TY - CHAP
T1 - Asymptotic performance in adaptive H∞ control
AU - Rangan, Sundeep
AU - Poolla, Kameshwar
PY - 1996
Y1 - 1996
N2 - In adaptive control, it is often useful to distinguish between transient and asymptotic performance. In this paper, we formulate a notion of asymptotic performance for an H∞ adaptive control problem, and consider the problem in the simple case where the unknown plant is one of a finite number of known, possible models. We consider two plant cases: a) the plants are simply static nonlinear functions, and b) the plants are linear and time-invariant. Our main result is that, for both cases, the optimal asymptotic H∞ performance is no better than the optimal performance in the transient phase. We conclude that increased input-output data does not improve the achievable H∞ performance. Instead, parametric uncertainty results in a persistent performance degradation, and this uncertainty cannot be resolved, even with infinite data.
AB - In adaptive control, it is often useful to distinguish between transient and asymptotic performance. In this paper, we formulate a notion of asymptotic performance for an H∞ adaptive control problem, and consider the problem in the simple case where the unknown plant is one of a finite number of known, possible models. We consider two plant cases: a) the plants are simply static nonlinear functions, and b) the plants are linear and time-invariant. Our main result is that, for both cases, the optimal asymptotic H∞ performance is no better than the optimal performance in the transient phase. We conclude that increased input-output data does not improve the achievable H∞ performance. Instead, parametric uncertainty results in a persistent performance degradation, and this uncertainty cannot be resolved, even with infinite data.
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M3 - Chapter
AN - SCOPUS:0030402783
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 3755
EP - 3759
BT - Proceedings of the IEEE Conference on Decision and Control
A2 - Anon, null
T2 - Proceedings of the 35th IEEE Conference on Decision and Control. Part 4 (of 4)
Y2 - 11 December 1996 through 13 December 1996
ER -