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Max-Min Optimal Control of Constrained Discrete-Time Systems


M. Baric, Sasa V. Rakovic, Th. Besselmann, M. Morari

IFAC World Congress, Seoul, Korea, pp. 8803 - 8808

This paper considers the optimal control problem for constrained discrete–time systems affected by measured and bounded disturbances and uncertainties in the underlying system equations. This manuscript utilizes the framework in which the current values of disturbances and uncertainties are known while the available information about their future realizations is that they are constrained by set–membership relations and their values will be, in addition, known at the future times when the future corresponding robust optimal control action is applied. This problem setting naturally leads to the sup–inf robust optimal control problems. Three classes of discrete–time systems encountered frequently in control engineering and permitting the characterization of the corresponding sup–inf value functions and robust optimal control policies are examined in more detail. The characterization of the max–min value function and robust optimal control policies is, for these particular cases, obtained by employing the dynamic programming, that requires solutions to a sequence of parametric linear programs. Some simple examples are provided to highlight the difference between the max–min and min–max robust optimal control problems.

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% Autogenerated BibTeX entry
@InProceedings { BarEtal:2008:IFA_3031,
    author={M. Baric and Sasa V. Rakovic and Th. Besselmann and M. Morari},
    title={{Max-Min Optimal Control of Constrained Discrete-Time
    booktitle={IFAC World Congress},
    pages={8803 -- 8808},
    address={Seoul, Korea},
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