Solving the Hamilton-Jacobi Equation
This chapter reviews some major approaches for solving the Hamilton-Jacobi equation (HJEs), and present one algorithm that may yield global solutions. It discusses some popular polynomial and Taylor-series approximation methods for solving the HJEs and examines a factorization approach which may yie...
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| description | This chapter reviews some major approaches for solving the Hamilton-Jacobi equation (HJEs), and present one algorithm that may yield global solutions. It discusses some popular polynomial and Taylor-series approximation methods for solving the HJEs and examines a factorization approach which may yield exact and global solutions. It explores the extension of this approach to Hamiltonian mechanical systems. The chapter proposes some major approaches for solving the Hamilton-Jacobi-Bellman equation (HJBE) and Hamilton-Jacobi-Isaacs equation (HJIE) that have been proposed in the literature. In a recursive procedure for the HJBE for a class of nonlinear systems. It presents a factorization approach that may yield exact global solutions of the HJIE for the class of affine nonlinear systems. The chapter deals with a discussion of sufficiency conditions for the existence of exact solutions to the HJIE which are provided by the Implicit-function Theorem. |
| doi_str_mv | 10.1201/b10734-13 |
| format | Book Chapter |
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It discusses some popular polynomial and Taylor-series approximation methods for solving the HJEs and examines a factorization approach which may yield exact and global solutions. It explores the extension of this approach to Hamiltonian mechanical systems. The chapter proposes some major approaches for solving the Hamilton-Jacobi-Bellman equation (HJBE) and Hamilton-Jacobi-Isaacs equation (HJIE) that have been proposed in the literature. In a recursive procedure for the HJBE for a class of nonlinear systems. It presents a factorization approach that may yield exact global solutions of the HJIE for the class of affine nonlinear systems. 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| ispartof | Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations, 2011, p.333-357 |
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| language | eng |
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| source | O'Reilly Online Learning: Academic/Public Library Edition |
| subjects | Calculus of variations MATHEMATICS Power generation & distribution |
| title | Solving the Hamilton-Jacobi Equation |
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