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arXiv · 1501.04578

Stabilization of polynomial dynamical systems using linear programming based on Bernstein polynomials

Mohamed Amin Ben Sassi·Sriram Sankaranarayanan
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Abstract

In this paper, we deal with the problem of synthesizing static output feedback controllers for stabilizing polynomial systems. Our approach jointly synthesizes a Lyapunov function and a static output feedback controller that stabilizes the system over a given subset of the state-space. Specifically, our approach is simultaneously targeted towards two goals: (a) asymptotic Lyapunov stability of the system, and (b) invariance of a box containing the equilibrium. Our approach uses Bernstein polynomials to build a linear relaxation of polynomial optimization problems, and the use of a so-called "policy iteration" approach to deal with bilinear optimization problems. Our approach can be naturally extended to synthesizing hybrid feedback control laws through a combination of state-space decomposition and Bernstein polynomials. We demonstrate the effectiveness of our approach on a series of numerical benchmark examples.

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Mohamed Amin Ben Sassi, Sriram Sankaranarayanan. 2015-01-19. Stabilization of polynomial dynamical systems using linear programming based on Bernstein polynomials. https://arxiv.org/abs/1501.04578

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