An approximation scheme for the minimum time function. (English) Zbl 0723.49024

Bardi, M; Falcone, M.

SIAM J. Control Optimization 28, No. 4, 950-965 (1990).

Summary: This paper presents an approximation scheme for the nonlinear minimum time problem with compact target. The cheme is derived from a discrete dynamic programming principle and the main convergence result is obtained by applying techniques related to discontinuous viscosity solutions for Hamilton-Jacobi equations. The convergence is proved under general controllability assumptions on both the continuous-time and the discrete- time systems. An explicit sufficient condition on the system and the target ensuring the desired controllability is given. This condition is shown to be necessary and sufficient for the Lipschitz continuity of the minimum time function if the target is smooth. An extension to the case of a point-shaped target is given.

MSC:

49L20	Dynamic programming in optimal control and differential games
93C55	Discrete-time control/observation systems
49L25	Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
93C99	Model systems in control theory

Keywords:

approximation scheme; nonlinear minimum time problem; compact target; discontinuous viscosity solutions; Hamilton-Jacobi equations; continuous-time