Accelerated Learning Control for Point-to-Point Tracking Systems

In this study, we investigate the accelerated learning control schemes for point-to-point tracking systems (PTSs) with measurement noise. The asymptotic convergence of the generated input sequence has been a long-standing open issue for point-to-point tracking problems because there are infinite possible input candidates that can drive the system dynamics to track the desired reference at specified time instants. An accelerated gradient algorithm and its generalized version with a novel direction regulation matrix are proposed, with the learning gain is adaptively triggered by the practical tracking errors. The learning gain remains constant at the early stage and begins to decrease after a certain number of iterations. The input sequence generated by the proposed scheme converges to a specified limit for any fixed initial input, with the limit being closest to the initial input, in a certain sense. Numerical simulations are provided to verify the theoretical results.