Finite-horizon optimal control and stabilization of time-scalable systems

Author

Fax, J. Alexander ; Murray, Richard M.

Author_Institution

Eng. & Appl. Sci., California Inst. of Technol., Pasadena, CA, USA

Volume

1

fYear

2000

fDate

2000

Firstpage

748

Abstract

We consider the optimal control of time-scalable systems. The time-scaling property is shown to convert the PDE associated with the Hamilton-Jacobi-Bellman (HJB) equation to a purely spatial PDE. Solution of this PDE yields the value function at a fixed time, and that solution can be scaled to find the value function at any point in time. Furthermore, in certain cases the unscaled control law stabilizes the system, and the unscaled value function acts as a Lyapunov function for that system. The PDE is solved for the well-known example of the nonholonomic integrator

Keywords

Lyapunov methods; optimal control; partial differential equations; stability; Hamilton-Jacobi-Bellman equation; Lyapunov function; finite-horizon optimal control; nonholonomic integrator; spatial PDE; stabilization; time-scalable systems; unscaled control law; value function; Control systems; Cost function; Equations; Lyapunov method; Mechanical systems; Optimal control; Satellites; Scalability; Vehicle dynamics; Vehicles;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2000. Proceedings of the 39th IEEE Conference on

Conference_Location

Sydney, NSW

ISSN

0191-2216

Print_ISBN

0-7803-6638-7

Type

conf

DOI

10.1109/CDC.2000.912858

Filename

912858