Spatial instabilities and size limitations of flocks

Veerman, J. J. P.; Stošić, Borko; Olverá, Arturo

doi:10.3934/nhm.2007.2.647

Cited by 12 publications

(24 citation statements)

References 4 publications

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“…We have obtained enough properties of the circular system to derive the transients the original path system (5). The transient we analyze is when the platoon is in steadystate and the leader starts to move with unit velocity (8).…”

Section: Transients In the Path Systemmentioning

confidence: 99%

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Transients of platoons with asymmetric and different Laplacians

Herman

Martinec

Veerman

2016

Systems & Control Letters

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We consider an asymmetric control of platoons of identical vehicles with nearest-neighbor interaction. Recent results show that if the vehicle uses different asymmetries for position and velocity errors, the platoon has a short transient and low overshoots. In this paper we investigate the properties of vehicles with friction. To achieve consensus, an integral part is added to the controller, making the vehicle a third-order system. We show that the parameters can be chosen so that the platoon behaves as a wave equation with different wave velocities. Simulations suggest that our system has a better performance than other nearest-neighbor scenarios. Moreover, an optimization-based procedure is used to find the controller properties

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Section: Transients In the Path Systemmentioning

confidence: 99%

“…The properties of such control are investigated in [2,7,8]. One of the advantages is linear scaling of the H ∞ norm with the number of vehicles [8]. The main drawback is a very long transient for a higher number of vehicles and sensitivity to noise [9].…”

Section: Introductionmentioning

confidence: 99%

Transients of platoons with asymmetric and different Laplacians

Herman

Martinec

Veerman

2016

Systems & Control Letters

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“…However, the transients are not solely determined by the eigenvalues. The price to pay for the better convergence rate is that the H ∞ norm of the transfer functions in the platoon scales exponentially in N for asymmetric strings (compared to linear scaling for symmetric strings [26]). This extremely bad scaling was first shown for a double-integrator model in [25] and later generalized to an arbitrary agent model in [11] and to an arbitrary transfer function in [12].…”

Section: Introductionmentioning

confidence: 99%

Disturbance scaling in bidirectional vehicle platoons with different asymmetry in position and velocity coupling

2017

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This paper considers a string of vehicles where the local control law uses the states of the vehicle's immediate predecessor and follower. The coupling towards the preceding vehicle can be chosen different to the coupling towards the following vehicle, which is often referred to as an asymmetric bidirectional string. Further, the asymmetry for the velocity coupling can be chosen differently to the asymmetry in the position coupling. It is investigated how the effect of disturbance on the control errors in the string depends on the string length. It is shown, that in case of symmetric position coupling and asymmetric velocity coupling, linear scaling can be achieved. For symmetric interaction in both states, i.e., in symmetric bidirectional strings, the errors scale quadratically in the number of vehicles. When the coupling in position is asymmetric, exponential scaling may occur or the system might even become unstable. The paper thus gives a comprehensive overview of the achievable performance in linear, asymmetric, bidirectional platoons. The results reveal that symmetry in the position coupling and asymmetry in velocity coupling qualitatively improves the performance of the string. Extensive numerical results illustrate the theoretical findings.

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“…If symmetric coupling is implemented, the norm grows only linearly [13], [14] but the step response suffers from very long transients-the eigenvalues get arbitrarily close to the origin. This can be alleviated using a wave-absorbing controller implemented on either end of the platoon [15].…”

Section: Introductionmentioning

confidence: 99%

Scaling in Bidirectional Platoons With Dynamic Controllers and Proportional Asymmetry

Herman

Martinec

Hurák

et al. 2017

IEEE Trans. Automat. Contr.

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Abstract-We consider platoons composed of identical vehicles with an asymmetric nearest-neighbor interaction. We restrict ourselves to intervehicular coupling realized with dynamic arbitrary-order onboard controllers such that the coupling to the immediately preceding vehicle is proportional to the coupling to the immediately following vehicle. Each vehicle is modeled using a transfer function and we impose no restriction on the order of the vehicle. The platoon is described by a transfer function in a convenient product form. We investigate how the H-infinity norm and the steady-state gain of the platoon scale with the number of vehicles. We conclude that if the open-loop transfer function of the vehicle contains two or more integrators and the Fiedler eigenvalue of the graph Laplacian is uniformly bounded from below, the norm scales exponentially with the growing distance in the graph. If there is just one integrator in the open loop, we give a condition under which the norm of the transfer function is bounded by its steady-state gain-the platoon is string-stable. Moreover, we argue that in this case it is always possible to design a controller for the extreme asymmetry-the predecessor following strategy.

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Spatial instabilities and size limitations of flocks

Cited by 12 publications

References 4 publications

Transients of platoons with asymmetric and different Laplacians

Transients of platoons with asymmetric and different Laplacians

Disturbance scaling in bidirectional vehicle platoons with different asymmetry in position and velocity coupling

Scaling in Bidirectional Platoons With Dynamic Controllers and Proportional Asymmetry

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