یک روش منطقی مبتنی بر برنامه نویسی خطی برای تثبیت دینامیک چندجملهای

In this paper, we consider the problem of synthesizing static output feedback controllers for stabilizing polynomial systems. We jointly synthesize a Lyapunov function and a static output feedback controller that stabilizes the system over a given subset of the state-space. Motivated by the numerical issues that are commonly faced using SOS (Sum of Squares)/SDP (Semi-Definite Programming) solvers, we examine a linear programming (LP) based alternative approach that can yield more precise results, in practice. Our approach uses Bernstein polynomials to relax parametric polynomial optimization problems into bilinear optimization problems (BP). Subsequently, we approach the bilinear inequalities using a modified alternating minimization approach that alternates between solving linear programs on complementary sets of variables. Finally, we provide a comparison between our approach and BMI (bilinear matrix inequalities) solvers that tackle the same problem. We conclude that LP/BP relaxation approach is promising and can be more efficient than SDP/BMI relaxations.