On Solving of a Special Optimization Problem Connected with Determination of Invariant Sets of Dynamical Systems

摘要

Problem of nonconvex optimization, which is met on control synthesis and minimizes domain of localization of invariant set of nonlinear systems, is considered. For this problem solving we use equivalent to it quadratic problem, for determination of the lowest estimate of optimal value of the objective function dual approach is used. We state and prove sufficient condition for the property that the mentioned approach gives optimal value of the objective function and the point of global extremum of the initial problem.