Adaptive Learning Control For Nonlinearly Parameterized Systems With Time-varying Delays

As an important branch of intelligent control theory, learning control (LC) is feasible in dealing with the nonlinear uncertain systems. Compared to linear parameterization, nonlinear parameterization is more appropriate for a wider range of nonlinear uncertain systems. However, the study progress about LC of nonlinearly parameterized systems is slow. There are many aspects to be further studied and improved. In addition, time delay widely exists in various engineering systems. The presence of time delay not only reduces the performance of control, but indeed undermines the stability of closed-loop systems.This paper considers LC from an adaptive control viewpoint. Based on Lyapunov stability theory, new algorithms are proposed for LC of nonlinearly parameterized systems and nonlinearly parameterized systems with time delays. The main results are as follows. Firstly, for a class of nonlinearly parameterized systems with unknown time-varying parameters, a new adaptive iterative learning control approach is proposed to ensure the tracking error converging to zero in the mean-square sense on the finite interval. The time-varying nonlinearly parameterized function is well resolved by using parameter separation technique and signal replacement mechanism. By constructing a composite energy function, the stability of closed-loop system is also proved. Secondly, an adaptive iterative learning control approach is designed for a class of nonlinearly parameterized systems with unknown time-varying parameters and time-varying delays. By reconstructing the system equation, all unknown time-varying terms including the time-varying delay are combined into an unknown time-varying vector which is estimated by an iterative adaptation mechanism. By constructing a Lyapunov-Krasovskii-like composite energy function, we prove the boundedness of all signals and the convergence of tracking error. Thirdly, the tracking control on the infinite time for a class of nonlinearly parameterized systems with periodically time-varying parameters and time-varying delays is further studied. A new adaptive repetitive learning control is proposed to ensure the tracking error converging to zero in the mean-square sense on a cycle, and the boundedness of all signals of closed-loop system is proved. Finally, the simulation researches are done for every method, which illustrate the effectiveness and feasibility of the proposed algorithms.