Finite-Time Iterative Learning Control:Feedback-Aided Strategies

Iterative learning control(ILC) has become a popular technique against inaccuracy in modeling when the required task is repetitive over a finite interval. In the ILC systems, the previous tracking errors are applied to the control action to update the control law, then the output of the system can converge to the desired trajectory over the entire operations. In the majority of the ILC investigations, it is assumed that the initial state of the system at each cycle is reset at the initial state value of the desired trajectory. However, it is hardly implementable in the real world to reset the initial state exactly at the desired one. The topic of performance improvement, in the presence of a fixed initial state shift between iterative initial state and the desired one, is worth researching.Based on contraction mapping method, this thesis presents the feedback-aided iterative learning control schemes for the systems in the presence of a fixed initial state shift between iterative initial state and the desired one. The main work and contributions of this thesis are summarized as follows:1. Based on PD-type learning law, the feedback-aided PD-type learning law and the generalized feedback-aided learning law are proposed to speed up the convergence rate of the learning process and improve stability of the systems performance. The sufficient conditions for convergence of the learning control algorithms are derived. The limit trajectories by applying the learning algorithms are deduced.2. Based on the open-loop iterative learning law, the feedback-aided strategies and the finite-time control strategies are adopted in the design of iterative learning controllers. The feedback-aided finite-time iterative learning control algorithms are proposed in the presence of a fixed initial state shift between iterative initial state and the desired one. The sufficient conditions for convergence of the learning control algorithms are derived, and the limit trajectories by applying the learning algorithms are given.3. Based on the design methods of the power attracting law and fast attracting law, the double power attracting law is proposed. The Gauss hyper-geometric function and its properties are adopted to the analysis of the stability and convergence performance. And the convergence time expression is deduced. The convergence rate of the tracking errors are compared between the three attracting laws.4. When a larger fixed initial state shift presents between iterative initial state and the desired one, in order to further speed up the convergence rate of the learning process, two kinds of improved feedback-aided finite-time iterative learning control schemes are proposed. The sufficient conditions for convergence of the learning control algorithms are derived, the limit trajectories and convergence time expressions by applying the learning algorithms are given.5. This thesis presents three feedback-aided finite-time iterative learning control schemes for nonlinear systems in the presence of a fixed initial state shift between iterative initial state and the desired one. The sufficient conditions for convergence of the learning control algorithms are derived, the limit trajectories and convergence time expressions by applying the learning algorithms are given. It is showed that the error can be reached to zero in a finite time.