An H-Infinity norm minimization approach for adaptive control
Muse, Jonathan Adam
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This dissertation seeks to merge the ideas from robust control theory such as H-Infinity control design and the Small Gain Theorem, L stability theory and Lyapunov stability from nonlinear control, and recent theoretical achievements in adaptive control. The fusion of frequency domain and linear time domain ideas allows the derivation of an H-Infinity Norm Minimization Approach (H-Infinity-NMA) for adaptive control architecture that permits a control designer to simplify the adaptive tuning process and tune the uncertainty compensation characteristics via linear control design techniques, band limit the adaptive control signal, efficiently handle redundant actuators, and handle unmatched uncertainty and matched uncertainty in a single design framework. The two stage design framework is similar to that used in robust control, but without sacrificing performance. The first stage of the design considers an ideal system with the system uncertainty completely known. For this system, a control law is designed using linear H-Infinity theory. Then in the second stage, an adaptive process is implemented that emulates the behavior of the ideal system. If the linear H-Infinity design is applied to control the emulated system, it then guarantees closed loop system stability of the actual system. All of this is accomplished while providing notions of transient performance bounds between the ideal system and the true system. Extensions to the theory include architectures for a class of output feedback systems, limiting the authority of an adaptive control system, and a method for improving the performance of an adaptive system with slow dynamics without any modification terms. Applications focus on using aerodynamic flow control for aircraft flight control and the Crew Launch Vehicle.