Quadratically saturated regulator for constrained linear systems

Author

Verriest, Erik I. ; Pajunen, Graiyna A.

Author_Institution

Sch. of Electr. & Comput. Eng., Georgia Inst. of Technol., Atlanta, GA, USA

Volume

41

Issue

7

fYear

1996

fDate

7/1/1996 12:00:00 AM

Firstpage

992

Lastpage

995

Abstract

The problem of stabilization and null-controllability of open-loop unstable discrete-time multi-input systems with constraints on the inputs and the controls is addressed in this paper. First necessary and sufficient conditions for solvability of the problem are derived. They guarantee the existence of a linear controller leaving the state constraint set for the closed-loop system positively invariant. An optimal control law is computed, and the admissible set of initial conditions is given such that along trajectories of the closed-loop system the state and input constraints are satisfied. Then the domain of feasible initial conditions is enlarged using a saturating control if such is feasible

Keywords

closed loop systems; control system synthesis; controllability; discrete time systems; linear systems; multivariable control systems; nonlinear control systems; optimal control; stability; state feedback; closed-loop system; constrained linear systems; linear controller; necessary and sufficient conditions; null-controllability; open-loop unstable discrete-time multi-input systems; optimal control law; quadratically saturated regulator; solvability; stabilization; state constraint set; Control design; Control systems; Linear systems; Matrix decomposition; Open loop systems; Regulators; Singular value decomposition; State feedback; Sufficient conditions; Vectors;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.508902

Filename

508902