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A Method for Robust Receding Horizon Output Feedback of Constrained Systems

Goulart P. J. and Kerrigan E. C.

February 2006
Technical Report: CUED/F-INFENG/TR.538

Abstract

This paper considers output feedback control of linear discrete-time systems with convex state and input constraints and subject to bounded state disturbances and output measurement errors. We show that the non-convex problem of finding a constraint admissible affine output feedback policy, to be used in conjunction with a fixed linear state observer, can be converted to an equivalent convex problem. When used in the design of a time-varying robust receding horizon control (RHC) law, we derive conditions under which the resulting closed-loop system is guaranteed to satisfy the system constraints for all time, given an initial state estimate and bound on the state estimation error. When the state estimation error bound matches the minimal robust positively invariant (mRPI) set for the system error dynamics, we show that this control law is actually time-invariant, but its calculation generally requires solution of an infinite-dimensional optimisation problem. Finally, using an invariant outer approximation to the mRPI error set, we develop a time-invariant control law that can be computed by solving a finite-dimensional, tractable optimisation problem at each time step, which guarantees that the closed-loop system satisfies the constraints for all time

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BibTex Entry

@TechReport{goulart:kerrigan:2006a,: author = {Goulart P. J. and Kerrigan E. C.},; institution = {Department of Engineering, University of Cambridge},; title = {A Method for Robust Receding Horizon Output Feedback of Constrained Systems},; year = {2006},; bibkey = {goulart:kerrigan:2006a},; month = {February},; note = {CUED/F-INFENG/TR.538}
}



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