On Adaptive Output Feedback Dynamic Surface Control Of Stochastic Nonlinear Systems

Stochastic nonlinear systems are a class of nonlinear dynamic systems with random dynamic characteristics with wide range of applications and are difficult to control. The stability analysis and controller design of them are of theoretical significance and wide application value. In recent years, the research of stochastic nonlinear systems is given more and more attention by many scholars both at home and abroad. In this paper, based on dynamic surface control technique and K-filters, several adaptive output feedback control schemes are proposed for stochastic nonlinear systems with unmeasured states. The main contributions are highlighted as follows:Firstly, an adaptive output-feedback control scheme is presented for a class of stochastic nonlinear systems with dynamic uncertainties and unmeasured states by using the approximation capability of neural networks and Young’s inequality. K-filters are designed to estimate the unmeasured states. The changing supply function is adapted to solve the problem of dynamical uncertainties. By combining dynamic surface control technique with backstepping method, the explosion of complexity in traditional backstepping design is avoided and the calculation is reduced. Through theoretical analysis, it is proved that all signals in the closed-loop control system are shown to be semi-globally uniformly ultimately bounded in probability, and the output of the system converges to a small neighborhood of the origin.Secondly, based on stochastic small-gain theorem, an adaptive neural control scheme is investigated for a class of stochastic nonlinear systems with unmodeled dynamics and unmeasured states as well as unknown high-frequency control gain. Neural networks are used to approximate the unknown nonlinear functions.The problem of over parameterization is avoided by combining dynamic surface control with output feedback control. Utilizing the appropriate coordinate transformation and Young’s inequality, the proposed scheme removes the matching condition of the system functions. The stability analysis is given to show that the closed-loop system is input-state practically stability in probability. All the signals in the closed-loop control system are shown to be semi-globally uniformly ultimately bounded in probability, and the output of the system converges to a small neighborhood of the origin.Thirdly, based on dynamic surface control technique, an adaptive output-feedback control approach is proposed for a class of stochastic nonlinear interconnected systems with both parametric uncertainties and unknown nonlinear interactions. By combining dynamic surface control method with output-feedback control, the explosion of complexity caused by the repeated differentiations on virtual control in traditional backstepping design is avoided, which extends the routine method of dynamic surface control. By applying K-filters to reconstruct the state of system, the designed adaptive controller can guarantee all the signals in the closed-loop control system are shown to be semi-globally uniformly ultimately bounded in probability, and the tracking error converges to a small residual set.Through the study of this dissertation, the adaptive output-feedback control problems for stochastic nonlinear systems with unmodeled dynamics and unmeasurable states have been properly solved, and by using the method of dynamic surface control, the tracking control problem is realized for a class of stochastic nonlinear interconnected systems. Simulation examples verify the effectiveness of the proposed control schemes.