For a non-linear MIMO feedback system, the robustness against uncertain time-variations in the feedback loop is investigated in an input-output framework. A general sufficient condition in terms of a bound on average rates of time-variation for the system to be stable is derived. The condition gives a tolerable limit on infrequent large variations or slow time-variation rate of a non-linear MIMO adaptive switching system.
This paper presents a new method for dynamic output feedback stabilizing controller design for decomposable systems with switching topology and delay. Our approach consists of two steps. In the first step, we model the decomposable systems with switching topology as equivalent LPV systems with a piecewise constant parameter. In the second step, we design stabilizing output feedbacks for these LPV systems in the presence of a time-varying output delay using a trajectory-based stability analysis approach. We do not impose any constraint on the delay derivative. Finally, we illustrate our approac…
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-qu…
Feedback stabilization of switched systems under arbitrary switching: A convex characterization
Aeronautics Institute of Technology (ITA)（巴西空军理工学院）；Politecnico di Torino（都灵理工大学）；Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systèmes（巴黎萨克雷大学、法国国家科学研究中心、中央苏佩莱克学院、信号与系统实验室）
We study a variant of online optimization in which the learner receives $k$-round $\textit{delayed feedback}$ about hitting cost and there is a multi-step nonlinear switching cost, i.e., costs depend on multiple previous actions in a nonlinear manner. Our main result shows that a novel Iterative Regularized Online Balanced Descent (iROBD) algorithm has a constant, dimension-free competitive ratio that is $O(L^{2k})$, where $L$ is the Lipschitz constant of the switching cost. Additionally, we provide lower bounds that illustrate the Lipschitz condition is required and the dependencies on $k$ an…
This paper considers the distributed filtering problem for a class of stochastic uncertain systems under quantized data flowing over switching sensor networks. Employing the biased noisy observations of the local sensor and interval-quantized messages from neighboring sensors successively, an extended state based distributed Kalman filter (DKF) is proposed for simultaneously estimating both system state and uncertain dynamics. To alleviate the effect of observation biases, an event-triggered update based DKF is presented with a tighter mean square error bound than that of the time-driven one b…
In this work, the problem of switching control design for DC-DC boost converter is considered, in the case of operation under uncertain equilibrium condition arising due to perturbations in the input and load parameters. Assuming that these uncertain parameters are generated via a known linear exo-system, a parameter estimator is designed to update the equilibrium point for the switching controller in real-time. In order to mitigate the noise amplification problem associated with the designed parameter estimator, the estimation error injection term is filtered via a set of first-order filters …
Adaptive Control of Uncertain Pure-feedback Nonlinear Systems
Center for Control Theory and Guidance Technology, Harbin Institute of Technology（哈尔滨工业大学控制理论与制导技术研究中心）；School of Mechatronic Engineering, Harbin Institute of Technology（哈尔滨工业大学机电工程学院）
This paper proposes several definitions of robust stability for logic dynamical systems (LDSs) with uncertain switching, including robust/uniform robust set stability and asymptotical (or infinitely convergent)/finite-time set stability with ratio one. It is proved herein that an LDS is robustly set stable if and only if the destination set contains all loops (i.e., the paths from each state to itself); an LDS is uniformly robustly set stable, or finite-time set stable with ratio one, if and only if all states outside the destination set are unreachable from any self-reachable state; and an LD…
This paper investigates the problem of robust model predictive control (RMPC) of linear-time-invariant (LTI) discrete-time systems subject to structured uncertainty and bounded disturbances. Typically, the constrained RMPC problem with state-feedback parameterizations is nonlinear (and nonconvex) with a prohibitively high computational burden for online implementation. To remedy this, a novel approach is proposed to linearize the state-feedback RMPC problem, with minimal conservatism, through the use of semidefinite relaxation techniques. The proposed algorithm computes the state-feedback gain…
The distributed optimal output consensus problem for high-order multi-agent systems has been studied recently. In this paper, we further focus on the same problem for high-order multi-agent systems subject to parametric uncertainties and aim at distributed robust controllers by measurement output feedback. We first develop a dynamic compensator to estimate the expected optimal consensus point and convert the problem into several decentralized robust tracking problems. Then, by combining the integral control technique and dirty derivative observer technique, we constructively propose a distribu…
This paper investigates the distributed event-triggered control problem for a class of uncertain pure-feedback nonlinear multi-agent systems (MASs) with polluted feedback. Under the setting of event-triggered control, substantial challenges exist in both control design and stability analysis for systems in more general non-affine pure-feedback forms wherein all state variables are not directly and continuously available or even polluted due to sensor failures, and thus far very limited results are available in literature. In this work, a nominal control strategy under regular state feedback is…
