Title :
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
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;
Conference_Titel :
Decision and Control, 2001. Proceedings of the 40th IEEE Conference on
Conference_Location :
Orlando, FL
Print_ISBN :
0-7803-7061-9
DOI :
10.1109/.2001.981139
