Stabilizing a linear system with Saturation Through optimal control

Author

Goebel, Rafal

Volume

50

Issue

5

fYear

2005

fDate

5/1/2005 12:00:00 AM

Firstpage

650

Lastpage

655

Abstract

We construct a continuous feedback for a saturated system x(t)=Ax(t)+Bσ(u(t)). The feedback renders the system asymptotically stable on the whole set of states that can be driven to 0 with an open-loop control. The trajectories of the resulting closed-loop system are optimal for an auxiliary optimal control problem with a convex cost and linear dynamics. The value function for the auxiliary problem, which we show to be differentiable, serves as a Lyapunov function for the saturated system. Relating the saturated system, which is nonlinear, to an optimal control problem with linear dynamics is possible thanks to the monotone structure of saturation.

Keywords

Lyapunov methods; asymptotic stability; closed loop systems; feedback; linear systems; open loop systems; optimal control; Lyapunov function; asymptotic stability; auxiliary optimal control problem; closed-loop system; continuous feedback; convex cost; linear dynamics; linear system stabilization; monotone structure; open-loop control; saturated system; Control systems; Cost function; Eigenvalues and eigenfunctions; Hydraulic actuators; Linear systems; Lyapunov method; Nonlinear dynamical systems; Open loop systems; Optimal control; State feedback; Convex Lyapunov function; feedbacl stabilization; linear system; optimal control; saturating actuator;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2005.846522

Filename

1431044