Summary The trajectory tracking control problem for a class of nonlinear systems with uncertain parameters is considered in this article. A new adaptive finite‐time designed based on the backstepping method via command filters. filter mechanism can avoid calculation partial derivatives and solve “explosion complexity” design. compensation signals are introduced to eliminate errors produced by proposed guarantee error remains small neighborhood origin finite time, while practical stability...

This paper describes the robust H/sub /spl infin// filtering analysis and synthesis of nonlinear stochastic systems with state exogenous disturbance-dependent noise. We assume that measurement are corrupted by uncertain disturbance system dynamic is modeled Ito/spl circ/-type differential equations. For general systems, filter can be obtained solving second-order Hamilton-Jacobi inequalities. When worst-case considered in design procedure, a mixed 2//H/sub problem also solved minimizing...

This paper discusses the $H_{\infty}$ control problem for a class of nonlinear stochastic systems with both state- and disturbance-dependent noise. By means Hamilton--Jacobi equations, infinite finite horizon $H_\infty$ designs are developed. Some results on deterministic generalized to setting. We introduce some useful concepts such as "zero-state observability" detectability" which, together LaSalle invariance principle, yield valuable consequences in control.

In this paper, the generalized Lyapunov equation approach is used to study stochastic stabilization/detectability with state-multiplicative noise. Some practical test criteria for stabilization and detectability, such as Popov-Belevitch-Hautus criterion exact are obtained. Moreover, useful properties of derived based on critical stability detectability introduced in paper. As applications, first, linear quadratic regulator well related algebraic Riccati discussed extensively. Second,...

This technical note is concerned about the finite-time stability and stabilization for Itô stochastic systems with Markovian switching. A mode-dependent parameter approach proposed to give a sufficient condition stability, its superiority common analyzed. Moreover, studied two new conditions existence of state output feedback controllers are presented in terms coupled matrix inequalities. N-mode algorithm given solving obtained inequalities arising from stability(stabilization). Finally, an...

This technical note is concerned with a partially observed optimal control problem, whose novel feature that the cost functional of mean-field type. Hence determining time inconsistent in sense Bellman's dynamic programming principle does not hold. A maximum established using Girsanov's theorem and convex variation. Some nonlinear filtering results for backward stochastic differential equations (BSDEs) are developed by expressing solutions BSDEs as some Itô's processes. An illustrative...

This technical note is concerned with discussing the relationship between Nash equilibrium strategies and finite horizon H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control of time-varying stochastic systems subject to Markov jump parameters multiplicative noise. It revealed that equivalence these two problems depends on whether disturbance enters into diffusion term....

This paper is concerned with the open-loop linear-quadratic (LQ) Stackelberg game of mean-field stochastic systems in finite horizon. By means two generalized differential Riccati equations, follower first solves a LQ optimal control problem. Then, leader turns to solve an optimization problem for linear forward-backward equation. introducing new state and costate variables, we present sufficient condition existence uniqueness strategy terms solvability some equations convexity condition....

Abstract In this paper, finite‐time stability and stabilization problems for a class of linear stochastic systems are studied. First, new concept is defined systems. Then, based on matrix inequalities, some sufficient conditions under which the stochastically stable given. Subsequently, studied existence state feedback controller dynamic output presented by using inequality approach. An algorithm given solving inequalities arising from (stabilization). Finally, two examples employed to...

This paper discusses adaptive control problems of high-order stochastic nonlinear time-delay systems. Compared with the existing results, considered system involves uncertain parameters, intricate drift terms, and unknown time-varying delays. Based on a modified method adding power integrator Lyapunov-Krasoviskii functional technique, new controllers are successfully constructed to achieve objectives stabilization tracking, respectively. Examples given show effectiveness proposed strategies.

Based on discrete martingale theory, the LaSalle-type theorem for general discrete-time stochastic systems is obtained and almost sure stability in turn discussed. As applications, infinite horizon nonlinear optimal regulator investigated, a dynamical programming equation called Hamilton-Jacobi-Bellman also derived control.

This paper is concerned with the finite-time guaranteed cost control problem for stochastic Markovian jump systems incomplete transition rates. By a mode-dependent approach (MDA), several new sufficient conditions existence of state and output feedback controllers are provided, upper bound function more accurately expressed. Moreover, these results' superiorities analyzed shown. A N-mode optimization algorithm given to minimize function. Finally, detailed example utilized demonstrate merit...

Abstract This paper is concerned with the infinite horizon linear quadratic optimal control for discrete‐time stochastic systems both state and control‐dependent noise. Under assumptions of stabilization exact observability, it shown that law value exist, properties associated discrete generalized algebraic Riccati equation (GARE) are also discussed. Copyright © 2008 John Wiley Sons Asia Pte Ltd Chinese Automatic Control Society

In this note, we consider the finite horizon mixed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> / xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control problem for discrete-time stochastic linear systems subject to Markov jump parameters and multiplicative noise. Firstly, derive a bounded real lemma (SBRL), which is used establish necessary sufficient condition existence of via...