A comparison of fixed final time optimal control computational methods with a view to closed loop implementation using artificial neural networks

The purpose of this paper is to lay the foundations of a new generation of closed loop optimal control laws based on the plant state space model and implemented using artificial neural networks. The basis is the long established open loop methods of Bellman and Pontryagin, which compute optimal controls off line and apply them subsequently in real time. They are therefore open loop methods and during the period leading up to the present century, they have been abandoned by the mainstream control researchers due to a) the fundamental drawback of susceptibility to plant modelling errors and external disturbances and b) the lack of success in deriving closed loop versions in all but the simplest and often unrealistic cases. The recent energy crisis, however, has promoted the authors to re-visit the classical optimal control methods with a view to deriving new practicable closed loop optimal control laws that could save terawatts of electrical energy by replacement of classical controllers throughout industry. First Bellman�s and Pontryagin�s methods are compared regarding ease of computation. Then a new optimal state feedback controller is proposed based on the training of artificial neural networks with the computed optimal controls.