Solution of nonlinear optimal control problems using modified Hopfield neural networks

Daniel J. Stech

doi:10.1117/12.174238

1 May 1994 Solution of nonlinear optimal control problems using modified Hopfield neural networks

Daniel J. Stech

Author Affiliations +

Proceedings Volume 2192, Smart Structures and Materials 1994: Mathematics and Control in Smart Structures; (1994) https://doi.org/10.1117/12.174238
Event: 1994 North American Conference on Smart Structures and Materials, 1994, Orlando, FL, United States

Abstract

Solution of nonlinear optimal control problems on analog parallel networks is proposed. Recurrent neural networks whose dynamic equations have a Lyapunov function are developed. Such circuits relax to an equilibrium which is the minimum of the Lyapunov function. Nonlinear optimal control problems are formulated in terms of a Lyapunov function and thus are solved using the recurrent networks. Convergence for linear and nonlinear classes of problems is considered. The method is demonstrated by developing and simulating a network to solve a nonlinear vibration problem. Simulation results demonstrate solution times are accurate and extremely fast. Solution times are shown to be independent of the size of the problem.

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Daniel J. Stech "Solution of nonlinear optimal control problems using modified Hopfield neural networks", Proc. SPIE 2192, Smart Structures and Materials 1994: Mathematics and Control in Smart Structures, (1 May 1994); https://doi.org/10.1117/12.174238

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