Robustness and convergence rate of a discrete‐time learning control algorithm for a class of nonlinear systems

Abstract

In this paper, we apply a discrete‐time learning algorithm to a class of discrete‐time varying nonlinear systems with affine input action and linear output having relative degree one. We investigate the robustness of the algorithm to state disturbance, measurement noise and reinitialization errors. We show that the input and the state variables are always bounded if certain conditions are met. Moreover, we shown that the input error and state error converge uniformly to zero in absence of all disturbances. In addition, we show that, after a finite number of iterations, the convergence rate is exponential in l∞. A numerical example is added to illustrate the results. Copyright © 1999 John Wiley & Sons, Ltd.