LEARNING CONTROL ALGORITHMS FOR TRACKING SLOWLY VARYING TRAJECTORIES

To date, most of the available results in learning control have been u tilized in applications where a robot is required to execute the same motion over and over again, with a certain periodicity, This is due to the requirement that all learning algorithms assume that a desired ou tput is given a priori over the time duration t is an element of [0, T ]. For applications where the desired outputs are assumed to change '' slowly,'' we present a D-type, PD-type, and PID-type learning algorith ms. At each iteration we assume that the system outputs and desired tr ajectories are contaminated with measurement noise, the system state c ontains disturbances, and errors are present during reinitialization. These algorithms are shown to be robust and convergent under certain c onditions, In theory, the uniform convergence of learning algorithms i s achieved as the number of iterations tends to infinity, However, in practice we desire to stop the process after a minimum number of itera tions such that the trajectory errors are less than a desired toleranc e bound, We present a methodology which is devoted to alleviate the di fficulty of determining a priori the controller parameters such that t he speed of convergence is improved, In particular, for systems with t he property that the product matrix of the input and output coupling m atrices, CB, is not full rank. Numerical examples are given to illustr ate the results.