Exponential and practical exponential stability of second-order formation control systems

Suttner, Raik; Sun, Zhiyong

doi:10.1109/cdc40024.2019.9030064

Cited by 13 publications

(6 citation statements)

References 26 publications

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“…Convergence results in distance-based control cover the local stabilization of the desired shape, and besides some analytical expressions for some particular cases of singleintegrators [25], for double-integrator dynamics the neighborhoods or regions of attraction around q * (up to translations and rotations) are estimated numerically [26], [27], [28], [29].…”

Section: Variational Integrator Vs Euler Methodsmentioning

confidence: 99%

Forced Variational Integrators for the Formation Control of Multi-Agent Systems

Colombo¹,

Marina²

2020

Preprint

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Formation control of autonomous agents can be seen as a physical system of individuals interacting with local potentials, and whose evolution can be described by a Lagrangian function. In this paper, we construct and implement forced variational integrators for the formation control of autonomous agents modeled by double integrators. In particular, we provide an accurate numerical integrator with a lower computational cost than traditional solutions. We find error estimations for the rate of the energy dissipated along with the agents' motion to achieve desired formations. Consequently, this permits to provide sufficient conditions on the simulation's time step for the convergence of discrete formation control systems such as the consensus problem in discrete systems. We present practical applications such as the rapid estimation of regions of attraction to desired shapes in distance-based formation control.

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Section: Variational Integrator Vs Euler Methodsmentioning

confidence: 99%

Forced Variational Integrators for the Formation Control of Multi-Agent Systems

Colombo¹,

Marina²

2020

Preprint

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“…R is globally asymptotically stable for (25). Using that r 3 is positive, one can also show that the compact subset Θ := S 1 × {0} of T S 1 is input-to-state stable for (26) with (27) as "inputs".…”

Section: Planar Rigid Body With Two Thrustersmentioning

confidence: 97%

“…In this section, we apply the theory from Section 4 to two particular extremum seeking problems. Further applications can be found in [23,25].…”

Section: Examplesmentioning

confidence: 99%

“…Here, we use approximations of symmetric products to obtain information about descent directions of the objective function. Applications of this strategy to double-integrator points and unicycles can be found in [23,24,25]. In this paper, we investigate this new symmetric product approach to extremum seeking control for a more general class of mechanical systems and indicate further applications.…”

Section: Introductionmentioning

confidence: 99%

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Extremum Seeking Control for a Class of Nonholonomic Systems

Suttner¹

2020

SIAM J. Control Optim.

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We present a novel extremum seeking method for affine connection mechanical control systems. The proposed control law involves periodic perturbation signals with sufficiently large amplitudes and frequencies. A suitable averaging analysis reveals that the solutions of the closed-loop system converge locally uniformly to the solutions of an averaged system in the large-amplitude high-frequency limit. This in turn leads to the effect that stability properties of the averaged system carry over to the approximating closed-loop system. Descent directions of the objective function are given by symmetric products of vector fields in the averaged system. Under suitable assumptions, we prove that minimum points of the objective function are asymptotically stable for the averaged system and therefore practically asymptotically stable for the closed-loop system. We illustrate our results by examples and numerical simulations.

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“…The approach was first introduced in Reference 30 for the particular case of an acceleration-controlled unicycle and, since then, has been extended to a larger class of mechanical systems. 7,[31][32][33][34][35] The strategy for second-order dynamic systems shares certain similarities with the approach for first-order kinematic systems as described in the previous paragraph. It also involves periodic perturbation signals with sufficiently large amplitudes and frequencies to induce an approximation of Lie brackets.…”

Section: Introductionmentioning

confidence: 99%

Attitude optimization by extremum seeking for rigid bodies actuated by internal rotors only

Suttner,

Krstić

2023

Intl J Robust & Nonlinear

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SummaryIn this paper, we investigate the stabilizing effect of an extremum seeking control law on a class of underactuated Lagrangian control systems with symmetry. Our study is motivated by the problem of attitude optimization for satellites with reaction wheels. The goal is to minimize the value of an analytically unknown configuration‐dependent objective function without being reliant on measurements of the current configuration and velocity. This work extends our previous work on extremum seeking control for fully actuated mechanical systems on Lie groups in the absence of dissipation. We show that the earlier method for fully actuated systems can also be successfully applied to a certain class of underactuated systems, which are controlled by internal momentum exchange devices (reaction wheels) so that the total momentum is conserved. Conservation of momentum allows us to reduce the control system to a system on a smaller state manifold. The reduced control system is not of Lagrangian form but fully actuated. For the reduced control system we prove that the extremum seeking method leads to practical uniform asymptotic stability. We illustrate our findings by the example of a rigid body with internal rotors.

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Exponential and practical exponential stability of second-order formation control systems

Cited by 13 publications

References 26 publications

Forced Variational Integrators for the Formation Control of Multi-Agent Systems

Forced Variational Integrators for the Formation Control of Multi-Agent Systems

Extremum Seeking Control for a Class of Nonholonomic Systems

Attitude optimization by extremum seeking for rigid bodies actuated by internal rotors only

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