Nonsmooth Adaptive Control Design for a Large Class of Uncertain High-Order Stochastic Nonlinear Systems

This paper investigates the problem of the global stabilization via partial-state feedback and adaptive technique for a class of high-order stochastic nonlinear systems with more uncertainties/unknowns and stochastic zero dynamics. First of all, two stochastic stability concepts are slightly extended to allow the systems with more than one solution. To solve the problem, a lot of substantial technical difficulties should be overcome since the presence of severe uncertainties/unknowns, unmeasurable zero dynamics, and stochastic noise. By introducing the suitable adaptive updated law for an unknown design parameter and appropriate control Lyapunov function, and by using the method of adding a power integrator, an adaptive continuous (nonsmooth) partial-state feedback controller without overparameterization is successfully designed, which guarantees that the closed-loop states are bounded and the original system states eventually converge to zero, both with probability one. A simulation example is provided to illustrate the effectiveness of the proposed approach

Adaptive State-Feedback Stabilization for High-Order Stochastic Nonlinear Systems Driven by Noise of Unknown Covariance

This paper further considers more general high-order stochastic nonlinear system driven by noise of unknown covariance and its adaptive state-feedback stabilization problem. A smooth state-feedback controller is designed to guarantee that the origin of the closed-loop system is globally stable in probability

Stochastic Stabilization of Nonholonomic Mobile Robot with Heading-Angle-Dependent Disturbance

The problem of exponential stabilization for nonholonomic mobile robot with dependent stochastic disturbance of heading angle is considered in this paper. An integrator backstepping controller based on state-scaling method is designed such that the state of the closed-loop system, starting from a nonzero initial heading angle, is regulated to the origin with exponential rate in almost surely sense. For zero initial heading angle, a controller is designed such that the heading angle is driven away from zero while the position variables are bounded in a neighborhood of the origin. Combing the above two cases results in a switching controller such that for any initial condition the configuration of the robot can be regulated to the origin with exponential rate. The efficiency of the proposed method is demonstrated by a detailed simulation