Sinusoidal disturbance rejection in chaotic planar oscillators

Abstract

The main goal of this paper is to design a compensator able to restore the nominal behavior of a planar system, which is rendered chaotic by an unmeasurable sinusoidal disturbance input. To reach such a goal, some instruments, taken from algebraic geometry, are used to estimate the unmeasurable disturbance from the time derivatives of the output of the system and of the control input.

Algebraic approaches for the design of simultaneous observers for linear systems

“…g 2, 1 = 2y (3) + y (4) − y (5) , g 2, 2 = 4y (2) − 3y (4) + y (5) , g 2, 3 = 8y (1) + 5y (4) − 3y (5) , g 2, 4 = 16y (0) − 11y (4) + 5y (5) ,…”

“…Hence, by considering that y (1) y (2) y (3) y (4) y (5) , y (1) y (2) y (3) y (4) y (5) , and that the matrices on the right-hand side of the expressions above have full rank, by the same reasoning used in the proof of Theorem 1, one has that ⟨g 1, 1 , g 1, 2 , g 2, 1 , g 2, 2 , g 2, 3 , g 2, 4 ⟩ = ⟨y (0) , y (1) , …, y (5) ⟩, ⟨g 1, 3 , g 1, 4 , g 3, 1 , g 3, 2 , g 3, 3 , g 3, 4 ⟩ = ⟨y (0) , y (1) , …, y (5) ⟩ .…”

“…In various control and identification applications, the state of a dynamical system cannot be fully measured, thus leading to the need for tools capable of estimating unmeasured variables from available measurements. Several solutions to such a problem have been proposed for both linear [1] and non-linear [2][3][4][5][6] systems.…”

On partially minimum-phase systems and disturbance decoupling with stability

“…In this work, we extend the proposed methodology to the problem of output-disturbance decoupling with internal stability. The problem of decoupling, attenuating or rejecting the effect of perturbation acting over a nonlinear plant is of paramount importance from both practical and methodological points of view [11,12,13,14,15,16,17,18]. As well known, given a general plant disturbance decoupling is related to generating unobservability so to make the output evolutions independent upon the perturbations acting over the dynamics ([19, 20, 21, 22, 23]).…”

Editorial for the special issue on recent advances in adaptive methods for frequency estimation with applications

“…The paper in [8] investigates a control law for a class of chaotic planar oscillators which is able to restore their nominal dynamical behavior(i.e., the non-chaotic one, which is obtained in the absence of a disturbance). In particular, the authors make use of algebraic geometry to express the amplitude and the frequency of the sinusoidal disturbance as functions of the time derivatives of the control input and of the output.…”