Control Synthesis of Systems with Uncertain Parameters by Convex Optimization

Authors:	Pozo Montero Francesc, Universitat Politècnica de Catalunya, Spain Ikhouane Faycal, Universitat Politècnica de Catalunya, Spain Rodellar José, Universitat Politècnica de Catalunya, Spain
Topic:	2.3 Non-Linear Control Systems
Session:	Nonlinear Stabilization II
Keywords:	uncertainty parameters, nonlinear control, semidefinite programming, sum of squares decomposition

Abstract

The last few years witnessed an increasing interest in the problem of control synthesis of nonlinear systems. A recently derived stability criterion for nonlinear systems which has a remarkable convexity property and the development of numerical methods for verification of positivity allows the computation via semidefinite programming of stabilizing controllers for the case of systems with polynomial or rational vector fields. Using the theory of semialgebraic sets these computational tools are extended in this paper for the case of polynomial or rational systems with uncertainty parameters.