Tracking control by the Newton–Raphson method with output prediction and controller speedup

Abstract

Summary This paper presents a control technique for output tracking of reference signals in continuous‐time dynamical systems. The technique is comprised of the following three elements: (i) a fluid‐flow version of the Newton–Raphson method for solving algebraic equations, (ii) a system‐output prediction which has to track the future reference signal, and (iii) a speedup of the control action for enhancing the tracker's accuracy and, in some cases, stabilizing the closed‐loop system. The technique can be suitable for linear and nonlinear systems, implementable by simple algorithms, and can track reference points as well as time‐dependent reference signals. Though inherently local, the tracking controller is proven to have a global convergence for a class of linear systems. The derived theoretical results of the paper include convergence of the tracking controller and error analysis, and are supported by illustrative simulation and laboratory experiments.