Controller Design And Applications For Several Classes Of Nonlinear Systems

In the vast majority of applications, the essential problem in the design controller of nonlinear systems is that dynamics of the plant are partially known and can not be precisely known. Using the mathematical model for control system to deseribe the real plant, there exist unknowns and uncertainties between them. As an interesting researeh area control of nonlinear uncertain systems has attracted lots of researehers since 1950's. The uncertainties may degrade the performance of a controlled system or even make the closed-loop system unstable when they are not appropriately accounted for in the controller design stage. To deal with various unknowns and uneertainties, online estimation and robustness are the key in designing a sueeessful controller. Adaptive control, robust control and their combinations represent the effective means to deal with whatever uncertainties and achieve a guaranteed transient performance and final tracking accuracy.According to unknowns and uncertainties shown different form in plants, robust control of nonlinear time-delay systems, controller design and application for input affine nonlinear systems based on immersion and invariance are researched.(1) The problem of delay-dependent H? control for Lurie singular systems with state-delay is investigated. For the Lurie singular systems with unknown time-delay, delay-dependent sufficient conditions of stability and state feedback H? control law are obtained, ensuring the resultant closed-loop systems regularity, absence of impulses, global uniform asymptotically stable and a prescribed H? performance level. Further, the state feedback H? control law is given in terms of the feasible solutions of linear matrix inequalities (LMIs) under the non-convex constraints. And the proposed method can be easily extended into uncertainty, multiple delays and time-varying delays systems. Finally, a numerical example is provided to demonstrate validity of the proposed method.(2) The problem of delay-dependent stability analysis and controller design for a class of T-S fuzzy systems with interval state time-varying delay is considered. Based on Lyapunov stability theory, defining a new Lyapunov-Krasovskii functional and introducing some free-weighting matrices, a new delay-dependent criterion is given to ensure the systems asymptotically stable. The merit of the proposed conditions lies in the less conservativeness than the existing ones, which is achieved by considering the mean of time-delay interval and the introduction of the free variables. By the concept of parallel distributed compensation (PDC), a delay-dependent condition for the existence of a fuzzy state feedback control law with memory is proposed. Another merit is the consideration of the memory of the controller. All conditions are shown in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using the LMI optimization techniques. Two numerical examples are given to illustrate the feasibility and validity of the proposed approach.(3) The problem of immersion and invariance (I&I) control for a class of nonlinear systems is addressed. Based on selection of target system, a novel controller is obtained, which efficiently avoids choosing Lyapunov function. The designed controller guarantees that all trajectories of the closed-loop systems are asymptotically stable. The efficiency and effectiveness of the proposed method is demonstrated by simulation examples.(4) A new adaptive controller is designed based on dynamic scaling and filter for lower triangular system. Compared with the available adaptive results in the literature, the proposed adaptive approach does not necessarily need to satisfy the certainty equivalence principle, and allows for prescribed dynamics to be assigned to the parameter estimation error. The proposed adaptive state feedback controller that ensures all signals of closed-loop systems are globally bounded while keeping the output tracking error to the origin simultaneously. Finally, two comparatively simulation examples are given, highlighting the advantages of the proposed methodology.(5) For a class of nonlinear high-order lower-triangular systems with uncontrollable unstable linearization. A new smooth adaptive control design method using non-certainty equivalence principle and adaptive adding a power integrator is given. The proposed practically adaptive state feedback controller that ensures all signals of closed-loop systems are globally bounded while keeping the output tracking error to an arbitrary small neighborhood of the origin simultaneously. Finally, a numerical example is given.(6) A new adaptive controller is designed based on immersion and invariance for TCSC. Compared with the available adaptive results in the literature, the proposed adaptive approach does not invoke certainty equivalence, nor requires a linear parameterization and allows for prescribed dynamics to be assigned to the parameter estimation error. By choosing an appropriate target dynamics and manifold, an adaptive state feedback controller has been synthesized constructively to ensure all signals of closed-loop system are globally bounded.