Neural networks for optimal control

Theoretical methods based on Pontryagin´s maximum principle and Bellman´s dynamic programming exist for determining optimal controls for nonlinear dynamical systems with state and control constraints. However, these methods only yield control inputs as functions of time (i.e., open loop controls). In practical applications, where robust feedback controllers are preferred, such solutions cannot be directly used. In this paper we propose methods for circumventing the above difficulties, and indicate how neural networks, trained off-line, may find application in the future in the design of online controllers for complex systems