Adaptive Control of Nonlinear Systems

Miroslav Krstic, Department of Electrical and Computer Engineering, University of California, Santa Barbara

Traditional approach to adaptive control is not applicable to nonlinear systems. It relies on the fact that linear instability mechanisms are no faster than convergence rates of parameter estimators. In contrast, the instability phenomena in truly nonlinear systems have explosive character -- the state can escape to infinity in finite time. Therefore, we develop adaptive nonlinear designs which have either 1) parameter estimators as fast as the nonlinear instability phenomena, or 2) strong controllers which prevent incorrect, time-varying parameter estimates from causing finite escape. Transient performance has been a long-standing problem in adaptive control because traditional adaptive linear controllers can go through unpredictably large initial swings before they settle to a good asymptotic behavior. The accomplishment of our nonlinear adaptive designs is their capability to systematically improve both the peaks and the tails of transient responses, which we show analytically. The most interesting consequence is that for the first time we can prove that an adaptive controller achieves better performance than its nonadaptive counterpart. Asymptotic behavior of adaptive controllers has been an open problem because, in general, it was not even known if the parameter estimates converge to constant values. Our most recent result resolves this problem, and provides answers to some fundamental questions: Does the adaptive controller `converge' to a stabilizing controller? Can adaptation be disconnected after sufficiently long time? Miroslav Krstic received the BSEE (1989) degree from the University of Belgrade, Yugoslavia, and the MSEE (1992) degree from the University of California, Santa Barbara, where he has been since 1991. In 1993 he received the IEEE CDC Best Student Paper Award, and the UCSB Engineering Fellowship. His research interests include adaptive control of nonlinear and linear systems, robust nonlinear control, and applications.