Study On Adaptive Iterative Learning Control For Several Classes Of Nonlinear Systems

For the tracking control problem of the complex nonlinear systems on finite time interval, the much more effective control method is the iterative learning control technology, and this method has become one of the research core topics in intelligent control domain. In the iterative learning control theory and technology, the adaptive iterative learning control method receives more and more attention from the scholars. The main advantage of the method is that it needs not system dynamic satisfying globally Lipschitz condition, has simple learning algorithm, can complete high precision tracking of the desired trajectory on a finite time interval. However, because of the influence of the initial conditions to stability and convergence of the system, this is also the challenging of the use of the iterative learning control method. On the other hand, the non-uniform trajectory tracking problem is also a very important problem in iterative learning control. So it becomes the focus of scholars research. In addition, the time delay and time varying parameters in the actual system are two main factors causing the instability of the system. For time delay system with time varying parameters and chaos systems with time-varying parameters, this paper designs the effective adaptive iterative learning controller and adaptive controller, solves the tracking control problem and chaotic synchronization problem. The control direction problem is also a big difficulty in control field, the unknown control direction problem in iterative learning control is more difficult to deal, so this paper designs iterative learning controller for strict feedback nonlinear systems with unknown control direction. In addition, the existed nonlinearity of control input often damage the performance of the system. In the process of iterative learning controller design, the control input nonlinearity is also an important problem, so this paper also conducts the research of this problem. Specifically, we obtain the following research results.1. By using the backstepping technique, an iterative learning control strategy is presented for a class of nonlinear pure-feedback systems with initial state error using fuzzy logic system and strict feedback nonlinear system with initial state error and input nonlinearities using neural network, completes the trajectory tracking problem on the finite time interval [0,T]. A time-varying boundary layer is introduced to design an error function. The initial value of layer width is set according to the measured initial state errors and the width is then reduced along the time axis.Filtered signals are employed to circumvent algebraic loop problem, which makes that these controllers cannot be implemented directly. FLSs and NNs are introduced to learn the behavior of the unknown dynamics due to their universal approximation property. A typical series is introduced in order to handle the unknown bound of the approximation errors. There even exist initial state errors, the norm of tracking error vector will asymptotically converge to a tunable residual set as iteration goes to infinity and the learning speed can be easily improved if the learning gain is large enough.2. Based on the reasonable assumptions, by using appropriate Lyapunov-Krasovskii functional and backstepping technique to design NN learning laws and control law, an adaptive neural network iterative learning control approach is presented for a class of strict-feedback nonlinear time-delay systems with unknown non-linearly parameterised and time-varying disturbed function of known periods. Unknown nonlinear vector functions and unknown nonlinear time-delay functions are approximated by two FSE-RBF-neural networks, respectively, such that the requirements on the unknown nonlinear functions and the unknown nonlinear time-delay functions are relaxed.3. Based on the Lyapunov-like synthesis and Backstepping design technique design the controller, an iterative learning control strategy is presented for a class of nonlinear time-varying systems with known and unknown control direction to solve the non-uniform trajectory tracking problem. This can deal with system dynamics with non-global Lipschitz nonlinearities. Nussbaum function is used to deal with unknown control direction. The time-varying parameters are expanded into Fourier series with bounded remained term. A typical series is introduced in order to deal with the unknown bound of remained term and the non-uniform trajectory tracking.4. Based on the Lyapunov stability theory, the adaptive controller and the parametric updating law are obtained for global stability and asymptotic synchronization of the tracking error dynamics between the drive and the response systems. The hybrid function projective synchronization(HFPS) problem of chaotic systems and hyper-chaotic systems with uncertain periodically time-varying parameters. And by parameter updating laws, the nominal value of the unknown time-varying parameters and upper bound of truncation errors can be estimated. Fourier series expansion is used to parameterize uncertain periodically time-varying parameters.