Optimal Control Based on Continuous Hopfield Neural Network

For solving linear quadratic (LQ) optimal control problem of discrete-time systems, a new alternative method is developed based on continuous Hopfield neural network (CHNN). It can avoid the phenomena that the computation will increase exponentially with the increase of system dimension and control time-horizon while using discrete Hopfield neural network to solve the sptimal control. By this method, the LQ performance index is transformed into the energy function of CHNN, and the control sequence into the output vector of the neurons of CHNN. As a result, solving LQ dynamic optimization problem is equivalent to the operating process of CHNN from its initial state to the terminal state. The stable output vector of CHNN represents the optimal control sequence. The method can be applied to online optimal control for its little cost in computation and good real-time performance.