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.

UR - http://www.scopus.com/inward/record.url?scp=0030402783&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030402783&partnerID=8YFLogxK

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 -