Xue-Jun Xie

Adaptive backstepping controller design using stochastic small-gain theorem

A more general class of stochastic nonlinear systems with unmodeled dynamics and uncertain nonlinear functions are considered in this paper. With the concept of input-to-state practical stability (ISpS) and nonlinear small-gain theorem being extended to stochastic case, by combining stochastic small-gain theorem with backstepping design technique, an adaptive output-feedback controller is proposed. It is shown that the closed-loop system is practically stable in probability. A simulation example demonstrates the control scheme.

Brief paper: Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching

A more general class of stochastic nonlinear systems with Markovian switching are considered in this paper. As preliminaries, the stability criteria and the existence theorem of strong solution are firstly presented by using the inequality of mathematic expectation of Lyapunov function and its infinitesimal generator. The state-feedback controller is designed by regarding Markovian switching as constant such that the closed-loop system has a unique asymptotically stable solution. The output-feedback controller is designed based on a quadratic-plus-quartic-form Lyapunov function such that the closed-loop system has a unique asymptotically stable solution in unbiased case and has a unique bounded-in-probability solution in biased case.

Output Feedback Regulation of Stochastic Nonlinear Systems With Stochastic iISS Inverse Dynamics

This paper develops a unifying framework for output feedback regulation of stochastic nonlinear systems with more general stochastic inverse dynamics. The contributions of this work are characterized by the following novel features: (1) Motivated by the concept of integral input-to-state stability (iISS) in deterministic systems and stochastic input-to-state stability (SISS) using Lyapunov function in stochastic systems, a concept of stochastic integral input-to-state stability (SiISS) using Lyapunov function is first introduced, two important properties of SiISS are obtained: (i) SiISS is strictly weaker than SISS using Lyapunov function; (ii) SiISS is stronger than the minimum-phase property. However, only under the minimum-phase assumption, there is no dynamic output feedback control law for global stabilization in probability. (2) Almost sure boundedness, a reasonable and stronger concept than boundedness in probability, is introduced. The purpose of introducing the concept is to prove the boundedness and convergence of some signals in the closed-loop control system. (3) Some important mathematical tools which play an essential role in the boundedness and convergence analysis of the closed-loop system are established. (4) A unifying framework is proposed to design a dynamic output feedback control law, which drives the states to the origin almost surely while maintaining all the closed-loop signals bounded almost surely.

Brief paper: Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization

This paper investigates the adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization. By using the parameter separation lemma in [Lin, W., & Qian, C. (2002a). Adaptive control of nonlinearly parameterized systems: A nonsmooth feedback framework. IEEE Transactions on Automatic Control, 47, 757-774.] and some flexible algebraic techniques, and choosing an appropriate Lyapunov function, a smooth adaptive state-feedback controller is designed, which guarantees that the closed-loop system has an almost surely unique solution for any initial state, the equilibrium of interest is globally stable in probability, and the state can be regulated to the origin almost surely.

Brief paper: Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay

This paper investigates output-feedback control for a class of stochastic high-order nonlinear systems with time-varying delay for the first time. By introducing the adding a power integrator technique in the stochastic systems and a rescaling transformation, and choosing an appropriate Lyapunov-Krasoviskii functional, an output-feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability and the output can be regulated to the origin almost surely. A simulation example is provided to show the effectiveness of the designed controller.

Output Tracking of High-Order Stochastic Nonlinear Systems with Application to Benchmark Mechanical System

This note considers output tracking of high-order stochastic nonlinear systems without imposing any restriction on the high-order and the drift and diffusion terms. By using the backstepping design technique, a smooth state-feedback controller is given to guarantee that the solution process is bounded in probability and the error signal between the output and the reference signal can be regulated into a small neighborhood of the origin in probability. A practical example of stochastic benchmark mechanical system and simulation are provided to demonstrate the effectiveness of the control scheme.

Output-Feedback Stabilization of Stochastic High-Order Nonlinear Systems under Weaker Conditions

Under the weaker conditions on the power order and the nonlinear functions, this paper investigates the output-feedback stabilization problem for a class of stochastic high-order nonlinear systems. Based on the backstepping design method and homogeneous domination technique, the closed-loop system can be proved to be globally asymptotically stable in probability.

State-Feedback Control of High-Order Stochastic Nonlinear Systems with SiISS Inverse Dynamics

This technical note considers a class of high-order stochastic nonlinear systems with stochastic integral input-to-state stability (SiISS) inverse dynamics, and drift and diffusion terms depending upon the stochastic inverse dynamics and all the states. A new design and analysis approach to the problem of state-feedback global regulation is developed to guarantee that all the signals of the closed-loop system are bounded almost surely and the states can be regulated to zero almost surely.

A Homogeneous Domination Approach to State Feedback of Stochastic High-Order Nonlinear Systems With Time-Varying Delay

The homogeneous domination approach is introduced to solve the state feedback stabilization problem for stochastic high-order nonlinear systems with time-varying delay. Under the weaker conditions on the drift and diffusion terms, by using the homogeneous domination approach and solving several troublesome obstacles in the design and analysis procedure, a state feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability.

State feedback stabilization for stochastic feedforward nonlinear systems with time-varying delay

This paper investigates a class of stochastic feedforward nonlinear systems with time-varying delay. By introducing the homogeneous domination approach to stochastic systems, a state feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability.