Adaptive Controller Design For A Class Of Nonlinear Time-delay Systems

Strictly speaking, practical control systems are nonlinear, and always have uncertainties such as parameters perturbation, unmodeled dynamics or external disturbances, etc. So the system specified performance may be damaged. In addition, the existence of time delays may make the control analysis and design of nonlinear systems more complex and difficult. Therefore, the study of nonlinear time-delay systems with uncertainties has an important theoretical and practical significance.For the stability analysis and controller design of nonlinear time-delay systems, an effective method is based on the Lyapunov-Krasovskii functionals. In this thesis, Lyapunov-Krasovskii functionals were used to construct the Lyapunov function candidates such that the uncertainties from unknown time delays were compensated for. Robust adaptive controllers were designed for a class of uncertain nonlinear systems with delays in the state, which can guarantee the stability of the closed-loop systems. To prove the stability of the closed-loop systems, Lyapunov's stability theory was applied in the controller design.By combining backstepping design procedure with robust control strategy, a robust adaptive controller was proposed for a class of strict-feedback nonlinear systems with both unknown time delays and uncertainties from unknown parameters and nonlinear functions. Controller singularity problems were avoided by introducing an appropriate even function. It was proven that the proposed design procedure was able to guarantee global uniform ultimate boundedness of all the signals in the closed-loop systems. The tracking error was shown to converge to a small neighborhood of the origin. A simulation example was provided to illustrate the validity of the proposed controller.An adaptive neural network controller was presented for a class of strict-feedback nonlinear time-delay systems with unknown nonlinear functions. A radial basis function neural network was chosen to approximate the unknown nonlinear functions in this thesis. The developed control scheme was able to guarantee global uniform ultimate boundedness of all the signals in the closed-loop systems. The tracking error was proven to converge to a small compact set. A simulation example was provided to illustrate the effectiveness of the proposed approach.For the same second-order system, a robust adaptive controller was compared with an adaptive controller based on radial basis function neural network under the same conditions. Simulation results were provided to show the proposed neural network adaptive controller has well control behavior.