Verification of model predictive control laws using weispfenning's quantifier elimination by virtual substitution algorithm
2016 IEEE 55th Conference on Decision and Control, CDC 2016
2016 IEEE 55th Conference on Decision and Control (CDC)
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Siaulys, K., & Maciejowski, J. (2016). Verification of model predictive control laws using weispfenning's quantifier elimination by virtual substitution algorithm. 2016 IEEE 55th Conference on Decision and Control, CDC 2016, 1452-1457. https://doi.org/10.1109/CDC.2016.7798471
© 2016 IEEE. A method based on a quantifier elimination algorithm is suggested for obtaining explicit model predictive control (MPC) laws for linear time invariant systems with quadratic objective and polytopic constraints. The structure of the control problem considered allows Weispfenning's 'quantifier elimination by virtual substitution' algorithm to be used. This is applicable to first order formulas in which quantified variables appear at most quadratically. It has much better practical computational complexity than general quantifier elimination algorithms, such as cylindrical algebraic decomposition. We show how this explicit MPC solution, together with Weispfenning's algorithm, can be used to check recursive feasibility of the system, for both nominal and disturbed systems. Extension to cases beyond linear MPC using Weispfenning's algorithm is part of future work.
Engineering and Physical Sciences Research Council, and European Union Seventh Framework Programme FP7/2007-2013 grant agreement number 314 544, project “RECONFIGURE”.
European Commission (314544)
External DOI: https://doi.org/10.1109/CDC.2016.7798471
This record's URL: https://www.repository.cam.ac.uk/handle/1810/287166