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.

[1]  Keiji Konishi,et al.  Observer-based delayed-feedback control for discrete-time chaotic systems , 1998 .

[2]  Alberto Tesi,et al.  Stabilizing periodic orbits of forced systems via generalized Pyragas controllers , 1997 .

[3]  Yu-Ping Tian,et al.  Nonlinear recursive delayed feedback control for chaotic discrete-time systems , 2003 .

[4]  H. Nakajima On analytical properties of delayed feedback control of chaos , 1997 .

[5]  Toshimitsu Ushio,et al.  Dynamic delayed feedback controllers for chaotic discrete-time systems , 2001 .

[6]  H. Nakajima,et al.  Limitation of generalized delayed feedback control , 1998 .

[7]  Kestutis Pyragas,et al.  Experimental control of chaos by delayed self-controlling feedback , 1993 .

[8]  Yu-Ping Tian,et al.  Delayed feedback control of chaos in a switched arrival system , 2005, Proceedings. 2005 International Conference Physics and Control, 2005..

[9]  Enric Fossas,et al.  Stabilization of periodic orbits of the buck converter by time-delayed feedback , 1999 .

[10]  Toshimitsu Ushio,et al.  Recursive delayed feedback control for chaotic discrete-time systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[11]  Toshimitsu Ushio,et al.  Prediction-based control of chaos , 1999 .

[12]  Yu-Ping Tian,et al.  Full characterization on limitation of generalized delayed feedback control for discrete-time systems , 2004 .

[13]  Ömer Morgül,et al.  On the stability of delayed feedback controllers , 2003 .

[14]  Robert W. Carpick,et al.  Controlling Friction , 2006, Science.

[15]  Kestutis Pyragas Continuous control of chaos by self-controlling feedback , 1992 .

[16]  Kestutis Pyragas Control of chaos via an unstable delayed feedback controller. , 2001, Physical review letters.

[17]  Socolar,et al.  Controlling spatiotemporal dynamics with time-delay feedback. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  Takashi Hikihara,et al.  Experimental Stabilization of Unstable Periodic Orbit in Magneto-Elastic Chaos by Delayed Feedback Control , 1997 .

[19]  Wolfram Just,et al.  DELAYED FEEDBACK CONTROL OF PERIODIC ORBITS IN AUTONOMOUS SYSTEMS , 1998, chao-dyn/9808007.

[20]  Guanrong Chen,et al.  A separation principle for dynamical delayed output feedback control of chaos , 2001 .

[21]  Yu-Ping Tian,et al.  Stabilizing periodic solutions of nonlinear systems and applications in chaos control , 2005, IEEE Trans. Circuits Syst. II Express Briefs.

[22]  K Konishi,et al.  Coupled map car-following model and its delayed-feedback control. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  Xinghuo Yu,et al.  Stabilizing unstable periodic orbits of chaotic systems via an optimal principle , 2000, J. Frankl. Inst..

[24]  Toshimitsu Ushio,et al.  Stabilization of Unstable Periodic orbits of Chaotic Discrete-Time Systems Using Prediction-Based Feedback Control , 2002, Int. J. Bifurc. Chaos.

[25]  Gauthier,et al.  Stabilizing unstable periodic orbits in fast dynamical systems. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Yu-Ping Tian,et al.  Necessary and sufficient conditions for stabilizability of discrete-time systems via delayed feedback control , 2005 .

[27]  Hiroyuki Nakajima,et al.  Delayed Feedback Control with State Predictor for Continuous-Time Chaotic Systems , 2002, Int. J. Bifurc. Chaos.

[28]  Guanrong Chen,et al.  LINEAR TIME-DELAY FEEDBACK CONTROL OF A PATHOLOGICAL RHYTHM IN A CARDIAC CONDUCTION MODEL , 1997 .

[29]  Kentaro Hirata,et al.  Difference feedback can stabilize uncertain steady states , 2001, IEEE Trans. Autom. Control..