Bifurcation Control: Theories, Methods, and Applications

Chen, Guanrong; Moiola, Jorge L.; Wang, Hua O.

doi:10.1142/s0218127400000360

Cited by 336 publications

(186 citation statements)

References 119 publications

(156 reference statements)

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“…However, most control strategies view such behavior as damaging and try to mitigate it [1]. Relatively less work actively inserts bifurcations as part of a control strategy.…”

Section: Introductionmentioning

confidence: 99%

Switched Systems With Multiple Invariant Sets

Dorothy¹,

Chung²

2015

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This paper explores dwell time constraints on switched systems with multiple, possibly disparate invariant limit sets. We show that, under suitable conditions, trajectories globally converge to a superset of the limit sets and then remain in a second, larger superset. We show the effectiveness of the dwell-time conditions by using examples of switching limit cycles commonly found in robotic locomotion and flapping flight.

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“…However, most control strategies view such behavior as damaging and try to mitigate it [1]. Relatively less work actively inserts bifurcations as part of a control strategy.…”

Section: Introductionmentioning

confidence: 99%

Switched Systems With Multiple Invariant Sets

Dorothy¹,

Chung²

2015

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“…In order to calculate the parameters of 2 ( , ) u X a , evaluating the Jacobian of system (9) at the equilibrium yields: …”

Section: Adding the Controller 2 ( )mentioning

confidence: 99%

“…(16). In order to simplify the process, 2 2 c  is chosen in this case. So the three-dimensional segmentation problem is converted into a two-dimensional space segmentation problem.…”

Section: System Constraints Calculationmentioning

confidence: 99%

“…The parameters 0 c and 1 c in each region are examined to identify the set of values that satisfy the criteria. Finally, region Q is found, which is surrounded by 3 2 L is part of the curves of g  (from point B to C ). Point A , B , and C are three specific points on 01 cc  plane, where A is the crossover point of conditions (20) and (23).…”

Section: Calculation Of Parameters Using Cadmentioning

confidence: 99%

“…In the Hopf bifurcation control, the basic task is to change the system dynamics in order to achieve the desired properties, such as delaying the onset of an inherent bifurcation, changing the parameter value of an existing bifurcation point, stabilizing a bifurcated branch, modifying the shape or type of a bifurcation chain, optimizing the system performance near a bifurcation point, or a combination of some of these objectives [1][2].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Novel Parametric Controller Design Method for Hopf Bifurcation System

Lu¹,

Hou²,

Luo³

2017

IJCA

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Chaos, Bifurcations, and Their Control

Chen

2018

Wiley Encyclopedia of Electrical and Electronics Engineering

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The article starts with a self‐contained brief overview of fundamental topics on nonlinear dynamics, chaos, and bifurcations, reaching out to the contemporary subjects of controlling chaos, controlling bifurcations, and anticontrolling chaos.The section on nonlinear dynamics includes basic concepts of nonlinear dynamical systems, equilibria, limit sets, attractors, periodic orbit, limit cycles, Poincaré maps, homoclinic and heteroclinic orbits, Lyapunov stabilities, and the orbital stability of dynamical systems.In the section on chaos theory, the concept of chaos and its dynamical features are first introduced, followed by some measures and testing methods of chaos. Fractals and chaos in control systems are briefly described. In parallel, the section on bifurcations introduces several typical types of bifurcations and the period‐doubling bifurcations route to chaos. Similarly, bifurcations in control systems are briefly discussed.The above prepared the readers to step forward into the new realm of research on controlling chaos and controlling bifurcations, presented in the following two sections. Why chaos control and why bifurcation control are first motivated, by both theoretical challenges and real‐world examples. Then, some effective chaos control and bifurcation control methodologies are introduced, respectively, with distinctions from conventional control theory and techniques for nonchaotic especially linear systems.The last section is novel and unique‐anticontrolling chaos in the sense of creating chaos or retaining chaos, by means of control, when chaos is beneficial. This topic has a great potential in nonconventional applications of control theory and practice, with a corpus of opportunities in future technology and engineering.

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Bifurcation Control: Theories, Methods, and Applications

Cited by 336 publications

References 119 publications

Switched Systems With Multiple Invariant Sets

Switched Systems With Multiple Invariant Sets

A Novel Parametric Controller Design Method for Hopf Bifurcation System

Chaos, Bifurcations, and Their Control

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