Research Initiation Award: Adaptive Control System Redesignfor Improving Transient Performance

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Motivated by the observation that most existing results on adaptive control are qualitative in nature and address only asymptotic performance (such as stability and robustness), the main focus of the proposed project is to develop constructive design approaches for adaptive systems which take into account both the transient response and the steady-state response. A standard adaptive control system is designed by incorporating an identification scheme into the control system and replacing the unknown parameters with their estimates. Such design methodology is referred to as the "certainty equivalence principle"(CEP) in adaptive literature. It does not guarantee good transient performance of the resulting system since it passes on the error of identification to the design stage. In this project, we will redesign adaptive control systems to overcome the inherent constraint due to CEP design, and thus improve performance. A new design technique -- modeling error compensation (MEC) -- is proposed to achieve this goal. To accommodate the error due to misidentification and CEP design, we will use the information about the quality of the identification to introduce an additional control signal on top of the CEP design. This strategy provides a compensation mechanism that cannot be obtained via CEP design -- it compensates the effects of misidentification. We propose to study both theoretical and design aspects of the proposed adaptive scheme. We will also study the application of MEC to a class of nonadaptive designs, to find answers for the question whether and when an adaptive system will outperform a nonadaptive system.