<h2>AAS  96-109</h2><h2>DESIGN OF A DIGITAL LEARNING CONTROLLER USING A PARTIAL ISOMETRY</h2><h4>H. S. Jang and R. W. Longman, Columbia University</h4><h2> Abstract </h2>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.<br><br>