We present a methodology for the global sampled-data stabilization of systems with a compact absorbing set and input/measurement delays. The methodology is based on the Inter-Sample-Predictor, Observer, Predictor, Delay-Free Controller (ISP-O-P-DFC) scheme and the stabilization is robust to perturbations of the sampling schedule. The obtained results are novel even for the delay-free case.
Global Stabilization of Nonlinear Delay Systems With a Compact Absorbing Set
National Technical University of Athens（雅典国立技术大学）；University of California, San Diego（加州大学圣地亚哥分校）；Laboratoire GREYC CNRS-ENSICAEN（GREYC国家科学研究中心-ENSICAEN实验室）；Centre National de la Recherche Scientifique, CNRS-EECI SUPELEC（法国国家科学研究中心，CNRS-EECI苏佩莱克）
For nonlinear affine in the control systems, a Lie algebraic sufficient condition for sampled-data feedback semi-global stabilization is established. We use this result, in order to derive sufficient conditions for sampled-data feedback stabilization for a couple of three-dimensional systems.
Sufficient conditions are established for sampled-data feedback global asymptotic stabilization for nonlinear autonomous systems. One of our main results is an extension of the well known Artstein-Sontag theorem on feedback stabilization concerning affine in the control systems. A second aim of the present work is to provide sufficient conditions for sampled-data feedback asymptotic stabilization for two interconnected nonlinear systems. Lie algebraic sufficient conditions are derived for the case of affine in the control interconnected systems without drift terms.
Sampling arises simultaneously with input and output delays in networked control systems. When the delay is left uncompensated, the sampling period is generally required to be sufficiently small, the delay sufficiently short, and, for nonlinear systems, only semiglobal practical stability is generally achieved. For example, global stabilization of strict-feedforward systems under sampled measurements, sampled-data stabilization of the nonholonomic unicycle with arbitrarily sparse sampling, and sampled-data stabilization of LTI systems over networks with long delays, are open problems. In this …
The aim of this work is to design an explicit finite dimensional boundary feedback controller of sampled-data form for locally exponentially stabilizing the equilibrium solutions to semilinear parabolic equations. The feedback controller is expressed in terms of the eigenfunctions corresponding to unstable eigenvalues of the linearized equation. This stabilizing procedure is applicable for any sampling rate, not necessary to be small enough, and it tends to the continuous-times version when the sampling period tends to zero.
This paper presents the cyber-physcial model of a computer-mediated control system that is a seamless, fully synergistic integration of the physical system and the cyber system, which provides a systematic framework for synthesis of cyber-physical systems (CPSs). In our proposed framework, we establish a Lyapunov stabilty theory for synthesis of CPSs and apply it to sampled-data control systems, which are typically synonymous with computer-mediated control systems. By our CPS approach, we not only develop stability criteria for sampled-data control systems but also reveal the equivalence and i…
The present work extends recent results by second author concerning sampled-data feedback stabilization for affine in the control of nonlinear systems with nonzero drift term, under the presence of a generalized control Lyapunov function associated with appropriate Lie algebraic hypotheses concerning the dynamics of the system. The main results of present work, constitute a generalization of the well-known "Artstein-Sontag" theorem on asymptotic stabilization by means of an almost smooth feedback controller. The analysis is limited to the affine single-input nonlinear systems with nonzero drif…
High-Probability Sampled-Data Stabilization of General Nonlinear Stochastic Systems
Research Institute of Intelligent Complex Systems, Fudan University（复旦大学智能复杂系统研究院）；School of Mathematics Sciences, Fudan University（复旦大学数学科学学院）；Department of Mathematics and Statistics, University of Strathclyde（斯特拉斯克莱德大学数学与统计系）
This paper is devoted to the stabilization of the incompressible Euler equation with free surface. We study the damping of two-dimensional gravity waves by an absorbing beach where the water-wave energy is dissipated by using the variations of the external pressure.
This paper addresses stochastic stabilization in case where implementation of control policies is digital, i. e., when the dynamical system is treated continuous, whereas the control actions are held constant in predefined time steps. In such a setup, special attention should be paid to the sample-to-sample behavior of the involved Lyapunov function. This paper extends on the stochastic stability results specifically to address for the sample-and-hold mode. We show that if a Markov policy stabilizes the system in a suitable sense, then it also practically stabilizes it in the sample-and-hold s…
In this paper, we build up an output feedback law to stabilize a sampled-data controlled heat equation (with a potential) in a bounded domain $Ω$. The feedback law abides the following rules: First, we divide equally the time interval $[0,+\infty)$ into infinitely many disjoint time periods, and divide each time period into three disjoint subintervals. Second, for each time period, we observe a solution over an open subset of $Ω$ in the first subinterval, take sample from outputs at one time point of the first subinterval, add a time-invariant output feedback control over another open subset o…
This paper studies the problem of designing sampled-data observers and observer-based, sampled-data, output feedback stabilizers for systems with both discrete and distributed, state and output time-delays. The obtained results can be applied to time delay systems of strict-feedback structure, transport Partial Differential Equations (PDEs) with nonlocal terms, and feedback interconnections of Ordinary Differential Equations with a transport PDE. The proposed design approach consists in exploiting an existing observer, which features robust exponential convergence of the error when continuous-…
This work proposes a notion of robust reachability of one set from another set under constant control. This notion is used to construct a control strategy, involving sequential set-to-set reachability, which guarantees robust global stabilization of nonlinear sampled data systems with positive sampling rate. Sufficient conditions for robust reachability of one set from another under constant control are also provided. Finally, the proposed method is illustrated through two examples.
For general nonlinear autonomous systems, a Lyapunov characterization for the possibility of semi-global asymptotic stabilizability by means of a time-varying sampled-data feedback is established. We exploit this result in order to derive a Lie algebraic sufficient condition for sampled-data feedback semi-global stabilizability of affine in the control nonlinear systems with non-zero drift terms. The corresponding proposition constitutes an extension of the "Artstein-Sontag" theorem on feedback stabilization.
We study a sampled-data implementation of linear controllers that depend on the output and its derivatives. First, we consider an LTI system of relative degree $r\ge 2$ that can be stabilized using $r-1$ output derivatives. Then, we consider PID control of a second order system. In both cases, the Euler approximation is used for the derivatives giving rise to a delayed sampled-data controller. Given a derivative-dependent controller that stabilizes the system, we show how to choose the parameters of the delayed sampled-data controller that preserves the stability under fast enough sampling. Th…
