Given a linear discrete-time infinite-dimensional plant on a Hilbert space and disturbances of known waveform but unknown amplitude and phase, we show that there exists a stabilizing direct model reference adaptive control law with certain disturbance rejection and robustness properties. The central result is a discrete-time version of Barbalat-Lyapunov result for infinite dimensional Hilbert spaces. This is used to determine conditions under which a linear Infinite-dimensional system can be directly adaptively regulated. Our results are applied to adaptive control of general linear diffusion systems.
Direct Adaptive Control of Discrete-Time Infinite-Dimensional Systems in a Hilbert Space
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Balas, MJ, & Frost, SA. "Direct Adaptive Control of Discrete-Time Infinite-Dimensional Systems in a Hilbert Space." Proceedings of the ASME 2013 International Mechanical Engineering Congress and Exposition. Volume 4B: Dynamics, Vibration and Control. San Diego, California, USA. November 15–21, 2013. V04BT04A021. ASME. https://doi.org/10.1115/IMECE2013-64242
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