TY - GEN

T1 - An exact convex solution to receding horizon control

AU - Essick, Ray

AU - Lee, Ji Woong

AU - Dullerud, Geir

PY - 2012

Y1 - 2012

N2 - In this paper we provide an exact solution to the linear receding-horizon control problem in discrete time, a problem of long-standing interest. Considered are nominal systems with state space models that vary in time, whose controllers have access to the precise statespace model of the plant for a fixed number of steps into the future, but only have foreknowledge of the set of model values beyond this horizon. In fact, considered is a more general scenario where evolution within the latter set may be governed by an automaton. We provide a necessary and sufficient convex condition for the existence of a linear output feedback controller that can uniformly exponentially stabilize such a system, and do the same for a related disturbance attenuation problem. Each condition is in terms of a nested sequence of semidefinite programs, where (a) feasibility to any element provides an explicit controller; and (b) infeasibility implies that a controller does not exist for a given exponential decay rate. A simple physically-motivated example is used to illustrate the results, and in particular provides an instance in which foreknowledge of a model is required to stabilize it.

AB - In this paper we provide an exact solution to the linear receding-horizon control problem in discrete time, a problem of long-standing interest. Considered are nominal systems with state space models that vary in time, whose controllers have access to the precise statespace model of the plant for a fixed number of steps into the future, but only have foreknowledge of the set of model values beyond this horizon. In fact, considered is a more general scenario where evolution within the latter set may be governed by an automaton. We provide a necessary and sufficient convex condition for the existence of a linear output feedback controller that can uniformly exponentially stabilize such a system, and do the same for a related disturbance attenuation problem. Each condition is in terms of a nested sequence of semidefinite programs, where (a) feasibility to any element provides an explicit controller; and (b) infeasibility implies that a controller does not exist for a given exponential decay rate. A simple physically-motivated example is used to illustrate the results, and in particular provides an instance in which foreknowledge of a model is required to stabilize it.

UR - http://www.scopus.com/inward/record.url?scp=84869393279&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869393279&partnerID=8YFLogxK

U2 - 10.1109/acc.2012.6315646

DO - 10.1109/acc.2012.6315646

M3 - Conference contribution

AN - SCOPUS:84869393279

SN - 9781457710957

T3 - Proceedings of the American Control Conference

SP - 5955

EP - 5960

BT - 2012 American Control Conference, ACC 2012

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2012 American Control Conference, ACC 2012

Y2 - 27 June 2012 through 29 June 2012

ER -