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Nonlinear Games: examples and counterexamples

Doyle, John and Primbs, James A. and Shapiro, Benjamin and Nevistić, Vesna (1996) Nonlinear Games: examples and counterexamples. In: Proceedings of the 35th IEEE Conference on Decision and Control. IEEE Conference on Decision and Control-Proceedings. Vol.4. IEEE , Piscataway, NJ, pp. 3915-3920. ISBN 0-7803-3590-2.

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Popular nonlinear control methodologies are compared using benchmark examples generated with a “converse Hamilton-Jacobi-Bellman” method (CoHJB). Starting with the cost and optimal value function V, CoHJB solves HJB PDEs “backwards” algebraically to produce nonlinear dynamics and optimal controllers and disturbances. Although useless for design, it is great for generating benchmark examples. It is easy to use, computationally tractable, and can generate essentially all possible nonlinear optimal control problems. The optimal control and disturbance are then known and can be used to study actual design methods, which must start with the cost and dynamics without knowledge of V. This paper gives a brief introduction to the CoHJB method and some of the ground rules for comparing various methods. Some very simple examples are given to illustrate the main ideas. Both Jacobian linearization and feedback linearization combined with linear optimal control are used as “strawmen” design methods.

Item Type:Book Section
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Doyle, John0000-0002-1828-2486
Additional Information:© 1996 IEEE.
Series Name:IEEE Conference on Decision and Control-Proceedings
Record Number:CaltechAUTHORS:20140527-071022483
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Official Citation:Doyle, John; Primbs, James A.; Shapiro, B.; Nevistic, V., "Nonlinear games: examples and counterexamples," Decision and Control, 1996., Proceedings of the 35th IEEE Conference on , vol.4, no., pp.3915-3920 vol.4, 11-13 Dec 1996 doi: 10.1109/CDC.1996.577292
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:45912
Deposited On:28 May 2014 19:04
Last Modified:10 Nov 2021 17:18

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