Controlling Chaos with Simple Limiters

Corron, Ned J.; Pethel, Shawn D.; Hopper, Buckley A.

doi:10.1103/physrevlett.84.3835

Cited by 98 publications

(65 citation statements)

References 14 publications

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“…However, Corron et al (2000) present experimental evidence that chaos control can be accomplished using simple limiters and argue that chaos control can be practically applied to a much wider array of important problems than thought possible until recently. This method, which has been analytically and numerically explored by Wagner and Stoop (2000) and Stoop and Wagner (2003), simply restricts the phase space that can be explored.…”

Section: Article In Pressmentioning

confidence: 99%

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Commodity markets, price limiters and speculative price dynamics

Westerhoff

2005

Journal of Economic Dynamics and Control

104

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We develop a behavioral commodity market model with consumers, producers and heterogeneous speculators to characterize the nature of commodity price fluctuations and to explore the effectiveness of price stabilization schemes. Within our model, we analyze how nonlinear interactions between market participants can create either bull or bear markets, or irregular price fluctuations between bull and bear markets through a (global) homoclinic bifurcation. Both the imposition of a bottoming price level (to support producers) or a topping price level (to protect consumers) can eliminate such homoclinic bifurcations and hence reduce market price volatility. However, simple policy rules, such as price limiters, may have unexpected consequences in a complex environment: a minimum price level decreases the average price while a maximum price limit increases the average price. In addition, price limiters influence the price dynamics in an intricate way and may cause volatility clustering. r

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Section: Article In Pressmentioning

confidence: 99%

“…Next, we study the consequences of the limiter method -as suggested by Corron et al (2000) -on commodity price dynamics. Price limiters may easily be implemented in our framework.…”

Section: Simple Price Limitersmentioning

confidence: 99%

Commodity markets, price limiters and speculative price dynamics

Westerhoff

2005

Journal of Economic Dynamics and Control

104

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“…More insight into the wealth of the limiter control developed by Corron et al [Corron et al, 2000;Corron & Pethel, 2002;Myneni et al, 1999] and applied to this important aeroelastic problem is provided here. Limiter control uses small perturbations, in the form of a novel nonlinear feedback control plant, to neutralize system instabilities.…”

Section: Introductionmentioning

confidence: 99%

Active Aeroelastic Control of Lifting Surfaces via Jet Reaction Limiter Control

Rubillo

Bollt

Marzocca

2005

46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

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In this paper we present, the design and modeling of the novel nonlinear limiter control feedback control plant [Myneni et al., 1999;Corron et al., 2000;Corron & Pethel, 2002], applied for the first time here in an aeroelastic system, and actuated as a jet reaction torquer control of a wing with potentially chaotic dynamics. This study will provide a better understanding of the nonlinear dynamics of the open/closed-loop aeroelasticity of flexible wings with either steady or unsteady aerodynamic loads. The limiter control can be applied to either the plunging or pitching characteristic of the wing or to both of them. We show that the control can effectively suppress Limit Cycle Oscillations (LCO) and chaos well beyond the nominal flutter speed. This could lead to a practical implementation of the control mechanism on actual and future generation aircraft wings via implementation of a combination of propulsive/jet type forces, micro surface effectors and fluidic devices. Analysis of this control produced favorable results in the suppression of LCO amplitude and increased flutter boundaries for plunging and pitching motion. The limiting control has asymptotically zero power, and is simply implemented, making it a feasible solution to the problem of the chaotic dynamics of the oscillating airfoil.

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“…In practice, the problem of controller complexity is a very crucial issue and two fundamental issues in this direction have been identi ed [38,39]: one is that the cost implication and the density requirement for designing controllers, the other is that the need to make the complexity of the controller to be, at least comparable to, or less than, the device being controlled, if the controlling technique is desired to achieve a useful end far beyond mere scienti c curiosity. Indeed, the entire control goal would be untenable if a simple chaotic system requires a massively complex controller like the controller proposed in [40].…”

Section: Introductionmentioning

confidence: 99%

“…An important aspect of the problem of chaos control is how to realize the control of chaotic system by designing a simple and physically available controller [38], which is particularly signi cant both for theoretical research and practical applications. In practice, the problem of controller complexity is a very crucial issue and two fundamental issues in this direction have been identi ed [38,39]: one is that the cost implication and the density requirement for designing controllers, the other is that the need to make the complexity of the controller to be, at least comparable to, or less than, the device being controlled, if the controlling technique is desired to achieve a useful end far beyond mere scienti c curiosity.…”

Section: Introductionmentioning

confidence: 99%

Single state feedback stabilization of unified chaotic systems and circuit implementation

Jing

Fan

et al. 2014

Open Physics

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This paper focuses on the single state feedback stabilization problem of uni ed chaotic system and circuit implementation. Some stabilization conditions will be derived via the single state feedback control scheme. The robust performance of controlled uni ed chaotic systems with uncertain parameter will be investigated based on maximum and minimum analysis of uncertain parameter, the robust controller which only requires information of a state of the system is proposed and the controller is linear. Both the uni ed chaotic system and the designed controller are synthesized and implemented by an analog electronic circuit which is simpler because only three variable resistors are required to be adjusted. The numerical simulation and control in MATLAB/Simulink is then provided to show the e ectiveness and feasibility of the proposed method which is robust against some uncertainties. The results presented in this paper improve and generalize the corresponding results of recent works.

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Controlling Chaos with Simple Limiters

Cited by 98 publications

References 14 publications

Commodity markets, price limiters and speculative price dynamics

Commodity markets, price limiters and speculative price dynamics

Active Aeroelastic Control of Lifting Surfaces via Jet Reaction Limiter Control

Single state feedback stabilization of unified chaotic systems and circuit implementation

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