Recent Advances in Nonlinear Control

Professor Petar Kokotovic, Electrical and Computer Engineering Department, University of California, Santa Barbara

An elegant geometric theory has been developed during the last decade for feedback control of nonlinear systems with exact models. Much of current research is devoted to robust and adaptive extensions of this theory to nonlinear models with uncertainties. While in the robust paradigm the uncertainties are assumed to be within some known nonlinear bounds, in the adaptive paradigm they appear as parameters with unknown bounds.

Adaptive systems actively reduce uncertainty through parameter estimation. The adaptive approach is now addressing a new challenge. Nonlinear systems can "explode" before the estimation achieves its goal. Both robust and adaptive tools are needed to respond to this challenge.

This lecture will describe, in conceptual rather than technical terms, how complex nonlinear systems with severe uncertainties can be robustly stabilized and how their performance can be adaptively improved. Actual and potential engineering applications will also be discussed.