Abstract
In this paper, we present computational methods for approximate solution to the time-dependent first-order Hamilton–Jacobi equations (HJEs) arising in deterministic optimal control of nonlinear systems in state-space, as well as other areas of science and engineering. We establish convergence of the methods for optimal control problems and for the case of general nonlinear systems under fairly mild assumptions. Examples are then solved to demonstrate the effectiveness of the methods and the special case of affine nonlinear systems is also considered. Results are then extended to more general initial value problems of the HJE arising in other areas of science and engineering.
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