Control Design Of Classes Of Switched Systems With State Constraints

As an important class of hybrid systems, switched systems are of great significance both in theory development and engineering applications. Especially in the recent years, the successful applications of switched systems and switching control in aircraft engine control, robot control, power systems and networked systems control further arouse the positivity of researchers to study on this issue. Meanwhile, practical systems usually need to consider safety and physical limit of device, which constrains the state, therefore, to investigate the switched systems with state constraints is of great importance in theory and practice. However, due to the co-existence and interaction among the continuous dynamics, discrete dynamics and state constraints, the behavior of such systems is very complicated. The mechanism of such systems is far from clear. Many analysis and de-sign problems deserve further investigation. Unfortunately, to the best of our knowledge, results on this issue have been rarely found. This dissertation studies tracking control, sta-bilization, robust stabilization and H∞control of classes of switched systems with state constraints. The main contributions of this thesis are as follows.(1) Switching tracking control of a class of planar systems subject to given tran-sient performances of output is investigated. The traditional single static output feedback controller make a balance or a trade-off between the quickness and safety, but the effect is usually unsatisfied. To solve this problem, a switched static output feedback controller which consists of multiple static output feedback controllers and a conic switching law are designed under which the output of the closed-loop switched system can track a step sig-nal asymptotically with satisfying the given transient performances requirements. More-over, an optimal weighted transient performance measured by overshoot and settling time is obtained by solving a nonlinear programming problem.(2) The stabilization problem of a class of switched systems with state constraints is investigated in both continuous-time and discrete-time contexts. The system model is defined on a closed hypercube as all the state variables are constrained to a unit hyper-cube, for this reason, such system is sometimes referred to as a system subject to state saturation. An saturation-dependent improved average dwell time method is presented to take into account different decay rates of a Lyapunov function related to an active subsys-tem according to the saturations occurring or not. By using this improved average dwell time method, we give the sufficient conditions for stability and stabilizability of such switched systems and design the switched state feedback controllers. Furthermore, it is worth pointing out that the applications of this improved average dwell time method pro-duces smaller average dwell time than the standard average dwell time method does due to the different decay rates of Lyapunov function related to an active subsystem adopted according to whether saturation has occurred or not.(3) Based on the results of the stabilization problem previously, we further study the H∞control for this class of switched systems with state constraints in both continuous-time and discrete-time settings. Sufficient conditions for H∞control of such switched system with state constraints are first derived, and switched state feedback controllers are designed such that the closed-loop switched system subjects to state constraints is asymptotically stable and achieves a weighted L2-gain.(4) By utilizing the barrier Lyapunov function method, we discuss the stabilization and robust stabilization problems for a class of state-constrained switched nonlinear sys-tems in p-normal form. A switched nonlinear system in strict-feedback form can be re-garded as a special case of this system. By using the barrier Lyapunov function and the backstepping technique, bounded state feedback controllers of individual subsystems and a common Lyapunov function are explicitly constructed to asymptotically stabilize the closed-loop system under arbitrary switchings. Furthermore, we also give the corre-sponding result about robust stabilization.Finally, the results of the dissertation are summarized and further research topics are pointed out.