Fuzzy Iterative Learning Identification And Control Of Nonlinear Time-Varying Systems

Iterative learning control (ILC), for control systems performing repetitive tasks, updates the present control input signal by using information of the previous control input to achieve perfect tracking performance over finite time interval. ILC is essentially suitable for plants which confront strong nonlinearity and modeling difficulty. From the learning point of view, the existing learning approximation methods are mainly concerned about the estimation of constants, while iterative learning focuses on the learning of a time-varying track which is considered inviarint along the iteration axis, thereby it can be applied to estimate time-varying parameters over finite time interval. Based on the existing fuzzy approximation theory, this thesis discusses fuzzy iterative learning identification and control algorithms to solve the estimation problems of time-varying parameters for nonlinear time-varying systems. Our work mainly covers the following aspects:1. How the fuzzy approximation errors affect the convergence of system tracking error are discussed. Through Lyapunove-like synthesis, direct and indirect fuzzy ILC are developed for a class of nonlinear time-varying systems. Direct fuzzy ILC employs time-varying fuzzy system as an approximator to ideal control input, while indirect fuzzy ILC as approximators to nonlinear time-varying functions. Both of the control schemes apply iterative learning mechanism to update the time-varying parameters of fuzzy systems, and also resort sign function, saturation function and boundary estimate to eliminate the impact of fuzzy approximation errors. The proposed controllers guarantee the boundedness of all the system signals and the convergence of system tracking error along the iteration axis. Numerical simulations verify the validity of direct and indirect method, respectively.2. For a class of second-order nonlinear time-varying systems with random initial repositioning errors, both direct and indirect fuzzy ILC are established to achieve complete tracking of system output within a pre-specified time. Terminal sliding mode is introduced to boundary layer design. Respectively, time-varying fuzzy systems are used as approximators to ideal control input and nonlinear time-varying functions. The proposed control schemes guarantee that all the system signals remain bounded and tracking error converges to zero within a pre-specified time. Numerical simulations are carried out to demonstrate the effectiveness of terminal sliding mode approch.3. For a class of discrete nonlinear time-varying systems, time-varying fuzzy system is employed as identification model for nonlinear time-varying systems. Iterative learning least squares algorithm with dead-zone is developed to update time-varying parameters of fuzzy system along the iteration axis. To ensure convergence rate, but quickly dropped, an improved algorithm is further proposed by re-adjusting covariance matrix. The presented identification algorithms guarantee the estimation error converges to a bound pointwisely over finite time interval along the iteration axis. Numerical simulation verifies the effectiveness and convergence of the proposed algorithm.