Adaptive Fuzzy Control For Strict-Feedback Uncertain Nonlinear Time-Delay Systems

As the development of science and technology, the control problem of uncertainnonlinear time-delay systems is paid more and more attention to. Backstepping tech-nique and dynamic surface control (DSC) technique are efficient tools to study thecontrol problem of strict-feedback uncertain nonlinear time-delay systems. This dis-sertation uses backstepping and dynamic surface control as basic tools, combines adap-tive fuzzy approximation theory, stability theory of time-delay functional differentialequations, Lyaponov stability theory and decentralized control theory of interconnectedlarge-scale systems. We preliminarily focus on the problems of how to eliminate thein?uence of unknown time-delays and uncertainties which may harm to the stability ofthe system, and how to simplify the structure of the controller. The main contributionsare outlined as follows:1. For the control problem of systems with completely unknown time-delays inthe outputs, a novel technique called delay replacement is proposed. Considering thesystems outputs will eventually track the reference signals, and the reference signals areused to be known as prior knowledge, so the delayed signals can be replaced with thereference signals. Adaptive robust technique is employed to deal with the replacementerror, and the in?uence of time-delays to the closed-loop systems is eliminated.2. The adaptive backstepping control theory and the adaptive DSC theory areextended to uncertain nonlinear systems with completely unknown time-delays. Anadaptive fuzzy backstepping control approach and an adaptive fuzzy DSC approach areproposed. The common assumptions on the delays are removed; the controller designdifficulty and the in?uence to stability of the closed loop system caused by the delaysare eliminated. It is proved that the tracking error can converge to an arbitrary smallneighborhood of the origin.3. The adaptive backstepping control theory and the adaptive DSC theory areextended to nonlinear large-scale systems with comeletely unknown time-delays andunknown interconnections. An adaptive fuzzy decentralized backstepping control ap-proach and an adaptive fuzzy decentralized DSC approach are proposed. The commonassumptions on the delays and the interconnections are removed; the controller designdifficulty and the in?uence to stability of the closed loop system caused by the delaysare eliminated. All of these two control approaches can garantee the stability of the closed loop large-scale systems.4. Based on a single approximator, an adaptive fuzzy DSC approach is proposedfor output-feedback uncertain nonlinear time-delay systems. Only one fuzzy logic sys-tem is employed in the controller design procedure, so that all the unknown items ofthe systems are compensated for. Thus, only one unknown parameter and one approxi-mation error are needed to be adjusted, so that the controller structure is simplified. Atthe same time, the"explosion of items"problem is avoided by using DSC technique.The proposed approached can ensure stability of the closed-loop systems and arbitrarysmall tracking errors are achieved.5. Based on a single approximator, an adaptive fuzzy decentralized dynamic sur-face controller is proposed. In each subsystem of output-feedback nonlinear time-delaylarge-scale systems with unknown interconnections and unknown delay signals, onlyone fuzzy approximator is needed to eliminate the in?uence of the unknown intercon-nections and time delays, so that the number of unknown parameters which are neededto be adjusted is reduced, and the controller structure is simplified. Based on LaSalle in-variance theory and the stability theory of time-delay functional differential equations,the closed loop system is proved to be bounded, and through adjusting parameters, thetracking errors can be arbitrary small.6. An adaptive fuzzy DSC approach is proposed for a class of systems with un-known time-delays and unknown virtual control coefficients. Based on delay replace-ment technique, the completely unknown delay signals are dealt with and the commonassumption about time-delays are not needed any more. Through integrating the non-linear functions and the unknown virtual control coefficients of the systems, one ap-proximator is used in each step of the controller design, so that the controller structureis simplified, and the control singularity problem is avoided. Based on constructingquasi-weighted Lyapunov-Krasoviskii functional, the stability of the closed-loop sys-tems can be ensured.