On the Projected Gradient Methods for Switched - Mode Systems Optimization

Advances in attractive ellipsoid method for robust control design

“…Our main idea is to study the auxiliary linearized system (5) and propose a constructive geometrical characterization of the corresponding minimal-size AE . Various linearization methods associated with the dynamic models given by ODEs have been long time recognized as a powerful tool for stabilization of the conventional control systems (see, eg, related works 1,15,[18][19][20][23][24][25][26][27][28][29][30] and the references therein).The geometric stability criterion for the linearized system (3) mentioned earlier is next used in the robust feedback control design procedure for the originally given nonlinear system (1). We now explain (qualitatively) the main advances in AEM we developed in this paper.…”

“…where k 1 and k 2 (·) are calculated in (23) and y v (·) is a solution to the closed-loop system (21) with the gain matrix K(·) determined by (23). We now apply Theorem 5 and get the expected estimation (16) for the ellipsoid  0 of the originally given nonlinear system (20).…”

“…where k 1 and k 2 (·) are defined in (23) and  is an ellipsoid determined by matrixP = diag( p 1 , p 2 ). The corresponding simulation results are shown on Figure 2 and Figure 3.…”