Output feedback adaptive control in the presence of unmodeled dynamics

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Chandramohan, Rajeev
Calise, Anthony J.
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This thesis outlines a method of output feedback adaptive control in the presence of matched unmodeled dynamics, uncertain control effectiveness and matched parametric uncertainties. An adaptive feedback controller that augments an assumed existing observer based linear controller is developed. The adaptive approach outlined here assumes that the uncertainty within the system can be linearly parameterized in terms of current and delayed values of inputs and measured outputs. New weight update laws are developed to show that all the signals in the system are uniformly ultimately bounded using a Lyapunov like analysis that depends on the existence of a positive definite solution of a parameter dependent Riccati equation in the presence of unmodeled dynamics, uncertain control effectiveness and parametric uncertainties. The unique attributes of this approach are that it can be used to augment an existing linear controller without modifying the parameters of that controller, it does not rely on the use of high gains in the adaptation law, and is adaptive to the presence of matched parametric uncertainties and unmodeled dynamics. One key difference between the proposed design and existing methods is that it does not rely on the use of a high gain observer or high gain error observer in the weight update law. The thesis also addresses the effect of noisy measurements on the performance of adaptive controllers by filtering the error signal employed in the weight update laws. Uniform ultimate boundedness of all signals is shown utilizing concepts of singular perturbation theory by treating the filter as a fast subsystem and the system dynamics together with weight update law as a slow subsystem. The design procedure is evaluated by augmenting an existing observer based controller with an adaptive controller to compensate for unmodeled dynamics, unknown control effectiveness and parametric uncertainties in the presence of noisy measurements for several aerospace applications that include a flexible satellite example and a 44-state highly flexible aircraft example.
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