Backpropagation for N-stage optimal control problems

The design of closed-loop feedforward control strategies to solve non-LQ (nonlinear, nonquadratic) optimal control problems is addressed. Due to the generality of optimization problems, conventional methods are difficult to apply. An approximate optimal solution is sought by constraining the control strategies to take on the structure of two chains (the feedback chain and the feedforward chain) of multilayer feedforward neural networks. This structure is based on the linear-structure preserving principle. After reducing the original functional problem to a nonlinear programming one, backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results for LQ and non-LQ problems show the effectiveness of the method