Feedback Control of Bifurcation and Chaos in Dynamical Systems

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Abstract:

Feedback control of bifurcation and chaos in nonlinear dynamical system is discussed. Open problems in bifurcation control are noted. The past two decades have witnessed a steadily increasing appreciation of nonlinear dynamics across a broad range of disciplines. Applications of bifurcation and chaos have appeared in many areas of science, engineering, and the social sciences. The main purpose of this article is to discuss the role which nonlinear dynamics has played in the cross-disciplinary field of automatic control. The article also discusses in some detail the analysis and control of period-doubling bifurcations, and application to control of the associated route to chaos. Thoughts on some open problems are given, emphasizing the needed interplay between nonlinear dynamics and control theory.

Author(s):
Abed, Eyad H. ; Wang, Hua O.
Author Organization(s):
MARYLAND UNIV COLLEGE PARK INST FOR SYSTEMS RESEARCH
Descriptive Note:
Technical research rept.
Supplementary Note:
Prepared in cooperation with the Department of Electrical Engineering, College Park, MD. Sponsored in part by National Science Foundation grants NSF-CDR-88-03012 and NSF-ECS-86-57561. To be published in "Recent Developments in Stochastic and Nonlinear Dynamics: Applications to Mechanical Systems," CRC Press, 1993.
Pagination:
0024

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release
Distribution Statement:
Approved For Public Release; Distribution Is Unlimited.

RECORD

Collection: TR
Identifying Numbers
Report Number(s):
ISR-TR-93-74
Contract/Grant Number(s):
AFOSR-90-0015, F49620-93-1-0186
Monitor Series:
AFOSR
 Subject Terms
Joint Capability Areas:
JCA_1.2_Force Preparation; JCA_1_Force Support; JCA_8_Building Partnerships
Communities of Interest:
No COI(s) Identified
Descriptor(s):
*CONTROL SYSTEMS, *DYNAMICS, *CHAOS, *FEEDBACK, *BIFURCATION(MATHEMATICS), *CONTROL THEORY, *NONLINEAR SYSTEMS, STABILIZATION, TRAJECTORIES, DIFFERENTIAL EQUATIONS, AUTOMATION, EQUILIBRIUM(GENERAL), PARAMETERS, PERFORMANCE(ENGINEERING), STABILITY
Field(s)/Group(s):
Numerical Mathematics, Theoretical Mathematics, Operations Research, Human Factors Engineering and Man Machine Systems
Keyword(s):
*FEEDBACK CONTROL, *BIFURCATION CONTROL, *NONLINEAR DYNAMICS, BIFURCATION THEORY, DYNAMICAL SYSTEMS, AUTOMATIC CONTROL, BIFURCATION PARAMETERS, BIFURCATION SOLUTIONS, FIXED POINTS, DYNAMIC FEEDBACK, PERIOD DOUBLING BIFURCATIONS
Report Date:
1992 Jan 01
Creation Date:
2006 Oct 11