An Analysis Technique for Optimization Based Control Applied to Quasi-LPV Plants

In this paper 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 on-line 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 suucient condition, which can be written as an inn-nite dimensional Linear Matrix Inequality (LMI) due to the quasi-LPV description of the plant. Finally, standard LPV gridding techniques are applied to obtain nite dimensional LMIs. This unique new framework lies at the intersection of three methodologies: Linear Parameter Varying (LPV) control , Model Predictive Control (MPC), and robust control, and handles the analysis of constrained nonlinear systems in a uniied framework. A simple example is used to illustrate the methodology.