3314 Perturbation Approach for Hamilton-Jacobi Equations of Nonlinear Control Systems : II. When all directions near equilibria are unstable

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  • 3314 非線形制御系のハミルトン・ヤコビ方程式に対する摂動論的アプローチ : II.平衡点のまわりのすべての方向が不安定である場合(非線形制御理論とその応用(1))

Abstract

We analytically study stabilizing solutions to Hamilton-Jacobi equations when all directions near equilibria are unstable, that is, the eigenvalues of the Jacobian matrix at the equilibria are all positive. Applying a perturbation approach, we obtain analytical approximations of stable manifolds in the corresponding Hamiltonian systems, and use their relation to the stabilizing solutions. An illustrative example is given for the two-dimensional Lotka-Volterra system and the theoretical result for the stable manifold is compared with a numerical computation to demonstrate the validity of our method.

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