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arXiv · 1412.3861

Min-max piecewise constant optimal control for multi-model linear systems

Félix A. Miranda·Fernando Castaños·Alexander Poznyak
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Abstract

The present work addresses a finite-horizon linear-quadratic optimal control problem for uncertain systems driven by piecewise constant controls. The precise values of the system parameters are unknown, but assumed to belong to a finite set (i.e., there exist only finitely many possible models for the plant). Uncertainty is dealt with using a min-max approach (i.e., we seek the best control for the worst possible plant). The optimal control is derived using a multi-model version of Lagrange's multipliers method, which specifies the control in terms of a discrete-time Riccati equation and an optimization problem over a simplex. A numerical algorithm for computing the optimal control is proposed and tested by simulation.

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Félix A. Miranda, Fernando Castaños, Alexander Poznyak. 2014-12-12. Min-max piecewise constant optimal control for multi-model linear systems. https://doi.org/10.1093/imamci%2Fdnv030

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