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A simplification of the backpropagation-through-time algorithm for optimal neurocontrol

Backpropagation-through-time (BPTT) is the temporal extension of backpropagation which allows a multilayer neural network to approximate an optimal state-feedback control law provided some prior knowledge (Jacobian matrices) of the process is available. In this paper, a simplified version of the BPTT algorithm is proposed which more closely respects the principle of optimality of dynamic programming. Besides being simpler, the new algorithm is less time-consuming and allows in some cases the discovery of better control laws. A formal justification of this simplification is attempted by mixing the Lagrangian calculus underlying BPTT with Bellman-Hamilton-Jacobi equations. The improvements due to this simplification are illustrated by two optimal control problems: the rendezvous and the bioreactor.