The Research Of Nonlinear Adaptive Iterative Learning Control

In last two decades, the control theory of nonlinear systems becomes one of hot topics in the fields of automatic control. The adaptive control based on Backstepping technique as a method of nonlinear control theory ensures the stability and asymptotic tracking convergence of unmatched nonlinear systems with time-invariant uncertainties, instead of time-varying parametric uncertainties. However, when the control direction is unknown, the plant has of mixed parametric uncertainties and non-uniform trajectories, the above mentioned adaptive algorithm can not deal with these problems. Now, Nussbaum gain technique is an effective method to solve the problem of unknown control directions; iterative learning control is a kind of control methodology effectively dealing with repeated control problems, after some iterations, perfect tracking can be achieved over a finite time interval, but the present method has some defects, such as global Lipchitz continuity of nonlinear functions, uniform trajectory (independent of iteration) etc. Thus, how to incorporate Backstepping technique, Nussbaum gain technique and iterative learning control into solve problems of unknown control direction and non-uniform tracking trajectory is a subject worthwhile to research.Motivated by the above discussion, the main results of this paper are summarized as follows:Firstly, an output feedback stabilized control algorithm is proposed for a class of nonlinear time-delay systems with parametric uncertainties and multiple unknown control directions. Nussbaum function is used to deal with unknown control coefficients and Backstepping technique is used to design an adaptive control law. By constructing a Lyapunov-Krasvoskii functional, it is proved that the system is stable and its states are asymptotically convergent to zero, guaranteeing all signals bounded. Secondly, a hybrid adaptive iterative learning control method is proposed for a class of hybrid parametric nonlinear time-delay systems with unknown control direction.Nussbaum function is used to deal with unknown control; the approach consisted of a differential-deference type updating law can deal with non-uniform trajectory tracking problem. By constructing a Lyapunov-Krasvoskii functional, it is proved that the system is stable and its states are asymptotically convergent to zero, guaranteeing all signals bounded over a finite interval. Thirdly, an adaptive iterative learning control algorithm is proposed for a class of high-order hybrid parametric nonlinear systems with unknown control gain, which are repeatable on a finite time interval. By using modified Backstepping technique, parameters reconstructed technique and piecewise integration mechanism. The algorithm is consisted of a differential-deference type updating law and a learning control law, which can deal with the tracking problem with iterative changing desired trajectory. By constructing a Lyapunov-like functional, one can guarantee the tracking error converging to zero in terms of mean-square on the finite interval and guarantee all signals bounded in a finite time interval. Lastly, the simulation researches are done to every method, which illustrate the effectiveness and feasibility of the proposed algorithms.