Adaptive and Robust Nonlinear Control

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9528370 Kokotovic This is a proposal for continuation of our NSF Grant #ECS-9203491 which expires on August 31, 1995. Part one of the proposal summarizes the results under our current grant which have been presented in a 550-page monograph, and in over 20 refereed journal papers and more numerous conference papers. Among our major accomplishments are new recursive adaptive and robust design procedures ("backstepping") for nonlinear systems with parametric and functional uncertainties. For our adaptive designs we have derived performance bounds which, in the case of linear systems, show that they outperform traditional adaptive schemes. Although our current results have been extremely well received by the research community and have also stimulated interest in applications, our critical examination of their limitations has motivated the main topics of this proposal: first, to continue to the development from feasible to implementable designs, and, second, to develop new design procedures for larger classes of systems. We also propose to initiate an in-depth study of structure-specific robustness properties of nonlinear feedback loops, especially those diagnosed by our adaptive procedures. To make our recursive procedures more attractive for applications, we propose to develop lean backstepping designs which avoid wasteful cancellations and reduce control effort. For this purpose we will further develop our inverse-optimal designs. To extend the classes of systems, we plan to develop new forwarding procedures as upper-triangular analogs of backstepping. We will extend characterizations of uncertainties by application-motivated "shape" uncertainties and develop "shape-robust" controllers. Our robustness studies will quantify performance-robustness trade-offs and develop redesigns to enhance robustness while minimizing the loss of performance. Our NSF-supported research provides a theoretical base for, and is motivated by, our industrial cooperation with United Technologies, Ford Motor Company and Rockwell International. ***