Stability Analysis And Control Design For Nonlinear Cascaded Systems

The problems of stability analysis and control design of nonlinear system are very important areas in nonlinear control theory. Recently years, nonlinear cascaded system has been researched widely and some achievements have been obtained.In this dissertation, the stability and control design problem of nonlinear cascaded systems was studied further. In the first part, the background of nonlinear cascaded systems is introduced. In the second part, some theorems interrelated with this dissertation have been introduced. In the third and the fourth parts, nonlinear cascaded systems are studied in two different methods. The main content and results are given as follows:The first, the problem of robust stabilization for a class of uncertain nonlinear cascaded systems is researched. The methods that are proposed by Su and Fu were introduced and improved to deal with the robust stabilization for a class of multi-dimension uncertain nonlinear cascaded systems. According to the structure characteristic of the system, an approach is presented to transform the cascaded system into a base subsystem and an extension subsystem. Via the assumption that the base subsystem is globally asymptotically stabilizable, according to the quadratic stability of the local linear model, a non-quadratic Lyapunov function with an integral term is structured and the control law is designed. Under the control law, the closed-loop system is globally asymptotically stable and local quadratically stable.The second, the backstepping method was introduced to deal with the stability analysis and control design for multi-dimension nonlinear cascaded systems. Based on the results obtained on strict parameter system, the presented new method extended the backstepping method to pure parameter system. The main idea of the design is as follow. For each subsystem, a virtual control is introduced, a Lyapunov function for each step is structured, and then the virtual control α_i and tuning function τ_i of each step are designed. The algorithm is modified step by step in the recursive design approach. In the final step, the actual update law for parameter estimate and the actual feedback control law are designed. Under the control law, the closed-loop system is uniform stable.