Nonlinear discrete system stabilisation by an evolutionary neural network

Abstract

This paper presents the application of an evolutionary neural network controller in a stabilisation problem involving an inverted pendulum. It is guaranteed that the resulting closed-loop discrete system is asymptotically stable. The process of training the neural network controller can be treated as a constrained optimisation problem where the equality constraint is derived from the Lyapunov stability criteria. The decision variables in this investigation are made up from the connection weights in the neural network, a positive definite matrix required for the Lyapunov function and matrices for the stability constraint while the objective value is calculated from the closed-loop system performance. The optimisation technique chosen for the task is a variant of genetic algorithms called a cooperative coevolutionary genetic algorithm (CCGA). Two control strategies are explored: model-reference control and optimal control. In the model-reference control, the simulation results indicate that the tracking performance of the system stabilised by the evolutionary neural network is superior to that controlled by a neural network, which is trained via a neural network emulator. In addition, the system stabilised by the evolutionary neural network requires the energy in the level which is comparable to that found in the system that uses a linear quadratic regulator in optimal control. This confirms the usefulness of the CCGA in nonlinear discrete system stabilisation applications. © Springer-Verlag Berlin Heidelberg 2006.