On partial contraction analysis for coupled nonlinear oscillators

Wang, Wei; Slotine, Jean‐Jacques E.

doi:10.1007/s00422-004-0527-x

Cited by 472 publications

(493 citation statements)

References 83 publications

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“…To obtain a sufficient condition, one can use global stability analysis, like Lyapunov's direct method (Belykh et al, 2006(Belykh et al, , 2005(Belykh et al, , 2004aChen, 2006Chen, , 2008Li et al, 2009;Chua, 1994, 1995a,b,c) or contraction theory (Aminzare and Sontag, 2015;Li et al, 2007;Lohmiller and Slotine, 1998;Pham and Slotine, 2007;Russo and Di Bernardo, 2009;Tabareau et al, 2010;Wang and Slotine, 2005).…”

Section: Master Stability Formalism and Beyondmentioning

confidence: 99%

“…Equally important was the realization that these universal topological features are the result of the common dynamical principles that govern their emergence and growth. At the same time we learned that the topology fundamentally affects the dynamical processes taking place on these networks, from epidemic spreading (Cohen et al, 2000;Pastor-Satorras and Vespignani, 2001) to synchronization (Nishikawa et al, 2003;Wang and Slotine, 2005). Hence, it is fair to expect that the network topology of a system also affects our ability to control it.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Control principles of complex systems

Liu¹,

Barabási²

2016

Rev. Mod. Phys.

543

349

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A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: it requires an accurate map of the network that governs the interactions between the system's components, a quantitative description of the dynamical laws that govern the temporal behavior of each component, and an ability to influence the state and temporal behavior of a selected subset of the components. With deep roots in nonlinear dynamics and control theory, notions of control and controllability have taken a new life recently in the study of complex networks, inspiring several fundamental questions: What are the control principles of complex systems? How do networks organize themselves to balance control with functionality? To address these here we review recent advances on the controllability and the control of complex networks, exploring the intricate interplay between a system's structure, captured by its network topology, and the dynamical laws that govern the interactions between the components. We match the pertinent mathematical results with empirical findings and applications. We show that uncovering the control principles of complex systems can help us explore and ultimately understand the fundamental laws that govern their behavior.

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Section: Master Stability Formalism and Beyondmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Control principles of complex systems

Liu¹,

Barabási²

2016

Rev. Mod. Phys.

543

349

View full text Add to dashboard Cite

show abstract

“…with which phase lag the activity of the oscillator is synchronized with the perturbation. An interesting approach to desing specific phase lags is the to use contraction theory (Wang & Slotine, 2005). …”

Section: Reactive: Temporary Entrainment and Shape Changesmentioning

confidence: 99%

Engineering entrainment and adaptation in limit cycle systems

2006

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Periodic behavior is key to life, and is observed in multiple instances and at multiple time scales in our metabolism, our natural environment, and our engineered environment. A natural way of modelling or generating periodic behavior is done by using oscillators, i.e. dynamical systems that exhibit limit cycle behavior. While there is extensive literature on methods to analyze such dynamical systems, much less work has been done on methods to synthesize an oscillator to exhibit some specific desired characteristics. The goal of this article is two-fold: (1) to provide a framework for characterizing and designing oscillators, and (2) to review how classes of well known oscillators can be understood and related to this framework.The basis of the framework is to characterize oscillators in terms of their fundamental temporal and spatial behavior, and in terms of properties that these two behaviors can be designed to exhibit. This focus on fundamental properties is important because it allows us to systematically compare a large variety of oscillators which might at first sight appear very different from each other. We identify several specifications that are useful for design, such as frequency-locking behavior, phaselocking behavior, and specific output signal shape. We also identify two classes of design methods by which these specifications can be met, namely off-line methods and on-line methods. By relating these specifications to our framework and by presenting several examples of how oscillators have been designed in the literature, this article provides a useful methodology and toolbox for designing oscillators for a wide range of purposes. In particular the focus on synthesis of limit cycle dynamical systems should be useful both for engineering and for computational modelling of physical or biological phenomena.

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“…Using partial contraction analysis as in [10], [14], [15], one can find a lower limit of k > 0 that ensures the exponential synchronization of the oscillators in the CPG layer. Once synchronized, the diffusively coupled terms (e.g., q 1 − q 2 ) vanish and thus each oscillator behaves as if it were uncoupled to exhibit its intrinsic limit-cycle behavior.…”

Section: A Top-down Open-loop Approachmentioning

confidence: 99%

“…The amplitude and the phase lag can be computed given the input frequency. By ignoring the transient behavior, we can reduce the preceding model in (13)(14)(15)(16) as…”

Section: B Top-down Cpg With Feedback Couplingmentioning

confidence: 99%

CPG-based Control of a Turtle-like Underwater Vehicle

Seo¹,

Chung²,

Slotine³

2008

Robotics: Science and Systems IV

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Abstract-We present a new bio-inspired control strategy for an autonomous underwater vehicle by constructing coupled nonlinear oscillators, similar to the animal central pattern generators (CPGs). Using contraction theory, we show that the network of oscillators globally converges to a specific pattern of oscillation. We experimentally validate the proposed control law using a turtle-like underwater vehicle, whose fin actuators successfully exhibit a pattern that resembles the motion of fore limbs of a swimming sea turtle. In order to further fulfill the potential of the CPG-based control, we propose to feed back the actuator states to the coupled oscillators, thereby achieving not only the synchronization of the oscillators, but also the synchronization of actual foil states. Such a closed-loop version of CPGs makes the controller more robust and practical in the presence of external disturbances.

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On partial contraction analysis for coupled nonlinear oscillators

Cited by 472 publications

References 83 publications

Control principles of complex systems

Control principles of complex systems

Engineering entrainment and adaptation in limit cycle systems

CPG-based Control of a Turtle-like Underwater Vehicle

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