Adaptive Learning Control Of Nonlinear Systems

Learning control aims at achieving the desired system performance through directly updating the control input, either repeatedly over a fixed finite time interval, or repetitively over an infinite time interval periodicity.Learning control approaches can be in general classified into iterative learning control(ILC) and repetitive learning control(RLC). The former is based on contraction mapping theory, and the latter is based on the small gain theorem which can be viewed as the extension of contraction mapping theory to the infinite time interval.By introducing a parametric adaptation mechanism, the adaptive control system is able to achieve asymptotic tracking convergence in the presence of constant parametric uncertainties. However, no adaptive control algorithms developed hitherto can solve unknown parameters with arbitrarily fast and non-vanishing variations.When the plant has mixed parametric(time-varying and time-invariant parameters) uncertainties or the time-varying gain coefficient, how to make full use of the prior information and design ILC and RLC by adaptive control, have become a new subject worthwhile to research.This dissertation considers the ILC and RLC from an adaptive control viewpoint, based on the Lyapunov-like energy function approaches, which avoids some drawbacks and restricted assumptions of traditional learning control. The main contributions included in the dissertation are summarized as follows.1. A novel adaptive iterative learning control approach is proposed for high-order nonlinear systems with structure uncertainties and external distureances, by combining the Backstepping method, the linearly parametrized with the parameter regrouping technique. The approach consisted of a differential-deference type updating law and a learning control law, can deal with the non-uniform trajectory tracking problem,which avoids the restricted on the tracking trajectory in the traditional ILC. A sufficient condition of tracking error converging to zero in the means of mean-square on the finite interval is also given by constructing a novel composite energy function.2. An adaptive iterative learning control of nonlinear systems with mixed-type parameters and unknown time-varying control coefficients is developed by combining the modifying Backstepping approach with the parameter regrouping technique, which can handle the iteration-varying trajectory tracking problem. A differential-difference type adaptive law and an adaptive iterative learning controller are constructed to ensure the asymptotic convergence of tracking error in the sense of square error norm on the finite interval, by introducing a Lyapunov-like function, a sufficient condition of the convergence of the method is also given.3. Combining the pointwise integral mechanism with the feedback linearization approach, a novel adaptive repetitive learning control for nonlinear systems with time-varying and time-invariant parameters is proposed. It can be applied to the time-varying parametric uncertainty systems with unknown compact set, rapid time-varying, periodic and where the prior knowledge is the periodicity only. A differential-difference adaptive law and an adaptive repetitive learning control are constructed to ensure the asymptotic convergence of the extended tracking error in the sense of square error norm. Also, a sufficient condition of the convergence of the method is given.4. A design approach to the adaptive repetitive learning controller is proposed for a class of nonlinear systems with time-varying and time-invariant parameters by combining the Backstepping technique with the pointwise integral mechanism. It can be applied in the time-varying parametric uncertainty systems with unknown compact set, rapid time-varying, periodic and only the prior knowledge is the periodicity. A periodic mixed adaptive law and an adaptive control law are constructed to ensure the asymptotic convergence of the tracking error in the sense of square error norm. And a sufficient condition of the convergence of the method is also given.5. Combining the pointwise integral mechanism, the parameter regrouping technique with the modifying Backstepping approach, a novel adaptive repetitive learning control for high-order nonlinear systems with unknown control coefficients and mixed parameters is proposed. It can be applied to the time-varying parametric uncertainty systems with unknown compact set, rapid time-varying, periodic and where the prior knowledge is the periodicity only. A differential-difference mixed-type adaptive law and an adaptive repetitive learning control are constructed to ensure the asymptotic convergence of the tracking error in the sense of square error norm. Also, a sufficient condition of the convergence of the method is given.6. A design approach to the adaptive repetitive learning controller is proposed for a class of nonlinearly parameterized systems with time-varying and time-invariant parameters by combining the parameter regrouping technique with the feedback linearization approach, It can be applied to the time-varying parametric uncertainty systems with rapid time-varying, periodic and where the prior knowledge is the periodicity only. A differential-difference coupled-type adaptive law and an adaptive repetitive learning control are constructed to ensure the asymptotic convergence of the extended tracking error in the sense of square error norm. Also, a sufficient condition of the convergence of the method is also given. The results are extended to a class of high-order nonlinearly parameterized systems with unknown time-varying control coefficients and mixed parameters.7. A novel adaptive repetitive learning control for nonlinearly parameterized systems with unknown control coefficients and mixed parameters is proposed by combining the system replacement technique, the pointwise integral mechanism with the parameter regrouping approach, It can be applied to the time-varying parametric uncertainty systems with rapid time-varying, periodic and where the prior knowledge is the periodicity only. A differential-difference coupled-type adaptive law and an adaptive repetitive learning control are constructed to ensure the asymptotic convergence of the tracking error in the sense of square error norm. Also, a sufficient condition of the convergence of the method is given.8. The problem of a learning control approach is applied to the generalized projective synchronization of different chaotic systems with unknown periodically time-varying parameters. Using the Lyapunov-Krasovskii functional stability theory, a differential-difference mixed-type parametric learning law and an adaptive learning control law are constructed to make the states of two different chaotic systems asymptotically synchronized. The scheme is successfully applied to the generalized projective synchronization between Lorenz system and Chen system. Moreover, numerical simulations results are used to verify the effectiveness of the proposed scheme.