Bilevel programming for analysis of low-complexity control of linear systems with constraints

In this paper we use bilevel programming to find the maximum difference between a reference controller and a low-complexity controller in terms of the infinity-norm difference of their control laws. A nominal MPC for linear systems with constraints, and a robust MPC for linear systems with bounded additive noise are considered as reference controllers. For possible low-complexity controllers we discuss partial enumeration (PE), Voronoi/closest point, triangulation, linear controller with saturation, and others. A small difference in the norm between a low-complexity controller and a robust MPC may be used to guarantee closed-loop stability of the low-complexity controller and indicate that the behaviour or performance of the low-complexity controller will be similar to that of the reference one. We further discuss how bilevel programming may be used for closed-loop analysis of model reduction.


Published in:
Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 946-951
Presented at:
Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC), Shanghai, China, 15-18 December 2009
Year:
2009
Publisher:
IEEE
Laboratories:


Note: The status of this file is: EPFL only


 Record created 2011-10-24, last modified 2018-01-28

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