Stabilization And H_∞Control For Switched Nonlinear Systems In Lower Triangular Form

As a particular class of hybrid systems, switched systems are of great significance in both theory development and engineering applications. Since most control systems are inherently nonlinear, the research of switched nonlinear systems has drawn considerable attention in the field of control. Because of the inherent hybrid characteristic of switched systems, coupled with the complexity of nonlinear system itself, as well as the co-design of controllers and switching signals, the study of switched nonlinear systems is usually very difficult and no systematic and effective methods are available. Exploiting structure properties of switched nonlinear systems combined with modern control techniques is an effective way to study synthesis problems of switched nonlinear systems. Switched nonlinear system in lower triangular form is an important class of switched systems. However, almost no results on such kind of switched systems have been reported up to now.This dissertation studies the stabilization and the H∞control problems for several classes of switched nonlinear systems in lower triangular form based on a constructive method. The main contributions are as follows.Chapter2concerns the global stabilization problem of switched nonlinear systems in lower triangular form under arbitrary switchings. First, for a class of switched nonlinear systems in lower triangular, where the sign of the gain functions of the same order of each subsystem are the same, both a common Lyapunov function and the state feedback controllers are simultaneously constructed by Backstepping to achieve the global stabilization under arbitrary switchings. In particular, a systematic approach of constructing a common stabilizing function is also presented. By Backstepping, the global stabilization of switched nonlinear systems in nested lower triangular form is studied under arbitrary switchings for the first time.Chapter3considers the global stabilization problem for a class of switched nonlinear systems in lower triangular form under a pre-given switching law with dwell time. Both the sufficient conditions for stabilization and the controllers are obtained. The sign of the gain of the same order of each subsystem may not be the same. We first design two classes of controllers for subsystems, each of which contains a tuning parameter. Then, we design controller selection mechanism to decide which class of controller is activated and then design a parameter tuning mechanism to tune these parameters online. Finally, asymptotic stability of the closed-loop switched system is obtained under the pre-given switching law with dwell time.Chapter4studies the global robust stabilization for a class of uncertain switched nonlinear systems in lower triangular form. Both the switching signal and the controller are constructed. By Backstepping, the individual controllers for subsystems is first designed, each of which is not required to stabilize the corresponding subsystem. Then, based on the single Lyapunov function method, the switching signal is designed. As a special case, the global robust stabilization under arbitrary switchings is obtained.Chapter5discusses the robust H∞control problem for a class of non-minimum-phase switched nonlinear systems, where each subsystem is in lower triangular form. Sufficient conditions for solvability of such problem are given. By Backstepping, both a design technique for controller and a switching law are provided to solve the H∞control problem under the designed switching law.Chapter6investigates the transient trajectory shaping control problem for a class of nonlinear systems. A two-stage switching control strategy is proposed to deal with the problem. With the help of output error transformation technique, the controllers for each stage are designed for the corresponding transformed system by Backstepping technique, which constrain the tracking error within a set of pre-designed boundaries during each stage. When the tracking error equals a pre-specified value, the controller designed by the first stage is switched to the one designed by the second stage, then the output tracking error transient trajectory travels within a specifically boundary.Chapter7studies the sampled-data control problem for a class of nonlinear systems with block triangular form with controller failure. The upper bounded on sampling intervals is not greater than a prescribed constant. Conditions under which the system is still exponentially stable in presence of controller failure are explored. With the help of input delay method, sampled-data control system with controller failure is modeled as a switched delay system. Based on the average dwell time method, sufficient conditions are provided to guarantee the exponential stability of the considered system when controller failure occurs. The existence conditions of controller are given in terms of the solvability of a set of linear matrix inequalities.The conclusions and perspectives end the dissertation.