Event Abstract

Back to Event

A Comparison of Fixed Final Time Optimal Control Computational Methods with a View to Closed Loop IM

Xavier Matieni1* and Stephen Dodds1
  • 1 University of East London, School of Computing Information Technology and Engineering, United Kingdom

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.

References

1. Bellman R., (1957). Dynamic Programming, Princeton, NJ: Princeton University Press.

2. Pontryagin L. S., (1959), Optimal Control Processes. Usp. Mat. Nauk 14, 3

3. Bolttyanskii, V. G., Gamkrelidze, R.V., and Pontryagin, L. S, (1960), The Mathematical Theory of Optimal Processes, I. The Maximum Principle, Izv., Akad., Nauk, SSR, Ser. Mat. 24, 3.

4. Bellman, R., Dreyfus S. E. (1962), Applied Dynamic Programming, Princeton, NJ: Princeton University Press.

5. Pearson A. B., ‘Synthesis of a Minimum Energy Controller subject to Average Power Constraint, in Proceedings of the 1962 Joint Automatic Control Conference, New York, pp. 19-4-1 to 19-4-6.

6. Shinners S. M., (1992), Modern Control System Theory and Design, John Wiley & Sons, pp 632-668.

7. Sunan, H., Kok K. and Kok Z (2004), Neural Network Control: Theory and Application, Research Studies Press Ltd.

8. Picton P., (2000), Neural Networks, Palgrave.

Conference: Bernstein Conference on Computational Neuroscience, Frankfurt am Main, Germany, 30 Sep - 2 Oct, 2009.

Presentation Type: Poster Presentation

Topic: Dynamical systems and recurrent networks

Citation: Matieni X and Dodds S (2009). A Comparison of Fixed Final Time Optimal Control Computational Methods with a View to Closed Loop IM. Front. Comput. Neurosci. Conference Abstract: Bernstein Conference on Computational Neuroscience. doi: 10.3389/conf.neuro.10.2009.14.067

Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters.

The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated.

Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed.

For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions.

Received: 26 Aug 2009; Published Online: 26 Aug 2009.

* Correspondence: Xavier Matieni, University of East London, School of Computing Information Technology and Engineering, London, United Kingdom, xamat@hotmail.com