In this paper, a new polynomial chaos based framework for analyzing linear systems with probabilistic parameters is presented. Stability analysis and synthesis of optimal quadratically stabilizing controllers for such systems are presented as convex optimization problems, with exponential mean square stability guarantees. A Monte-Carlo approach for analysis and synthesis is also presented, which is used to benchmark the polynomial chaos based approach. The computational advantage of the polynomial chaos approach is shown with an example based on the design of an optimal EMS-stabilizing controller, for an F-16 aircraft model.
Probabilistic Data Association-Feedback Particle Filter for Multiple Target Tracking Applications
Coordinated Science Laboratory and the Department of Mechanical Science and Engineering at the University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校协同科学实验室与机械科学与工程系）
This paper considers linear discrete-time systems with additive disturbances, and designs a Model Predictive Control (MPC) law incorporating a dynamic feedback gain to minimise a quadratic cost function subject to a single chance constraint. The feedback gain is selected online and we provide two selection methods based on minimising upper bounds on predicted costs. The chance constraint is defined as a discounted sum of violation probabilities on an infinite horizon. By penalising violation probabilities close to the initial time and assigning violation probabilities in the far future with va…
This note studies the robust output feedback stabilization problem of a class of multi-input multi-output invertible nonlinear systems, for which an "ideal" state feedback based on feedback linearization can be designed under certain mild assumptions. By systematically designing a set of extended low-power high-gain observers, we show that this "ideal" linearizing feedback law can be approximately estimated, which provides a robust output feedback stabilizer such that the origin of the resulting closed-loop system is semiglobally asymptotically stable.
This paper investigates the stabilization of probabilistic Boolean networks (PBNs) via a novel pinning control strategy based on network structure. In a PBN, the evolution equation of each gene switches among a collection of candidate Boolean functions with probability distributions that govern the activation frequency of each Boolean function. Owing to the stochasticity, the uniform state feedback controller, independent of switching signal, might be out of work, and in this case, the non-uniform state feedback controller is required. Subsequently, a criterion is derived to determine whether …
We present a method for feedback motion planning of systems with unknown dynamics which provides probabilistic guarantees on safety, reachability, and goal stability. To find a domain in which a learned control-affine approximation of the true dynamics can be trusted, we estimate the Lipschitz constant of the difference between the true and learned dynamics, and ensure the estimate is valid with a given probability. Provided the system has at least as many controls as states, we also derive existence conditions for a one-step feedback law which can keep the real system within a small bound of …
This note studies the robust output feedback stabilization problem of multi-input multi-output invertible nonlinear systems with output-dependent multipliers. An "ideal" state feedback is first designed under certain mild assumptions. Then, a set of extended low-power high-gain observers is systematically designed, providing a complete estimation of the "ideal" feedback law. This yields a robust output feedback stabilizer such that the origin of the closed-loop system is semiglobally asymptotically stable, while improving the numerical implementation with the power of high-gain parameters up t…
Robust imitation learning seeks to mimic expert controller behavior while ensuring stability, but current methods require accurate plant models. Here, robust imitation learning is addressed for stabilizing poorly modeled plants with linear dynamic output feedback. Open-loop input-output properties are used to characterize an uncertain plant, and the feedback matrix of the dynamic controller is learned while enforcing stability through the controller's open-loop QSR-dissipativity properties. The imitation learning method is applied to two systems with parametric uncertainty.
We consider the problem of designing robust state-feedback controllers for discrete-time linear time-invariant systems, based directly on measured data. The proposed design procedures require no model knowledge, but only a single open-loop data trajectory, which may be affected by noise. First, a data-driven characterization of the uncertain class of closed-loop matrices under state-feedback is derived. By considering this parametrization in the robust control framework, we design data-driven state-feedback gains with guarantees on stability and performance, containing, e.g., the $\mathcal{H}_…
Synergistic hybrid feedback refers to a collection of feedback laws that allow for global asymptotic stabilization of a compact set through the following switching logic: given a collection of Lyapunov functions that are indexed by a logic variable, whenever the currently selected Lyapunov function exceeds the value of another function in the collection by a given margin, then a switch to the corresponding feedback law is triggered. This kind of feedback has been under development over the past decade and it has led to multiple solutions for global asymptotic stabilization on compact manifolds…
In this paper, we propose a robust Kalman filtering framework for systems with probabilistic uncertainty in system parameters. We consider two cases, namely discrete time systems, and continuous time systems with discrete measurements. The uncertainty, characterized by mean and variance of the states, is propagated using conditional expectations and polynomial chaos expansion framework. The results obtained using the proposed filter are compared with existing robust filters in the literature. The proposed filter demonstrates better performance in terms of root mean squared error and rate of co…
RWTH Aachen University（亚琛工业大学）；Ingenieurgesellschaft Auto und Verkehr (IAV)（IAV汽车与交通工程公司）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. While learning-based control has the potential to yield superior performance in demanding applications, robustness to uncertainty remains an important challenge. Since Bayesian methods quantify uncertainty of the learning results, it is natural to incorporate these uncertainties into a robust design. In contrast to most state-of-the-art approaches that consider worst-case estimates, we leverage the learning method's posterior distribution i…
Solving nonlinear model predictive control problems in real time is still an important challenge despite of recent advances in computing hardware, optimization algorithms and tailored implementations. This challenge is even greater when uncertainty is present due to disturbances, unknown parameters or measurement and estimation errors. To enable the application of advanced control schemes to fast systems and on low-cost embedded hardware, we propose to approximate a robust nonlinear model controller using deep learning and to verify its quality using probabilistic validation techniques. We pro…
In this paper we consider multi-agent coalitional games with uncertain value functions for which we establish distribution-free guarantees on the probability of allocation stability, i.e., agents do not have incentives to defect from the grand coalition to form subcoalitions for unseen realizations of the uncertain parameter. In case the set of stable allocations, the so called core of the game, is empty, we propose a randomized relaxation of the core. We then show that those allocations that belong to this relaxed set can be accompanied by stability guarantees in a probably approximately corr…
This paper provides a control protocol for the robust output feedback consensus of networked heterogeneous nonlinear negative-imaginary (NI) systems. Heterogeneous nonlinear output strictly negative-imaginary (OSNI) controllers are applied in positive feedback according to the network topology to achieve output feedback consensus. The main contribution of this paper is extending the previous studies of the robust output feedback consensus problem for networked heterogeneous linear NI systems to nonlinear NI systems. Output feedback consensus is proved by investigating the internal stability of…
Classical sufficient conditions for ensuring the robust stability of a dynamical system in feedback with a nonlinearity include passivity, small gain, circle, and conicity theorems. We present a generalized version of these results for arbitrary semi-inner product spaces. Our result is purely algebraic, and holds even when the conventional discrete or continuous-time causal dynamical systems are replaced by general nonlinear relations, where there need not exist a notion of time. Our result clarifies when the sufficient conditions for robust stability are also necessary, and explains why stron…
We introduce a sequential learning algorithm to address a robust controller tuning problem, which in effect, finds (with high probability) a candidate solution satisfying the internal performance constraint to a chance-constrained program which has black-box functions. The algorithm leverages ideas from the areas of randomised algorithms and ordinal optimisation, and also draws comparisons with the scenario approach; these have all been previously applied to finding approximate solutions for difficult design problems. By exploiting statistical correlations through black-box sampling, we formal…
The University of Texas at Dallas（德克萨斯大学达拉斯分校）；The Australian National University（澳大利亚国立大学）
We propose a robust data-driven output feedback control algorithm that explicitly incorporates inherent finite-sample model estimate uncertainties into the control design. The algorithm has three components: (1) a subspace identification nominal model estimator; (2) a bootstrap resampling method that quantifies non-asymptotic variance of the nominal model estimate; and (3) a non-conventional robust control design method comprising a coupled optimal dynamic output feedback filter and controller with multiplicative noise. A key advantage of the proposed approach is that the system identification…
In this work, we propose a framework to learn feedback control policies with guarantees on closed-loop generalization and adversarial robustness. These policies are learned directly from expert demonstrations, contained in a dataset of state-control input pairs, without any prior knowledge of the task and system model. We use a Lipschitz-constrained loss minimization scheme to learn feedback policies with certified closed-loop robustness, wherein the Lipschitz constraint serves as a mechanism to tune the generalization performance and robustness to adversarial disturbances. Our analysis exploi…
We construct a robust stabilizing feedback law for the viscous Saint-Venant system of Partial Differential Equations (PDEs) with surface tension and without wall friction. The Saint-Venant system describes the movement of a tank which contains a viscous liquid. We assume constant contact angles between the liquid and the walls of the tank and we achieve a spill-free exponential stabilization with robustness to surface tension by using a Control Lyapunov Functional (CLF). The proposed CLF provides a parameterized family of sets which approximate the state space from the interior. Based on the C…
