P-Type Learning Control Using a Forgetting Factor

Abstract

A learning control scheme using a forgetting factor and a long term memory is proposed, in which outputs refer to velocity coordinates and the next command input is modified by the residual error between the desired output and actual output. Robustness problems of the scheme against initialization errors and fluctuations of dynamics are treated rigorously for a class of linear mechanical systems. First, the uniform boundedness of output trajectories during repetitive learning is proved on the basis of the passivity of the mechanical system. Next, the convergence of output trajectories to an &-neighborhood of the desired output trajectory is proved. The size of the E-neighborhood depends on the magnitude of initialization errors and fluctuations of dynamics.