Dynamic tracking optimization by continuous Hopfield neural network

A neural controller based on continuous Hopfield neural network (CHNN) is developed to solve the dynamic tracking optimal control problem for linear, time-variant, discrete-time and multivariable systems. In this study, CHNN is designed to perform the function of an optimal controller. The CHNN is constructed by establishing the equivalence between linear quadratic (LQ) optimal performance index of control system and the energy function of CHNN. Stability of the CHNN is analyzed from a theoretical perspective, too. As a result, solving LQ dynamic tracking optimal problem is equivalent to operating associated Hopfield network from its initial state to the terminal state that represents the optimal control sequence. In order to extend optimal control from finite time horizon into infinite time horizon and realize closed loop control, an online rolling optimization algorithm is applied. Numerical simulation shows that the design method above is correct and feasible.