Modular stability tools for distributed computation and control

Slotine, Jean‐Jacques E.

doi:10.1002/acs.754

Cited by 76 publications

(94 citation statements)

References 54 publications

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“…In 4.2.1 and 4.2.2, the input-equivalence preservation condition of section 4.1 is implicitly assumed, and the results reflect similar combination properties of contracting systems [27,43,46]. More generally, as long as input-equivalence is preserved, any combination property for contracting systems can be easily "translated" into a combination property for synchronizing systems.…”

Section: Typology Of Combinationsmentioning

confidence: 95%

“…Furthermore, all transformations Θ corresponding to the same M lead to the same eigenvalues for the symmetric part F s of F [43], and thus to the same contraction rate | sup x,t λ max (F)|.…”

Section: Nonlinear Contraction Theorymentioning

confidence: 98%

“…One such interpretation, as in [43] for contracting systems, is to assume that for a given systemẋ = f(x, t), several types of additive couplings L i (x, t) lead stably to the same invariant set, but to different synchronized behaviors. Then any convex combination (α i (t) ≥ 0, i α i (t) = 1) of the couplings will lead stably to the same invariant set.…”

Section: Parallel Combinationmentioning

confidence: 99%

“…This section reviews basic results of nonlinear contraction theory [27,28,43,48], which is the main stability analysis tool used in the paper. Essentially, a nonlinear time-varying dynamic system will be called contracting if initial conditions or temporary disturbances are forgotten exponentially fast, i.e., if trajectories of the perturbed system return to their nominal behavior with an exponential convergence rate.…”

Section: Nonlinear Contraction Theorymentioning

confidence: 99%

See 3 more Smart Citations

Stable concurrent synchronization in dynamic system networks

2007

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In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple "rhythms" interacting and functional assemblies combining neural oscillators of many different types. Mathematically, stable concurrent synchronization corresponds to convergence to a flow-invariant linear subspace of the global state space. We derive a general condition for such convergence to occur globally and exponentially. We also show that, under mild conditions, global convergence to a concurrently synchronized regime is preserved under basic system combinations such as negative feedback or hierarchies, so that stable concurrently synchronized aggregates of arbitrary size can be constructed. Robustnesss of stable concurrent synchronization to variations in individual dynamics is also quantified. Simple applications of these results to classical questions in systems neuroscience and robotics are discussed.

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Section: Typology Of Combinationsmentioning

confidence: 95%

Section: Nonlinear Contraction Theorymentioning

confidence: 98%

Section: Parallel Combinationmentioning

confidence: 99%

Section: Nonlinear Contraction Theorymentioning

confidence: 99%

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Stable concurrent synchronization in dynamic system networks

2007

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“…Despite the flexibility of the modular control scheme, rigorous proofs for stability, convergence and robustness are lacking and performance is usually analyzed with computer simulations like in gain scheduling (but see (Lohmiller and Slotine 1998;Slotine and Lohmiller 2001;Slotine 2003)). Also, it remains unclear whether explicit estimation of state or a direct adaptive control mechanism is actually used in such an internal model.…”

Section: Modular Internal Models As Multi-model Adaptive Controlmentioning

confidence: 99%

Internal models in sensorimotor integration: perspectives from adaptive control theory

2005

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Internal model and adaptive control are empirical and mathematical paradigms that have evolved separately to describe learning control processes in brain systems and engineering systems, respectively. This paper presents a comprehensive appraisal of the correlation between these paradigms with a view to forging a unified theoretical framework that may benefit both disciplines. It is suggested that the classic equilibrium-point theory of impedance control of arm movement is analogous to continuous gain-scheduling or high-gain adaptive control within or across movement trials, respectively, and that the recently proposed inverse internal model is akin to adaptive sliding control originally for robotic manipulator applications. Modular internal models architecture for multiple motor tasks is a form of multi-model adaptive control. Stochastic methods such as generalized predictive control, reinforcement learning, Bayesian learning and Hebbian feedback covariance learning are reviewed and their possible relevance to motor control is discussed. Possible applicability of Luenberger observer and extended Kalman filter to state estimation problems such as sensorimotor prediction or the resolution of vestibular sensory ambiguity is also discussed. The important role played by vestibular system identification in postural control suggests an indirect adaptive control scheme whereby system states or parameters are explicitly estimated prior to the implementation of control. This interdisciplinary framework should facilitate the experimental elucidation of the mechanisms of internal model in sensorimotor systems and the reverse engineering of such neural mechanisms into novel brain-inspired adaptive control paradigms in future.

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