DocumentCode :
800755
Title :
Control of Constrained Discrete-Time Systems With Bounded \\ell _{2} Gain
Author :
Goulart, Paul J. ; Kerrigan, Eric C. ; Alamo, Teodoro
Author_Institution :
NEC Labs. America Inc., Princeton, NJ
Volume :
54
Issue :
5
fYear :
2009
fDate :
5/1/2009 12:00:00 AM
Firstpage :
1105
Lastpage :
1111
Abstract :
We consider the problem of designing a control law for a constrained linear system with bounded disturbances that ensures constraint satisfaction over an infinite horizon, while also guaranteeing that the closed-loop system has bounded lscr2 gain. To this end, we propose a receding horizon control strategy based on the repeated calculation of optimal finite horizon feedback policies. We parameterize these policies such that the input at each time is an affine function of current and prior states, and minimize a worst-case quadratic cost where the disturbance energy is negatively weighted as in H infin control. We show that the resulting receding horizon controller has two advantages over previous results for this problem. First, the policy optimization problem to be solved at each time step can be rendered convex-concave, with a number of decision variables and constraints that grows polynomially with the problem size, thereby making its solution amenable to standard techniques in convex optimization. Second, the achievable lscr2 gain of the resulting closed-loop system is bounded and non-increasing with increasing control horizon. A numerical example is included to demonstrate the improvement in achievable lscr2 gain relative to existing methods.
Keywords :
Hinfin control; closed loop systems; constraint theory; discrete time systems; feedback; infinite horizon; linear systems; predictive control; Hinfin control; bounded lscr2 gain; closed-loop system; constrained discrete-time systems; constrained linear system; constraint satisfaction; infinite horizon; optimal finite horizon feedback; receding horizon control; Constraint optimization; Control systems; Cost function; Feedback; Infinite horizon; Linear systems; Open loop systems; Optimal control; Polynomials; Robust control; Constrained systems; receding horizon control (RHC); robust control; robust optimization; uncertain systems;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.2009.2013002
Filename :
4907225
Link To Document :
بازگشت