Time-optimal terminal control using neural networks

Multilayer neural networks, trained by the backpropagation through time algorithm (BPTT), are used successfully as state-feedback controllers for nonlinear terminal control problems. Current BPTT techniques do not deal systematically with open final-time situations such as minimum-time problems. An extension of BPTT to open final-time problems called time-optimal backpropagation-through-time (TOBPTT) is presented. The derivation uses Lagrange multiplier methods for constrained optimization. The algorithm is tested on a Zermelo problem, and the resulting trajectories compare favorably with classical optimal control results