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

摘要

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