TY - GEN
T1 - H∞-optimal control for singularly perturbed systems. Part I
T2 - Proceedings of the 1992 American Control Conference
AU - Pan, Zigang
AU - Basar, Tamer
N1 - Funding Information:
*Received 23 April 1991; revised 19 November 1991; received in final form 11 March 1992. The original version of this paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor H. Kimura under the direction of Editor H. Kwakernaak. t Research supported in part by the U.S. Department of Energy under Grant DE-FG-02-88-ER-13939, in part by the National Science Foundation under Grant ECS 1-5-30496, and in part by the Joint Services Electronics Program under Contract N00014-84-c-0149. z~ An abridged version was presented at the 1992 American Control Conference, Chicago, IL, 24-26 June, 1992. § Coordinated Science Laboratory and the Department of Electrical and Computer Engineering, University of Illinois, 1101 W. Springfield Avenue, Urbana, IL 61801, U.S.A.
PY - 1992
Y1 - 1992
N2 - We study the H∞-optimal control of singularly perturbed linear systems under perfect state measurements. Using a differential game theoretic approach, we show that as the singular perturbation parameter ε approaches zero, the optimal disturbance attenuation level for the full-order system under a quadratic performance index converges to a value that is bounded above by the maximum of the optimal disturbance attenuation levels for the slow and fast subsystems under appropriate 'slow' and 'fast' quadratic cost functions. Furthermore, we construct a composite controller based on the solution of the slow and fast games, which guarantees a desired achievable performance level for the full-order plant, as ε approaches zero. A 'slow' controller, however, is not generally robust in this sense, but still under some conditions, which are delineated in the paper, the fast dynamics can be totally ignored. The paper also studies optimality when the controller includes a feedforward term in the disturbance.
AB - We study the H∞-optimal control of singularly perturbed linear systems under perfect state measurements. Using a differential game theoretic approach, we show that as the singular perturbation parameter ε approaches zero, the optimal disturbance attenuation level for the full-order system under a quadratic performance index converges to a value that is bounded above by the maximum of the optimal disturbance attenuation levels for the slow and fast subsystems under appropriate 'slow' and 'fast' quadratic cost functions. Furthermore, we construct a composite controller based on the solution of the slow and fast games, which guarantees a desired achievable performance level for the full-order plant, as ε approaches zero. A 'slow' controller, however, is not generally robust in this sense, but still under some conditions, which are delineated in the paper, the fast dynamics can be totally ignored. The paper also studies optimality when the controller includes a feedforward term in the disturbance.
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U2 - 10.23919/acc.1992.4792432
DO - 10.23919/acc.1992.4792432
M3 - Conference contribution
AN - SCOPUS:0026984817
SN - 0780302109
SN - 9780780302105
T3 - Proceedings of the American Control Conference
SP - 1850
EP - 1854
BT - Proceedings of the American Control Conference
PB - Publ by American Automatic Control Council
Y2 - 24 June 1992 through 26 June 1992
ER -