Advances in attractive ellipsoid method for robust control design

Abstract

Our contribution is devoted to a further theoretic development of the attractive ellipsoid method (AEM). We consider dynamic models given by nonlinear ordinary differential equations in the presence of bounded disturbances. The resulting robustness analysis of the closed-loop system incorporates the celebrated Clarke invariancy concept (an analytic extension of the celebrated Lyapunov methodology). We finally obtain a new general geometric characterization of the AEM-based approach to the robust systems design. Moreover, we also discuss the corresponding numerical aspects of the proposed theoretical extensions of the method. The theoretic results obtained in this contribution are finally illustrated by a practically oriented computational example. KEYWORDSattractive ellipsoid method, nonlinear systems, robust control 1418

Robust control for state constrained systems based on composite barrier Lyapunov functions

“…Figure 5 depicts the convex-hull of the proposed ellipsoids. Applying Algorithm 1, with the scalar = 0.01 and matrices Q , Q described in (29), the obtained solution to the feasibility problem stated in the main theorem is presented in Figure 6. The continuous blue line shows the behavior of the system trajectories inside and outside the convex region (Q( * )).…”

“…The work in Reference 17 describes the use of ellipsoids as reliable estimations of invariant sets for dynamical systems. Some extensions for this approach can be found in References 29,30. Despite the benefits and simplicity of the ellipsoidal calculus, the region size is somewhat conservative.…”

Attitude Control for a satellite with inertial wheels based on Attractive Ellipsoids Method

“…V. Azhmyakov et. al [1] presents a robust control algorithm based on Attractive Ellipsoids, for dynamic systems described by nonlinear ordinary differential equations, where these present bounded perturbations. It is worth mentioning that, in this work, a class of non-autonomous linear systems was analyzed, in addition one of the advantages it shows is that the dimension of LMI is smaller than those shown in the classical methods.…”

Robust gain-scheduling H∞ control of uncertain continuous-time systems having magnitude- and rate-bounded actuators: An application of full block S-procedure

“…[48], applies a saturated sliding mode control method in which magnitude and rate limitations are formulated for systems having known and unknown bounded uncertainties. A nonlinear attractive ellipsoidal approach is proposed by [4] to avoid the hard quasi-Lipschitz assumptions. Moreover, [46] introduces a new projection algorithm for adaptive control of these systems.…”