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An Integration method over a moving window for exponential convergence in adaptive control without persistency of excitation

Yayla, Metehan
Adaptive control has great capabilities in control of uncertain systems to maintain a consistent and desired performance. Another control methodology concerning the uncertain systems is the robust control. It is well-known that the robust control has advantages of dealing with external disturbances, unmodeled dynamics, and quickly varying uncertain parameters. Nonetheless, robustness against these environmental, and parametric uncertainties degrades the tracking performance. Besides, adaptive control can tolerate parameterizable uncertainties to guarantee the closed-loop stability. Hence, the solution becomes the adaptive augmentation of robust baseline controller, Model Reference Adaptive Control (MRAC). Baseline MRAC ensures asymptotic tracking performance using instantaneous data, but parameter convergence is achieved if and only if the system signals are persistently exciting (PE). Furthermore, without PE, even boundedness of the signals are not guaranteed in the presence of bounded disturbances. To address this, many robust modifications are introduced in the literature. However, parameter convergence remained as an open question. Recently introduced Concurrent Learning Model Reference Adaptive Control (CL-MRAC) solved this issue using recorded data concurrently with the current data assuming the state derivatives are available. In this thesis, a new integration method for exponential stability without PE is introduced. Proposed method uses the time histories of the system signals and control inputs for the online identification of uncertainties. Once these identified parameters are available, weight update law in conjunction with σ-modification is updated. Eventually, global exponential stability is established. The algorithm does not require PE, and state derivatives are not used in the identification.