Hamilton-Jacobi偏微分方程式の一解法

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  • A New Method of Solving the Hamilton-Jacobi Partial Differential Equation

説明

A New method of solving the Hamilton-Jacobi partial differential equation is proposed. Hamilton-Jacobi partial differential equations are often used for solving nonlinear-H∞-control problems or nonlinear-optimal-control problems. Some trajectories of the Hamiltonian system which is generated from the Hamiltonian function related to the Hamilton-Jacobi equation give a stable manifold of the system approximately, so they produce the derivative of the storage function. From their trajectories, the solution of the Hamilton-Jacobi equation is approximated with Bezier interpolation. The initial states of the trajectories are given by the linear system which approximates the dynamics on the stable manifold.

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