Optimal Control of Switched Systems Based on Continuous Hopfield Neural Network

Abstract

In this paper, a new approach is proposed for the optimal control problem of switched systems. This approach, based on Continuous Hopfield Neural Network (CHNN), has been used to find the optimal switching instants to minimize a performance index that is defined over a finite time horizon and transformed into the energy function of CHNN. The switching instants present the output vector of the neurons of CHNN. As a result, solving a dynamic optimization problem is equivalent to operating associated CHNN from its initial state to the terminal state. Based on the stable output vector of CHNN, which represents the optimal switching instants, we can find the optimal control sequence. As CHNN works in parallel and as it is of real-time characteristic, the present method is easier to satisfy the requirement of real-time control and is promising in application. We demonstrate via numerical examples the effectiveness of the proposed approach where the results are compared to those obtained by conventional methods, such as simple gradient and Quasi-Newton methods, and other non-conventional methods such as the Particle Swarm Optimization (PSO). By applying the proposed algorithm on a hydraulic system, it seems a general solution for the optimal control problem of switching instants, for a number of reasons; first, no regularity in the performance function is required; second, it is valid for many dynamics, and finally, it provides a global optimum.