TY - JOUR
T1 - Parameter identification for uncertain linear systems with partial state measurements under an H∞ criterion
AU - Pan, Zigang
AU - Başar, Tamer
N1 - Manuscript received August 4, 1995; revised March 14, 1996. Recommended by Associate Editor, V. Solo. This work was supported in part by the U.S. Department of Energy under Grant DOE-DEFG-02-94ER13939 and in part by the National Science Foundation under Grant NSF-ECS-93-12807. 2. Pan is with the Center for Control Engineering and Computation, Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106 USA. T. Bagar is with the Coordinated Science Laboratory, University of Illinois, Urbana, IL 61801 USA (e-mail: [email protected] .uiuc.edu). Publisher Item Identifier S 001 8-9286(96)06778-5.
PY - 1996
Y1 - 1996
N2 - This paper addresses the worst-case parameter identification problem for uncertain single-input/single-output (SISO) and multi-input/multi-outpnt (MIMO) linear systems under partial state measurements and derives worst-case identifiers using the cost-to-come function method. In the SISO case, the worst-case identifier obtained subsumes the Kreisselmeier observer as part of its structure with parameters set at some optimal values. Its structure is different from the common least-squares (LS) identifier, however, in the sense that there is additional dynamics for the state estimate, coupled with the dynamics of the parameter estimate in a nontrivial way. In the MIMO case as well, the worst-case identifier has additional dynamics for the state estimate which do not appear in the conventional LS-based schemes. Also for both SISO and MIMO problems, approximate identifiers are obtained which are numerically much better conditioned when the disturbances in the measurement equations are "small." The theoretical results are then illustrated on an extensive numerical example to demonstrate the effectiveness of the identification schemes developed.
AB - This paper addresses the worst-case parameter identification problem for uncertain single-input/single-output (SISO) and multi-input/multi-outpnt (MIMO) linear systems under partial state measurements and derives worst-case identifiers using the cost-to-come function method. In the SISO case, the worst-case identifier obtained subsumes the Kreisselmeier observer as part of its structure with parameters set at some optimal values. Its structure is different from the common least-squares (LS) identifier, however, in the sense that there is additional dynamics for the state estimate, coupled with the dynamics of the parameter estimate in a nontrivial way. In the MIMO case as well, the worst-case identifier has additional dynamics for the state estimate which do not appear in the conventional LS-based schemes. Also for both SISO and MIMO problems, approximate identifiers are obtained which are numerically much better conditioned when the disturbances in the measurement equations are "small." The theoretical results are then illustrated on an extensive numerical example to demonstrate the effectiveness of the identification schemes developed.
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U2 - 10.1109/9.536499
DO - 10.1109/9.536499
M3 - Article
AN - SCOPUS:0030241939
SN - 0018-9286
VL - 41
SP - 1295
EP - 1311
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 9
ER -