Learning control based on local linearization by using DFT

Learning control is one of the most interesting subjects in robotics field, and several works on this topic were extensively investigated. Learning control is necessary for high-speed and high-precision trajectory control in cases where an objective system includes uncertain parameters and/or has practical limitations on the feedback control. Conventional learning control methods, however, have a problem concerning how to determine a learning operator that guarantees the convergence of the scheme without a priori knowledge of an objective system. For instance, designing learning controllers that will work for complex robot systems, such as pneumatic robots with complicated dynamics or robots with complex sensory feedback, is extremely difficult. This article provides a new type of learning control scheme for a class of discrete-time nonlinear systems. The algorithm of proposed learning control utilizes local linearization techniques by using Discrete Fourier Transform (DFT) to design the learning operator and the numerical function iterative techniques. In our case, the secant method is used, which can find the best learning operator by itself at each learning step, in other words, at each calculation step of iteration. This proposed learning algorithm has been extensively tested by simulation on the computer. © 1994 John Wiley & Sons, Inc.