A construction procedure using characteristics for viscosity solutions of the Hamilton-Jacobi equation

Author

Bayen, Alexandre M. ; Tomlin, Claire J.

Author_Institution

Dept. of Aeronaut. & Astronaut., Stanford Univ., CA, USA

Volume

2

fYear

2001

fDate

2001

Firstpage

1657

Abstract

This paper provides a procedure to generate C₁ or (C ₀, PC₁) solutions of a 1D Hamilton-Jacobi equation with a non-smooth Hamiltonian, based on the method of characteristics. The C₁ solutions constructed are classical solutions. We prove, using examples, that the (C₀, PC₁) constructed solutions are the viscosity solutions, with help of a minimax-viscosity equivalence. We show how shock waves and voids are generated by initial conditions. We show with 2D examples how this technique might be applied to differential games

Keywords

aerodynamics; aerospace control; computational fluid dynamics; differential games; initial value problems; minimax techniques; optimal control; partial differential equations; reachability analysis; shock waves; viscosity; (C₀, PC₁) solutions; 1D Hamilton-Jacobi equation; C₁ solutions; differential games; initial conditions; method of characteristics; minimax-viscosity equivalence; nonsmooth Hamiltonian; shock waves; solution construction procedure; viscosity solutions; voids; Air safety; Character generation; Contracts; Electric shock; Equations; Jacobian matrices; Minimax techniques; Optimal control; Shock waves; Viscosity;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2001. Proceedings of the 40th IEEE Conference on

Conference_Location

Orlando, FL

Print_ISBN

0-7803-7061-9

Type

conf

DOI

10.1109/.2001.981139

Filename

981139