A SIMPLIFICATION OF THE BACKPROPAGATION-THROUGH-TIME ALGORITHM FOR OPTIMAL NEUROCONTROL

Backpropagation-through-time (BPTT) is the temporal extension of backp ropagation which allows a multilayer neural network to approximate an optimal state-feedback control law provided some prior knowledge (Jaco bian matrixes) of the process is available. In this paper, a simplifie d version of the BPTT algorithm is proposed which more closely respect s the principle of optimality of dynamic programming. Besides being si mpler, the new algorithm is less time-consuming and allows in some cas es the discovery of better control laws. A formal justification of thi s simplification is attempted by mixing the Lagrangian calculus underl ying BPTT with Bellman-Hamilton-Jacobi equations. The improvements due to this simplification are illustrated by two optimal control problem s: the rendezvous and the bioreactor.