arXiv subjects

Gal Barkai

Publications and source records attributed to Gal Barkai.

5 recordsLinked to original sources

arXiv2026

How network perturbations distort agreement trajectories in LTI multi-agent systems

Distributed coordination of multi-agent systems frequently relies on cooperative protocols designed to achieve agreement on a prescribed, non-trivial trajectory. While the robustness of such protocols to various uncertainties is well documented, existing literature universally assumes that the target agreement trajectory itself remains invariant. This assumption may hold in ideal cases, but we prove that network perturbations can vastly modify the asymptotic agreement trajectory. We first investigate the exact trajectories of Linear Time-Invariant (LTI) agents subjected to dynamic coupling uncertainties by establishing a new Laplace-domain criterion that characterizes the specific closed-loop poles governing the perturbed agreement manifold. To formalize our analysis, we introduce the notion of structure-preserving dynamics, perturbations that maintain the null space of the communication graph's Laplacian, and contrast them with transmission only dynamics, affecting only the adjacency matrix. We prove a critical fragility within standard cooperative output regulation schemes: while static consensus is uniquely robust to heterogeneous transmission delays, synchronization to periodic trajectories is destroyed by arbitrarily small transmission delays. Furthermore, we demonstrate that for d-regular topologies, uniform transmission perturbations can easily shift the system to synchronize with an unexpected, entirely new frequency. These findings expose a previously unidentified vulnerability in classical robust synchronization, demonstrating that transmission dynamics necessitate fundamental structural modifications to networked reference generators.

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arXiv2026

Transient-Safe Platooning via Dynamic Headway

Managing autonomous vehicle platoons requires a delicate balance between string stability and rigorous safety. This challenge is intensified by aggressive transients, such as highway merging. Although Constant Time Headway (CTH) spacing is the industry standard for Cooperative Adaptive Cruise Control, it lacks formal safety guarantees during significant velocity deviations. This letter proposes a computationally efficient control framework that considers a linear time-invariant model for the dynamics of each vehicle, while ensuring formal transient safety and stability. By introducing a spacing policy that naturally converges to CTH at steady state, we establish platoon safety as an inductive property. We derive a non-linear and saturated control law for the lead follower and provide sufficient initial conditions to guarantee velocity non-negativity and safety throughout the platoon for any CTH-based followers' control law. Numerical examples indicate the proposed methodology may be applicable even under non-nominal setups.

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arXiv2026

From open-loop representations to closed-loop feedback implementations in differential games: A numerical case study

Solutions to pursuit-evasion and surveillance-evasion differential games are typically computed and expressed using open-loop representations, with the synthesis of feedback strategies significantly less common. We propose a numerical scheme for obtaining feedback strategies for the recently introduced prying-pedestrian surveillance-evasion differential game. The scheme involves computing feedback strategies as input-output maps approximated via neural networks trained using data obtained from open-loop representations of solutions. Simulations show the effectiveness of neural networks trained with an appropriate learning-loss function. Since optimal feedback strategies are discontinuous, as a second contribution, the potential loss/gain of individual players is subsequently studied for players using sample-and-hold feedback compared to continuous-time feedback.

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arXiv2025

On two-degrees-of-freedom agreement protocols

We propose a distributed two-degrees-of-freedom (2DOF) architecture for driving autonomous, possibly heterogeneous, agents to agreement. The scheme mirrors classical servo structures, separating local feedback from network filtering. This separation enables independent network-filter design for prescribed noise attenuation and allows controller heterogeneity to reject local disturbances, including disturbances exciting unstable agreement poles -- which is known to be impossible via standard diffusive couplings. The potential of the framework is illustrated via two numerical examples.

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arXiv2022

On the Internal Stability of Diffusively Coupled Multi-Agent Systems and the Dangers of Cancel Culture

We study internal stability in the context of diffusively-coupled control architectures, common in multi-agent systems (i.e. the celebrated consensus protocol), for linear time-invariant agents. We derive a condition under which the system can not be stabilized by any controller from that class. In the finite-dimensional case the condition states that diffusive controllers cannot stabilize agents that share common unstable dynamics, directions included. This class always contains the group of homogeneous unstable agents, like integrators. We argue that the underlying reason is intrinsic cancellations of unstable agent dynamics by such controllers, even static ones, where directional properties play a key role. The intrinsic lack of internal stability explains the notorious behavior of some distributed control protocols when affected by measurement noise or exogenous disturbances.

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