The Stabilization Of Stochastic High-Order Nonholonomic Systems

Nonholonomic systems are a kind of very important mechanical systems,which have a wide application prospect.Therefore,the control problem of nonholonomic systems is more and more attention.The objectives of nonholonomic control systems can be classified as motion planning,stabilization and tracking control.This paper is largely concerned with the stabilization problems of stochastic high order noholonomic systems.Firstly,the background and development of nonholonomic control systems,stochastic nonlinear systems and stochastic nonholonomic systems are introduced.Some basic concepts and results are briefly given.The problems of state-feedback stabilization for stochastic high order nonholonomic systems with Markovian switching are discussed.Then,for stochastic high order nonhlonomic systems with nonlinear parametrization,a state-feedback controller is proposed.In the end,the problem of output-feedback stabilization for more general stochastic high order nonhlonomic is investigated.The main results and innovative points are summarized as follows:1.For stochastic high order nonholonomic systems with Markovian switching,we design the state-feedback controller and switching law,which guarantee that the closed systems are almost surely asymptotically stabilized.2.For stochastic high order nonhlonomic system with nonlinear parametrization,we design the state-feedback controller and switching law based on parameter separation technique and adding a power integrator Backstepping,which guarantee that the closed systems are asymptotically stabilized in probability and estimation of parameter are bounded in probability.3.When parts of the states are unmeasured,the output-feedback stabilization for more general stochastic high order nonhlonomic systems is discussed.By using homogeneous domination and sign function design approach,the designed controller and switching law guarantee that the closed systems are asymptotically stabilized in probability.4.Based on the research results mentioned above,some simulation examples are given.These simulation results with MATLAB show the effectiveness of designed controllers.