State feedback controller design for anti‐synchronization of Boolean control networks: An event‐based idea

Abstract

In this paper, we investigate the event‐based state feedback control for the anti‐synchronization of Boolean control networks (BCNs) under the configuration of drive‐response coupling. Two equivalence properties for the anti‐synchronization of BCNs are obtained by the algebraic representations of the logical dynamics. Based on the analysis of the event conditions, an algorithm is established to design the event‐based state feedback controller, and a necessary and sufficient condition guaranteeing the anti‐synchronization of the drive‐response coupled BCNs is formulated. An example is finally given to demonstrate the validity of the obtained results.

Analysis of synchronization of multiple identical metronomes on a cart via describing function approach

“…Consider the nonlinear behavior described in Equation ( 2) of a metronome. The DF from its angle to its driving torque denoted as N(a) is expressed in Equation (12) with…”

“…We obtain a and 𝜔 satisfying Equation (59) by treating Case 1 (a≥𝛾) and Case 2 (a < 𝛾) separately. First, for Case 1, from Equation (12) with Equations ( 14) and ( 15), we have…”

“…Similarly, if a + (∞)≥𝛾, by solving Equations ( 82) and (12) with Equations ( 14) and ( 15), we obtain…”

“…Synchronization occurs in many physical, biological, chemical, and social systems. Since Huygens had reported the synchronization phenomenon of the pair of pendulum clocks coupled with each other via the common base [1,2], studying synchronization has attracted considerable research interests and is a still hot topic in many disciplines [3][4][5][6][7][8][9][10][11][12][13][14][15]. For example, Sawicki et al [16] investigated the synchronization of coupled organ pipes by using two delay-coupled Van-der-Pol oscillators as a simplified model for the pipes.…”

“…Synchronization occurs in many physical, biological, chemical, and social systems. Since Huygens had reported the synchronization phenomenon of the pair of pendulum clocks coupled with each other via the common base [1,2], studying synchronization has attracted considerable research interests and is a still hot topic in many disciplines [3–15]. For example, Sawicki et al.…”