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The ultimate goal in control theory is to design control laws that achieve good performance for any member of a specific class of systems. Performance mainly either shows the ultimate behavior of a system (asymptotic) or monitors its behavior in time (transient). Analytical quantification and systematic improvement of transient performance are open problems in adaptive control. In this book, we will develop a theoretically tractable quantitative cost based approach to assess relative benefits of different robust adaptive controllers. We develop a comparative theory based on a nonsingular cost functional penalizing both state and control effort. Two rigorous results are presented demonstrating situations in which one controller is superior to the other and vice versa.
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