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arXiv · 2205.02913

Exponentially Stable Adaptive Optimal Control of Uncertain LTI Systems

Anton Glushchenko·Konstantin Lastochkin
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Abstract

A novel method of an adaptive linear quadratic (LQ) regulation of uncertain continuous linear time-invariant systems is proposed. Such an approach is based on the direct self-tuning regulators design framework and the exponentially stable adaptive control technique developed earlier by the authors. Unlike the known solutions, a procedure is proposed to obtain a non-overparametrized regression equation (RE) with respect to the unknown controller parameters from an initial RE of the LQ-based reference tracking control system. On the basis of such result, an adaptive law is proposed, which under mild regressor finite excitation condition provides monotonous convergence of the LQ-controller parameters to an adjustable set of their true values, which bound is defined only by the machine precision. Using the Lyapunov-based analysis, it is proved that the mentioned law guarantees the exponential stability of the closed-loop adaptive optimal control system. The simulation examples are provided to validate the theoretical contributions.

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Anton Glushchenko, Konstantin Lastochkin. 2022-05-05. Exponentially Stable Adaptive Optimal Control of Uncertain LTI Systems. https://arxiv.org/abs/2205.02913

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