AAS 96-109

DESIGN OF A DIGITAL LEARNING CONTROLLER USING A PARTIAL ISOMETRY

H. S. Jang and R. W. Longman, Columbia University

Abstract

A previous learning control law based on contraction mapping was developed to give monotonic behavior during the learning transients. Here we determine the relationship between frequency response and singular values of a matrix of Markov parameters that appears in the learning algorithm. This relationship connects time domain with frequency domain techniques for learning control design. From this connection a new learning law is developed purely in the time domain, with faster convergence at high frequencies than the previous method. The inverse of a partial isometry is used, which is the by-product of polar decomposition of the system matrix in the repetition domain. In previous frequency response methods, difficulties were encountered when the desired trajectory was too short. A main advantage of the proposed learning law is its good behavior regardless of the length of the desired trajectory.