Research On Stability And Adaptive Control Of Several Classes Of Stochastic/Random Nonlinear Systems

In recent years,the study of stochastic/random nonlinear systems has received great attentions.Compared with deterministic nonlinear systems,stochastic/random nonlinear systems have more complex and variable performance due to the existence and influence of random disturbances.Stability is always the core problem of system analysis and synthesis.The uncertain parameter in system model and the parameter perturbation in system operation are often faced in controller design process.Therefore,the reaserch of stability and adaptive control for stochastic/random nonlinear systems has theoretical significance and practical application value.In this dissertation,Lyapunov stability theory,stochastic process theory and adaptive control theory,together with stochastic analysis technology and Backstepping method,are used to study the stability and adaptive control problem for stochastic nonlinear system driven by a white noise process(i.e.,Ito stochastic nonlinear systems)and random nonlinear system driven by a colored noise process,respectively.The main research contents are summarized as follows:For Ito stochastic nonlinear systems,firstly,some new stability and instability theorems for Ito stochastic nonlinear system are proposed and improve the existing stability and instability theorems.Simulation examples verify the correctness of the obtained theoretical results.Secondly,the obtained results of Ito stochastic nonlinear systems are extended to Ito stochastic nonlinear time delay systems which don't satisfy the local Lipschitz condition.Under the condition that Ito stochastic nonlinear time delay system has a unique solution,some finite-time stability and instability criteria of Ito stochastic nonlinear time delay systems are given and these criteria weaken the existing criteria respectively.Simulation examples verify the correctness of the theoretical findings.Finally,the obtained results of Ito stochastic nonlinear systems are extended to Ito stochastic nonlinear switched systems and a new stability criterion is presented for Ito stochastic nonlinear systems with arbitrary switching.For a class of Ito stochastic nonlinear strict feedback switched systems with stochastic inverse dynamics and input saturation,the auxiliary subsystem is introduced to compensate input saturation,and the adaptive Backstepping method is used to design an adaptive tracking controller,then the obtained stability criterion is applied to analyze the performance of the closed-loop system.The effectiveness and feasibility of the designed control strategy are verified by simulation examples.For random nonlinear systems driven by colored noise processes,firstly,some noise-to-state stability criteria of random nonlinear systems are improved,and some conditions in the existing results are relaxed.In addition,the noise-to-state instability definitions and criteria of random nonlinear systems are presented.Simulation examples verify the correctness of the theoretical results.Secondly,the obtained noise-to-state stability results of random nonlinear systems are extended to random nonlinear time delay systems.Under the conditions that the solution of random nonlinear time delay system exists and is unique,some noise-to-state stability criteria of random nonlinear time delay systems are proposed,and the problem of adaptive output feedback control for a class of random nonlinear strict feedback time delay systems is solved by using the obtained theoretical results.Finally,the noise-to-state stability results of random nonlinear systems are applied to the adaptive tracking control problem of a class of random nonlinear pure feedback Markovian switched systems.The auxiliary control subsystem is introduced to deal with the difficulty caused by non-affine control input in controller design process.Meanwhile,the improved Backstepping method is presented to deal with the non-affine state variables.The effectiveness and feasibility of the designed control strategy are verified by simulation examples.