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RECEDING HORIZON H ∞ CONTROL FOR SYSTEMS WITH A STATE‐DELAY
Author(s) -
Lee Young Sam,
Han Soo Hee,
Kwon Wook Hyun
Publication year - 2006
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1111/j.1934-6093.2006.tb00253.x
Subject(s) - saddle point , monotonic function , weighting , mathematics , control theory (sociology) , positive definite matrix , parameterized complexity , norm (philosophy) , exponential stability , horizon , mathematical optimization , computer science , control (management) , mathematical analysis , algorithm , eigenvalues and eigenvectors , medicine , physics , geometry , quantum mechanics , nonlinear system , artificial intelligence , political science , law , radiology
This paper proposes the receding horizon H ∞ control (RHHC) for linear systems with a state‐delay. We first proposes a new cost function for a finite horizon dynamic game problem. The proposed cost function includes two terminal weighting terms, each of which is parameterized by a positive definite matrix, called a terminal weighting matrix. Secondly, we derive the RHHC from the solution to the finite dynamic game problem. Thirdly, we propose an LMI condition under which the saddle point value satisfies the nonincreasing monotonicity. Finally, we show the asymptotic stability and H ∞ ‐norm boundedness of the closed‐loop system controlled by the proposed RHHC. Through a numerical example, we show that the proposed RHHC is stabilizing and satisfies the infinite horizon H ∞ ‐norm bound.