Iterative Learning Control With Randomly Iteration Varying Lengths

Iterative Learning Control (ILC) is a kind of intelligent control approach that is suitable for controlled systems repeatedly completing given task in a finite interval. The input signal of such systems are updated iteration by iteration, so that the actual output could follow the desired trajectory during the whole time interval asymptotically along the iteration index. However, the actual tracking problem does not always fulfill the strict requirements. For example, the operation length may vary among different iterations. In addition, the initial state of each iteration may not be identical, which could affects the ILC application scope in the actual process. So, the main work and results done by the following:1. This chapter proposes ILC for discrete-time linear systems with randomly iteration varying lengths. No prior information on the probability of random iteration length is required. The conventional P-type update law is used with a modified tracking error because of random iteration length. This chapter proves that under suitable conditions on learning gain matrix, the given algorithm is convergent to the specified target. Illustrative example verifies the effectiveness of the proposed algorithm.2. This chapter proposes ILC for discrete-time affine nonlinear systems with randomly iteration varying lengths, and iteration varying initial states in a bounded range. Then, this chapter introduces a new kind of lambda norm, and proves the convergence of the algorithm. The simulation experiment verifies the effectiveness of the proposed algorithm with an actual system model, and shows the influence of varying initial state.3. Two update laws from literature are used for the simulation studies of biped walking robot. One is the conventional P-type update law and the other one introduces an iterative averaging operator to the previous tracking information. Through the simulation experiments of the biped walking robot model with two update laws, respectively, we observe that both algorithms could achieve well tracking performance, but also have their own advantages and disadvantages.