Central suboptimal controller design for linear time-varying systems with unknown parameters

Michael V. Basin, Pedro Soto and Dario Calderon-Alvarez

International Journal of Systems Science, 2011, vol. 42, issue 5, 709-716

Abstract: This article presents the central finite-dimensional H∞ controller for linear time-varying systems with unknown parameters, that is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, this article reduces the original H∞ controller problem to the corresponding H2 controller problem, using the technique proposed in Doyle et al. [Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A. (1989), ‘State-space Solutions to Standard H2 and H Infinity Control Problems’, IEEE Transactions Automatic Control, 34, 831–847]. This article yields the central suboptimal H∞ controller for linear systems with unknown parameters in a closed finite-dimensional form, based on the corresponding H2 controller obtained in Basin and Calderon-Alvarez [Basin, M.V., and Calderon-Alvarez, D. (2008), ‘Optimal LQG Controller for Linear Systems with Unknown Parameters’, Journal of The Franklin Institute, 345, 293–302]. Numerical simulations are conducted to verify performance of the designed central suboptimal controller for uncertain linear systems with unknown parameters against the conventional central suboptimal H∞ controller for linear systems with exactly known parameter values.

Date: 2011
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DOI: 10.1080/00207721.2010.543492

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