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H_∞Control And Constrained Output Tracking Of Switched Nonlinear Systems

Posted on:2013-05-10Degree:DoctorType:Dissertation
Country:ChinaCandidate:B NiuFull Text:PDF
GTID:1228330467979827Subject:Control theory and control engineering
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As an important class of hybrid systems, switched nonlinear systems are of great significance both in theory development and engineering applications. Due to the exis-tence and interaction between the continuous dynamics and discrete switching signals, the behavior of the switched systems is very complicated, and many analysis and design problems deserve further investigation. H∞control and output tracking are two of the fun-damental problems in the study of switched systems, however, up to now results on such issues have been rarely reported. Based on the Lyapunov control theory, this dissertation focuses on the H∞control and constrained output tracking problems for some classes of switched nonlinear systems. The main contributions of this thesis are as follows.The problem of robust H∞control for a class of minimum phase uncertain switched nonlinear systems is studied. Based on the multiple Lyapunov functions approach, suffi-cient conditions for the solvability of the robust H∞control problem of the switched sys-tem and design of both state-dependent controllers and state-dependent switching laws are presented. Compared with the existing results, we consider the robust H∞control problem for the switched systems where the uncertain parameters are assumed to be in a known compact set for the first time, and the approach proposed can avoid solving the Hamilton-Jacobi-Isaacs (HJI) inequalities.The problem of H∞control for a class of non-minimum cascade switched nonlin-ear systems is studied by using the average dwell-time method. Each subsystem under consideration is composed of two cascade-connected parts:a nonlinear one which con-tain disturbance input and a linearizable and controllable one. Sufficient conditions for the stabilization and weighted L2-gain of the switched system are derived. The obtained results allow stabilizable subsystems and unstabilizable subsystems to coexist and the the-ory of the generalized inverse is used such that the switched system covers many models in the literature.The problem of robust H∞, control for a class of non-minimum phase cascade uncer-tain switched nonlinear cascade systems is addressed. By using the multiple Lyapunov functions approach, sufficient conditions for the solvability of the robust H∞control prob-lem of the switched system are presented. Then, the hybrid robust H∞control problem for a class of non-switched non-minimum cascade uncertain nonlinear systems is further considered.The problem of robust H∞control for a class of switched nonlinear systems con-taining neutral uncertainties is studied with average dwell time switching. Sufficient con-ditions for the solvability of the robust H∞control problem of the switched system and design both state feedback controllers and time dependent switching laws are proposed. The obtained results allow stabilizable subsystems and unstabilizable subsystems to co-existThe output tracking problem for a class of switched nonlinear systems in strict-feedback form subject to a constant output constraint is considered. In order to prevent transgression of the constraint, a barrier Lyapunov function (BLF) is employed, which grows to infinity when its arguments approach domain boundaries. Under the simultane-ous domination assumption, a continuous feedback controller for the switched system is constructed. Furthermore, asymptotic tracking is achieved without violation of the con-straint and all closed-loop signals keep bounded。 Then, we further studied the control design with the quadratic Lyapunov functions (QLF), which show that the control design based on the BLF needs weaker initial conditions than the one based on the QLF.The output tracking problem for a class of strict-feedback switched nonlinear non-linear under time-varying output constraints and full sate constraints is considered. First, when the switched system is subjected to time-varying and asymmetric output constraints, we employ an Asymmetric Time-Varying Barrier Lyapunov Function (ATBLF), which re-lies explicitly on time, to prevent the output from violating the constraints. Based on the simultaneous domination assumption, we design a continuous feedback controller for the switched system, which guarantees that asymptotic tracking is achieved without trans-gression of the constraints and all closed-loop signals remain bounded. Then, we further consider the case of full state constraints by adopting a barrier function for each step of the backstepping design.Finally, the results of the dissertation are summarized and further research topics are pointed out.
Keywords/Search Tags:switched systems, cascade switched nonlinear systems, stability, L2-gain, H_∞control, output tracking, Hamilton-Jacobi-Isaacs inequalities, constraints, barrierLyapunov function, common Lyapunov function, multiple Lyapunov functions, averagedwell time
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