Abstract
In this paper we consider optimal control by output feedback of a linear discrete-time system corrupted by an additive harmonic vector disturbance with known frequencies but unknown amplitudes and phases. We consider both a deterministic and a stochastic version of the problem. The object is to design a robust optimal regulator which is universal in the sense that it does not depend on the unknown amplitudes and phases and is optimal for all choices of these values. We show that, under certain natural technical conditions, an optimal universal regulator (OUR) exists in a suitable class of stabilizing and realizable linear regulators, provided the dimension of the output is no smaller than the dimension of the harmonic disturbance. When this dimensionality condition is not satisfied, the existence of an OUR is not a generic property, and consequently it does not exist from a practical point of view. For the deterministic problem we also show that, under slightly stronger technical conditions, any linear OUR is also optimal in a very wide class of nonlinear regulators. In the stochastic case we are only able to show optimality in the linear class of regulators.
This research was supported in part by grants from the Royal Swedish Academy of Sciences, INTAS, NUTEK and the Swedish Foundation for Strategic Research.
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Lindquist, A., Yakubovich, V.A. (1997). Optimal Damping of Forced Oscillations in Discrete-time Systems by Output Feedback. In: Stochastic Differential and Difference Equations. Progress in Systems and Control Theory, vol 23. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1980-4_16
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DOI: https://doi.org/10.1007/978-1-4612-1980-4_16
Publisher Name: Birkhäuser, Boston, MA
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