Output Feedback Control Of A Class Of Stochastic Nonlinear Systems

In the applied systems, due to the vast majority of uncertainties and dynamics of the plant, it is quite difficult to modify a target system precisely. And that is to say under most circumstances, we only have a small part of information of the target systems. Hence since 1950', the control theory of uncertain nonlinear systems has caused much attention of vast scholars. In order to meet the demand of closed systems, scientists expect for the desired performances of the controlled plant through proper manipulation of the uncertainties. To deal with the uncertainties and unknowns, estimate and robustness are the two key control processes. So state observation and robust control theory are widely used in the design process of controllers and make the controlled plants behaved as we hoped.According to the different forms of unknowns and uncertainties, in this dissertation we studied the stabilization analysis and control problems in a minimal phase stochastic nonlinear system, which has uncertain dynamics and the form of strict feedback. Base on the stochastic nonlinear robust control theory, we adopt the state observer and parameter estimator to make the closed system both have asymptotical stable equilibrium and satisfied quality for transient performance and final tracking accuracy.The main contents of this dissertation are outlined as follows:⑴For the stochastic nonlinear minimal systems with uncertain disturbance, the robust feedback control design to guarantee the stochastic asymptotical stable of that closed systems. At first we make a hypothesis that the inverse dynamic is stochastic input-to-state stable, also the drifting and diffused parts of the whole system rely on the inverse dynamic and output. Then a reduced order observer was formed to construct a new equivalent system. By the means of backstepping we gradually obtain the feedback control law, which guarantee the final controlled system to be noise-to-state stable, and have globally asymptotical stable equilibrium in probability with the absence of noise. Finally through a numerical example and simulation by MATLAB, the effectiveness of control law was illustrated. Compared with former studies throughout this chapter 3, we relax the restriction of the system uncertainties, and studied a more common question of disturbance resistance and asymptotical stable.⑵For a class of strict feedback stochastic nonlinear system with uncertain disturbance and unknown parameters, take into consideration of the frequent change caused by complexities and limits of practical control systems, we need to consider a more flexible control method such as adaptive robust control. First we set a reduced order observer for the immeasurable but observable states, and the adaptive estimator of unknown parameters. Then also by means of backsteeping we construct an adaptive robust control law gradually. At last through the analysis of the closed loop control system, we can see that equilibrium is globally asymptotical stable in probability when the noise does not exist by LaSalle-Yoshizawa theory. And according to the small-gain theory, the whole control system is H∞stable and disturbance resistant.