Adaptive Learning Control For Complex Nonlinear Systems

Learning control theory, including iterative learning control (ILC) and repetitive control (RC), is a powerful tool to handle the systems with repetitiveness or periodic signals. ILC mainly focuses on repeatable systems defined in the finite time interval. In ILC, the system control input of current trial is updated by the control information of past trials, so that the system output converges to the given desired trajectory. RC, which is defined in the infinite time domain, mainly deals with the tracking of periodic trajectory or the rejection of periodic disturbance. There are both differences and extensive links between ILC and RC. Thus they are able to be treated as the same type of systems essentially.In order to overcome the limitations of the traditional learning control in dealing with the problems associated with nonlinear dynamic systems, also to incorporate the learning control theory with the popular Lyapunov theory, adaptive learning control, which combines both the design methods of adaptive control and the concept of learning control, has been proposed and developed. After reviewing the adaptive learning control theory, this paper mainly tackles the problems of unknown control directions and unknown periods in nonlinear systems.Specifically speaking, the main work of this paper is as follows:(1) The continuous Nussbaum gain method is employed to tackle the problems associated with unknown control directions in the repetitive learning control (RLC) for continuous-time nonlinear systems. An important lemma, which facilitates the application of Nussbaum gain method in the Lyapunov theory based control design, is developed and introduced into RLC for a class of continuous nonlinear systems with unknown time-varying parameters. Then the continuous Nussbaum gain method is exploited to deal with the problems associated with unknown control directions in the RLC for high-order continuous-time nonlinear systems with strict feedback form and output feedback form.(2) The discrete Nussbaum gain method is employed to tackle the problems associated with unknown control directions in the ILC for discrete-time nonlinear systems. First we focus on ILC for a class of discrete nonlinear systems with unknown time-varying parameters and time-varying input gain. Then the discrete Nussbaum gain method is exploited to deal with the problems associated with unknown control directions in the ILC for high-order discrete-time nonlinear systems with strict feedback form and output feedback form. (3) Switching control is plugged into the adaptive learning control to tackle the problems of unknown period. The signal period is assumed to be the product of a known constant and an unknown integer. Thus, based on the adaptive learning control scheme, we can tune the estimate of period by appropriate switching logic. After the period estimate has reached a proper value, the tracking error can converge to zero asymptotically. The switching adaptive learning scheme is exploited to handle the trajectory tracking for a class of linearly parameterized systems with time-vary ing parameters of unknown periods.(4) The switching adaptive learning control method is employed to deal with the problem of disturbance rejection for a class of nonlinearly parameterized systems with disturbance of unknown period. The restrictions on the unknown parameters in the adaptive control for nonlinearly parameterized systems are removed. The estimates of period of disturbance and upper bound of both the disturbance and the unknown parameters are tuned by the proposed switching logic, so that the periodic disturbance can be rejected completely.