TY - JOUR
T1 - Continuous-Time Tracking Problems in an H∞ setting
T2 - A Game Theory Approach
AU - Shaked, Uri
N1 - Funding Information:
Manuscript received May 7, 1993; revised October 3, 1994. Recommended by Past Associate Editor, E. W. Kamen. This work was suppoxted in part by the Australian Research Council and the C&M Maus Chair at Tel Aviv University. U. Shaked is with the Department of Electrical Engineering-Systems, Tel-Aviv University, Tel-Aviv 69978, Israel. C. E. de Souza is with the Department of Electrical and Computer Engineering, The University of Newcastle, NSW 2308, Australia. IEEE Log Number 9410487.
PY - 1995/5
Y1 - 1995/5
N2 - This paper investigates the problem of finite-horizon H∞tracking for linear time-varying systems. Three tracking problems are considered, depending on whether the reference signal is perfectly known in advance, measured on-line, or previewed in fixed interval of time ahead. No a prion knowledge of a dynamic model for the reference signal is assumed. A game theory approach to the latter tracking problems is presented where, given a specific reference signal, the controllers play against nature which can choose any initial state and any bounded energy disturbance input and measurement noise. Necessary and sufficient conditions for the existence of a saddle-point equilibrium are determined, and H∞tracking controllers for both the cases of state and output feedback are derived. Tracking problems for time-invariant systems on infinite-horizon are also analyzed, and time invariant tracking controllers are obtained for zero initial conditions.
AB - This paper investigates the problem of finite-horizon H∞tracking for linear time-varying systems. Three tracking problems are considered, depending on whether the reference signal is perfectly known in advance, measured on-line, or previewed in fixed interval of time ahead. No a prion knowledge of a dynamic model for the reference signal is assumed. A game theory approach to the latter tracking problems is presented where, given a specific reference signal, the controllers play against nature which can choose any initial state and any bounded energy disturbance input and measurement noise. Necessary and sufficient conditions for the existence of a saddle-point equilibrium are determined, and H∞tracking controllers for both the cases of state and output feedback are derived. Tracking problems for time-invariant systems on infinite-horizon are also analyzed, and time invariant tracking controllers are obtained for zero initial conditions.
UR - http://www.scopus.com/inward/record.url?scp=0029304714&partnerID=8YFLogxK
U2 - 10.1109/9.384218
DO - 10.1109/9.384218
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AN - SCOPUS:0029304714
SN - 0018-9286
VL - 40
SP - 841
EP - 852
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 5
ER -