Jiandong Zhu

Nonlinear recursive delayed feedback control for chaotic discrete-time systems

In this Letter, a nonlinear recursive delayed feedback control strategy is proposed for stabilizing all the unknown fixed points of a chaotic discrete-time system. The proposed controller does not inherit the odd number limitation and relies on the system model only, i.e., the controller is independent of the information of the fixed points.

Stabilizing periodic solutions of nonlinear systems and applications in chaos control

In this paper, a simple nonlinear recursive delayed feedback controller is designed for stabilizing periodic solutions of a nonlinear system. The proposed controller is constructively designed and does not inherit the odd number limitation. The stability of the periodic solution of the closed-loop system is proved rigorously. Applying the control method to chaotic systems, one can effectively control chaos.

Decomposition with Respect to Outputs for Boolean Control Networks

Abstract This paper investigates the decomposition with respect to outputs for Boolean control networks (BCNs). Firstly, based on the linear representation of BCNs, some algebraic equivalent conditions are obtained. Secondly, the concept of perfect equal vertex partition (PEVP) is proposed for BCNs. Thirdly, a necessary and sufficient graphical condition based on the PEVP for the decomposability with respect to outputs is obtained. Finally, an equivalent condition of PEVP is derived to help to calculate a PEVP for a BCN.

STABILIZATION OF UNSTABLE PERIODIC SOLUTIONS BY NONLINEAR RECURSIVE DELAYED FEEDBACK CONTROL

This paper considers stabilization of unstable periodic solutions of nonlinear systems. Based on differential geometry method, a nonlinear recursive delayed feedback controller is designed. The concept of γ dynamics is introduced and the stability of the periodic solution of the closed-loop system is proved rigorously. The proposed control method does not have the odd number limitation. Simulation results are also presented for validating the effectiveness of the proposed method.

Nonlinear Protocols on Ellipsoids for Multi-Agent Systems

Abstract This paper investigates the consensus problem on ellipsoids for multi-agent systems. Simple nonlinear protocols are proposed to realize collective behavior on ellipsoids. For the high-dimensional nonlinear multi-agent systems, equilibrium sets are described exactly. By a generalized form of LaSalle invariance principle, some global dynamical properties are obtained. With the linear approximation method, some results on instability of some kinds of equilibria are obtained. Based on the above results, almost global consensus is achieved under some conditions. Simulation results are presented to show the effectiveness of proposed protocols.

Delayed feedback control: A survey and some new results

Abstract This paper presents the basic idea and the mathematical formulation of the delayed feedback control (DFC) methodology. Stability analysis including the well-known odd number limitation of the DFC is reviewed. Some new advances in characterization of the limitation of the DFC are presented. Finally, some open problems in this research field are discussed.

LIMITATION OF GENERALIZED DELAYED FEEDBACK CONTROL FOR DISCRETE-TIME SYSTEMS

Abstract In this paper, the stabilizability problem for chaotic discrete-time systems under the generalized delayed feedback control (GDFC) is addressed. It is proved that 0 I – A ) n + m is a necessary and sufficient condition of stabilizability via m -step GDFC for an n -order system with Jacobi A The condition reveals the limitation of GDFC more exactly than the odd number limitation. An analytical procedure of designing GDFC is proposed and illustrated by an example.