into the constraints instead of having them in the c…
Safe Control and Learning Using Generalized Action Governor
organization= School of Automotive Studies, Tongji University , city= Shanghai , postcode= 201804 , country= China；organization= Department of Aerospace Engineering, University of Michigan , city= Ann Arbor , postcode= 48109 , state= MI , country= USA；organization= Department of Aerospace Engineering, Embry-Riddle Aeronautical University , city= Daytona Beach , postcode= 32114 , state= FL , country= USA；organization= Department of Electrical Engineering, University of Texas at Arlington , city= Arlington , postcode= 76019 , state= TX , country= USA；organization= Hagler Institute for Advanced Study, Texas A\&M University , city= College Station , postcode= 77840 , state= TX , country= USA
Geometric Conditions for Lossless Convexification in Linear Optimal Control with Discrete-Valued Inputs: Real-Time Implementation for Spacecraft Rendezvous
In this paper we develop and analyse convex searches for Zames--Falb multipliers. We present two different approaches: Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) multipliers. The set of FIR multipliers is complete in that any IIR multipliers can be phase-substituted by an arbitrarily large order FIR multiplier. We show that searches in discrete-time for FIR multipliers are effective even for large orders. As expected, the numerical results provide the best $\ell_{2}$-stability results in the literature for slope-restricted nonlinearities. Finally, we demonstrate that the…
In this paper, we study a class of finite-time control problems for discrete-time positive linear systems with time-varying state parameters. Although several interesting control problems appearing in population biology, economics, and network epidemiology can be described as the class of finite-time control problems, an efficient solution to the control problem has not been yet found in the literature. In this paper, we propose an optimization framework for solving the class of finite-time control problems via convex optimization. We illustrate the effectiveness of the proposed method by nume…
The inverse linear-quadratic optimal control problem is a system identification problem whose aim is to recover the quadratic cost function and hence the closed-loop system matrices based on observations of optimal trajectories. In this paper, the discrete-time, finite-horizon case is considered, where the agents are also assumed to be homogeneous and indistinguishable. The latter means that the agents all have the same dynamics and objective functions and the observations are in terms of "snap shots" of all agents at different time instants, but what is not known is "which agent moved where" …
We consider the problem of computing the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints that admit quadratic relaxations. These non-convex constraints include semialgebraic sets and other smooth constraints with Lipschitz gradient. With these quadratic relaxations, a sufficient condition for set invariance is derived and it can be formulated as a set of linear matrix inequalities. Based on the sufficient condition, a new algorithm is presented with finite-time convergence to the actual maximal invariant set under mild assumptions. This algori…
The stabilization of unstable nonlinear systems and tracking control are challenging engineering problems due to the encompassed nonlinearities in dynamic systems and their scale. In the past decades, numerous observer-based control designs for dynamic systems in which the nonlinearity belongs to Lipschitz functions have been proposed. However, most of them only focus on output feedback and consequently, state feedback design remains less developed. To that end, this paper is dedicated to the problem of full-state feedback controller design for discrete-time Lipschitz nonlinear systems. In add…
Unlike for Linear Time-Invariant (LTI) systems, for nonlinear systems, there exists no general framework for systematic convex controller design which incorporates performance shaping. The Linear Parameter-Varying (LPV) framework sought to bridge this gap by extending convex LTI synthesis results such that they could be applied to nonlinear systems. However, recent literature has shown that naive application of the LPV framework can fail to guarantee the desired asymptotic stability guarantees for nonlinear systems. Incremental dissipativity theory has been successfully used in the literature …
University of Pennsylvania（宾夕法尼亚大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
Minimax optimization has been central in addressing various applications in machine learning, game theory, and control theory. Prior literature has thus far mainly focused on studying such problems in the continuous domain, e.g., convex-concave minimax optimization is now understood to a significant extent. Nevertheless, minimax problems extend far beyond the continuous domain to mixed continuous-discrete domains or even fully discrete domains. In this paper, we study mixed continuous-discrete minimax problems where the minimization is over a continuous variable belonging to Euclidean space an…
The dissipativity framework is widely used to analyze stability and performance of nonlinear systems. By embedding nonlinear systems in an LPV representation, the convex tools of the LPV framework can be applied to nonlinear systems for convex dissipativity based analysis and controller synthesis. However, as has been shown recently in literature, naive application of these tools to nonlinear systems for analysis and controller synthesis can fail to provide the desired guarantees. Namely, only performance and stability with respect to the origin is guaranteed. In this paper, inspired by the re…
University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of California, Santa Cruz（加州大学圣克鲁兹分校）
In this work, we analyze the properties of the solution to the covariance steering problem for discrete time Gaussian linear systems with a squared Wasserstein distance terminal cost. In our previous work, we have shown that by utilizing the state feedback control policy parametrization, this stochastic optimal control problem can be associated with a difference of convex functions program. Here, we revisit the same covariance control problem but this time we focus on the analysis of the problem. Specifically, we establish the existence of solutions to the optimization problem and derive the f…
