Constructive Control Design Of Switched Nonlinear Systems In Generalized Triangular Form

As an important class of hybrid systems, switched systems are an inherently mul-ti model dynamic systems, which are of great significance both in theory development and engineering applications. Since many practical systems are inherent nonlinearity, the research of switched nonlinear systems has received a great amount of attention in the field of control. However, due to the complexity arising from interaction between the system structure and switching, coupled with the co-design of controllers of subsystems and switching signals, the dynamic behavior of switched nonlinear systems become very complicated and this makes the design of switched nonlinear systems very difficult, and the lack of systematic and effective tools. How to exploit structure properties of switched systems combined with some constructive design techniques is an effective way to study synthesis problems of switched nonlinear systems. But, almost no results on such issues have been reported up to now.This dissertation studies the problem of stabilization, H∞control and output regula-tion for several classes of switched nonlinear systems in lower triangular and generalized triangular form, focusing on a constructive control design method. The main contribu-tions are as follows.1. The problem of global stabilization for a class of switched nonlinear systems in p-normal form whose subsystems are not assumed to be asymptotically stabilizable is investigated. First, using the convex combination method and the adding a power inte-grator technique, we construct a switching law and design state-feedback controllers of individual subsystems explicitly by a recursive design algorithm to guarantee asymptotic stability of the closed-loop system. Second, the designed method is also extended to the global stabilization problem of switched nonlinear systems in p-normal form with zero-dynamics. Unlike the existing results on systems in p-normal form where the power order is only positive odd integer, we allow positive even integer of the power order.2. The global stabilization problem for switched nonlinear systems in generalized triangular form is investigated. First, a sufficient condition for global stabilization of switched nonlinear systems is derived by exploiting the multiple Lyapunov functions (MLFs) method and the adding a power integrator technique. The solvability of the global robust stabilization problem for individual subsystem is not assumed. Second, our design approach removes the requirement of a triangular structure when applying backstepping. This design approach is applicable to a wider class of nonlinear systems with a gener-alized triangular structure. Also, a novel approach is proposed to deal with individual coordinate transformations for subsystems that are required when applying the backstep-ping recursive design scheme. Finally, the dual design of controllers and switching laws are constructive under the MLFs framework.3. The global robust stabilization problem is investigated for a class of multi-input switched nonlinear systems. The systems under study admit a structure which includes both the p-normal form and the nested lower triangular form as special cases. By exploit-ing the MLFs method and the adding a power integrator technique, a sufficient condition for the solvability of the global robust stabilization problem is derived by constructing state-feedback controllers for individual subsystems and a switching law under the MLFs framework.4. The problem of global stabilization of switched interconnected nonlinear systems whose all subsystems are input-to-state stable (ISS) and only some are ISS and others are not is investigated under switching signals with average dwell time. First, a small-gain theorem for switched nonlinear systems is established which provides a tool for analyzing the behavior of switched interconnected nonlinear systems. Second, a sufficient condition for global stabilization of switched interconnected nonlinear systems is derived by exploiting the average dwell time method and the small-gain technique. Finally, we simultaneously construct state-feedback controllers for subsystems and give a class of switching signals with average dwell time.5. The global stabilization problem for a class of switched nonlinear feedforward systems under arbitrary switchings is investigated. Based on the integrator forwarding technique and the common Lyapunov function (CLF) method, the global stabilization problem is studied for switched nonlinear feedforward system for the first time. First, a common coordinate transformation of all subsystems is exploited to avoid individual coordinate transformations for subsystems that are required when applying the forward-ing recursive design scheme. Second, based on this common coordinate transformation, bounded state feedback controllers for subsystems and a CLF are designed.6. The problem of H∞control for a class of switched nonlinear systems in p-normal form is investigated where the solvability of the H∞control problem for individual sub-systems is unnecessary. A sufficient condition for solvability of the H∞control problem is derived by using the generalized multiple Lyapunov functions (GMLFs) method and the adding a power integrator technique. The solvability condition is given in terms of partial differential inequalities of the form of Hamilton-Jacobi (HJ) inequality. Unlike the classical HJ inequality, which need to be satisfied in the whole state space, the provided HJ-like inequality is only required to hold in a subregion of the state space. Also, we simultaneously design controllers for subsystems and a switching law under the GMLFs framework.7. The global robust and decentralized output regulation problem for switched non-linear systems with stabilizable and unstabilizable subsystems based on the average dwell time method are studied. First, a new concept, namely switched internal model for switched nonlinear systems, is proposed, which provides a tool for solving the global output regulation problem of switched nonlinear systems. Second, it is worth pointing out that the output regulation problem of switched nonlinear systems may be possible to be unsolvable by means of some unconstrained switching law even if the solvability of the output regulation problem for individual subsystems is assumed. Therefore, how to find an appropriate switching law to solve the output regulation problem is of great im-portance. Here, a more general case is investigated, namely that not all output regulation problem for individual subsystems are assumed to be solvable. Finally, the global decen-tralized output regulation problem for a class of large-scale switched nonlinear systems with stabilizable and unstabilizable subsystems is investigated. Also, we simultaneously construct decentralized controllers for individual subsystems and give a class of switching signals with average dwell time.8. The adaptive disturbance rejection problem for a class of switched nonlinear sys-tems in strict-feedback form with unknown exosystem is investigated where the solvabil-ity of the disturbance rejection problem for subsystems is not assumed. First, a sufficient condition for the solvability of the adaptive disturbance rejection problem is given. A switched internal model of switched nonlinear systems in strict-feedback form is pro-posed. Second, in order to solve the problem in question, a constructive adaptive con-trol methodology is established on the basis of the MLFs method, backstepping and the changing supply functions technique. Finally, we simultaneously design adaptive state-feedback controllers for individual subsystems and a switching law.The conclusions and perspectives are presented in the end of the thesis.