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An Optimal Control Synthesis of Nonlinear Systems by Neural Network Backpropagation-Through-Time Algorithm

This work presents a new numerical algorithm for the time optimal control of nonlinear multivariable systems with control and state vectors constraints. The algorithm is based on the backpropagation-through-time algorithm (BPTT), which is used as a learning algorithm for recurrent neural networks. Also, a heuristic algorithm for the time optimal control is presented. This algorithm is based on the characteristics of penalty functions for control and state vectors constraints. The proposed algorithms are especially suitable for treating complicate state vector constraints. Also, the proposed algorithms provide better convergence properties then numerical algorithms based on conversion of optimal control problem into a nonlinear programming one. The algorithms are applied on the problem of the time optimal robot control with the state vector constraints in the form of obstacle avoidance.

Optimal Control, Nonlinear Systems, Robot Control, Gradient Algorithm, Backpropagation-Through-Time Algorithm

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