The Satabilization Of Stochastic Nonholonomic Systems

Feedback control, which mainly contains state-feedback control and output-feedback control, is one of the basic problems for the stabilization of stochasticnonlinear systems. This paper is largely concerned with the stabilization problems ofstochastic noholonomic systems. Firstly, the backgrounds and developments ofnonholonomic control systems, stochastic nonlinear systems and stochasticnonholonomic systems are introduced. A model of stochastic nonholonomic mobilerobots is given and the general form of stochastic nonholonomic chained systems isintroduced. Some basic concepts and results are briefly given. The problems ofstate-feedback stabilization for three types of uncertain stochastic nonholonomicsystems are discussed. Then, for stochastic nonhlonomic systems with Markovianswitching, we design state-feedback and output-feedback controllers. In the end, theproblem of state-feedback stabilization for stochastic nonhlonomic mobile robots isstudied. The main results and innovative points can be summarized as follows:1．For three types of uncertain stochastic nonholonomic systems, based onbackstepping method, we design the adaptive state-feedback controllers and switchinglaw, which guarantee that the closed systems are asymptotically stabilized inprobability.2．When parts of the states are unmeasured, the output-feedback stabilization forstochastic nonhlonomic systems with Markovian switching is discussed. A Sufficientcondition for almost surely bounded solution of stochastic nonholonomic systems withMarkovian switching is given. The designed controllers and switching law guaranteethat the closed systems are largly asymptotically stabilized in probability.3．If all states can be measured, we studied the state-feedback stabilization forstochastic nonhlonomic systems with Markovian switching.4．We establish the model of stochastic nonholonomic mobile robots based onvisual servoing, which are not strict triangle structure. The state-feedback controllers and switching law, which guarantee that the closed systems are asymptoticallystabilized in probability, are presented for stochastic nonhlonomic systems.5．Based on the research results mentioned above, some simulation examples,especially, stochastic nonholonomic mobile robots, are given. These simulation resultswith MATLAB show the effectiveness of designed controllers.