Exponential Convergence Rates of Nonlinear Mechanical Systems: The 1-DoF Case With Configuration-Dependent Inertia

Calzolari, Davide; Santina, Cosimo Della; Albu‐Schäffer, Alin

doi:10.1109/lcsys.2020.3004196

Cited by 5 publications

(10 citation statements)

References 11 publications

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“…Therefore, both e andė converge exponentially to zero [20], which in turn assures that (s, ı) converges exponentially to (s,ī). We need to show now that (6) and ( 9) are equivalent.…”

Section: B Trajectory Tracking Controllermentioning

confidence: 84%

Covid-19 and Flattening the Curve: a Feedback Control Perspective

Lauro

Kiss

Rus

et al. 2021

2021 American Control Conference (ACC)

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Many of the control policies that were put into place during the Covid-19 pandemic had a common goal: to flatten the curve of the number of infected people so that its peak remains under a critical threshold. This letter considers the challenge of engineering a strategy that enforces such a goal using control theory. We introduce a simple formulation of the optimal flattening problem, and provide a closed form solution. This is augmented through nonlinear closed loop tracking of the nominal solution, with the aim of ensuring close-to-optimal performance under uncertain conditions. A key contribution of this paper is to provide validation of the method with extensive and realistic simulations in a Covid-19 scenario, with particular focus on the case of Codogno -a small city in Northern Italy that has been among the most harshly hit by the pandemic.

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“…Therefore, both e andė converge exponentially to zero [20], which in turn assures that (s, ı) converges exponentially to (s,ī). We need to show now that (6) and ( 9) are equivalent.…”

Section: B Trajectory Tracking Controllermentioning

confidence: 84%

Covid-19 and Flattening the Curve: a Feedback Control Perspective

Lauro

Kiss

Rus

et al. 2021

2021 American Control Conference (ACC)

Self Cite

View full text Add to dashboard Cite

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“…Note that this is equivalent to a one dimensional mechanical system with configuration dependent inertia, which is similar to the one we studied in [13], albeit with a more general nonlinear impedance. Therefore, the results that we introduce in the following can be applied to one dimensional systems with configuration dependent inertia as special case.…”

Section: A Dynamics Along Smentioning

confidence: 89%

“…In the following we consider among all the possible τ verifying (5), the PD-like controller (13) where π S is a projection from R n to S, i.e., any function such that π S • γ is the identity, and κ(s), δ(s) are positive definite scalar functions. It is immediate to see that (13) verifies (5) for q ∈ S considering f (s,ṡ) = −κ(s)(s − s eq ) − δ(s)ṡ, and in view of (4).…”

Section: Existence and Feedback Enforcement Of Smentioning

confidence: 99%

“…We aim here at writing a compact description of the mechanical system dynamics when evolving on the manifold thanks to the action (13). To this end we differentiate onceq from (4), yieldingq = (s)s +˙ (s,ṡ)ṡ.…”

Section: A Dynamics Along Smentioning

confidence: 99%

“…We moved a first step towards a general solution to the problem in [13], where we tackled the case n = 1. The idea is here to introduce an energy-based change of coordinates which makes C(q,q) disappear, solving therefore the problem of its sign indefiniteness.…”

mentioning

confidence: 99%

See 2 more Smart Citations

PD-like Regulation of Mechanical Systems with Prescribed Bounds of Exponential Stability: the Point-to-Point Case

Calzolari

Santina

Albu‐Schäffer

2021

2021 American Control Conference (ACC)

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This letter discusses an extension of the famous PD regulator implementing point to point motions with prescribed exponential rates of convergence. This is achieved by deriving a novel global exponential stability result, dealing with mechanical systems evolving on unidimensional invariant manifolds of the configuration space. The construction of closed loop controllers enforcing the existence of such manifolds is then discussed. Explicit upper and lower bounds of convergence are provided, and connected to the gains of the closed loop controller. Simulations are carried out, assessing the effectiveness of the controller and the tightness of the exponential bounds.

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Exponential Synchronization of Stochastic Neural Networks with Time-Varying Delays and Lévy Noises via Event-Triggered Control

Tong

Chen

et al. 2021

Neural Process Lett

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Exponential Convergence Rates of Nonlinear Mechanical Systems: The 1-DoF Case With Configuration-Dependent Inertia

Cited by 5 publications

References 11 publications

Covid-19 and Flattening the Curve: a Feedback Control Perspective

Covid-19 and Flattening the Curve: a Feedback Control Perspective

PD-like Regulation of Mechanical Systems with Prescribed Bounds of Exponential Stability: the Point-to-Point Case

Exponential Synchronization of Stochastic Neural Networks with Time-Varying Delays and Lévy Noises via Event-Triggered Control

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