An analysis technique for optimization based control applied to quasi-LPV plants

We consider the problem of analyzing the stability of a discrete time nonlinear system in quasi-LPV form under an optimization based controller subject to constraints. We show that by representing the control law, which is computed online as the solution to a constrained optimization problem, by the Kuhn-Tucker conditions, stability questions can be reformulated as implications. A technique from robust control, the so-called S-procedure, reduces the implication to a sufficient condition, which can be written as an infinite dimensional linear matrix inequality (LMI) due to the quasi-LPV description of the plant. Finally, standard LPV gridding techniques are applied to obtain finite dimensional LMIs. This unique new framework lies at the intersection of three methodologies: linear parameter varying (LPV) control, model predictive control, and robust control, and handles the analysis of constrained nonlinear systems in a unified framework. A simple example is used to illustrate the methodology.