Descriptor System Modeling for Robustness in Control
Résumé
The robust control framework considers systems regulated close to an equilibrium point or a trajectory. Under these assumptions the systems are linear but dependent of many intricate features such as uncertainties, neglected dynamics, time-dependent parameters, isolated non-linearities, time-delays... Robustness is achieved when some performance can be assessed even for the worst configuration of these features. Mathematically, it boils down to proving that some complicated non-linear function of many indeterminates is negative when these indeterminates are constrained in sets that are themselves described by non-linear equations. In this talk we show that for many cases the Descriptor System Modeling that combines Algebraic and Differential Equations is highly useful to simplify (linearize) the problems. Combined to the S-variable approach which cleverly exploits Finsler's lemma, it provides easy to code Semi-Definite Programming relaxations. These numerically tractable relaxations are conservative, yet Descriptor-based liftings of the model allows to build hierarchies of relaxations with decreasing conservatism. In the talk we will give an insight on these theoretical results illustrated on some simple examples.
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