Data-Driven Gradient Descent Direct Adaptive Control for Discrete-Time Nonlinear SISO Systems

Abstract

A novel data-driven gradient descent (GD) adaptive controller, for discrete-time single-input and single output (SISO) systems, is presented. The controller operates as the least mean squares (LMS) algorithm, applied to a nonlinear system with feedback. Normalization of the learning rate parameter provides robustness of the overall system to modeling errors and environment nonstationarity. Convergence analysis reveals that the controller forces tracking error to zero, with bounded control signal and the controller weights. The experiments on the benchmark systems support the analysis.