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Convex Constrained Semialgebraic Volume Optimization: Application in System and Control

In this work, we introduce volume optimization problems where enables us to obtain a convex formulation for different challenging problems in the area of system and control. In volume optimization problems, we aim at maximizing the volume of a semialgebraic set under some semialgebraic constraints. Building on the theory of measures and moments as well as the duality theory, a sequence of finite semidefinite programmings are provided, whose sequence of optimal values is shown to converge to the optimal value of the original problem. We show that many different problems in the area of system and control can be cast as special cases of this framework. Particularly, in this paper, we address the problems of probabilistic control of uncertain systems as well as inner approximation of region of attraction and invariant sets of polynomial systems. Numerical examples are presented to illustrate the computational performance of the proposed approach.

Problem Formulation

Application in System and Control

Equivalent Convex Problem

Dual Problem




  • Ashkan Jasour and Constantino Lagoa ”Convex Constrained Semialgebraic Volume Optimization: Application in Systems and Control”, Under submission, 2016.

Subpages (1): Illustrative Example