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 infinitynorm 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.

• Type: Conference
• Year: 2009
• Where: CDC
• Authors: Henrik Manum, Colin Neil Jones, Johan Löfberg, Manfred Morari, Sigurd Skogestad
• Keywords: CDC 2009, Control Systems, Low-complexity Controller, Reference Controllers, Robust Mpc