Lyapunov stability-based control and identification of nonlinear dynamical systems using adaptive dynamic programming

Abstract

This paper presents a novel control and identification scheme based on adaptive dynamic programming for nonlinear dynamical systems. The aim of control in this paper is to make output of the plant to follow the desired reference trajectory. The dynamics of plants are assumed to be unknown, and to tackle the problem of unknown plant’s dynamics, parameter variations and disturbance signal effects, a separate neural network-based identification model is set up which will work in parallel to the plant and the control scheme. Weights update equations of all neural networks present in the proposed scheme are derived using both gradient descent (GD) and Lyapunov stability (LS) criterion methods. Stability proof of LS-based algorithm is also given. Weight update equations derived using LS criterion ensure the global stability of the system, whereas those obtained through GD principle do not. Further, adaptive learning rate is employed in weight update equation instead of constant one in order to have fast learning of weight vectors. Also, LS- and GD-based weight update equations are also tested against parameter variation and disturbance signal. Three nonlinear dynamical systems (of different complexity) including the forced rigid pendulum trajectory control are used in this paper on which the proposed scheme is applied. The results obtained with LS method are found more accurate than those obtained with the GD-based method.