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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