Hybrid System Stability Analysis of Multi-Lane Mixed-Autonomy Traffic

Sirui Li; Roy Dong; Cathy Wu

Home/Archive/arXiv

arXiv · 2310.07689

Hybrid System Stability Analysis of Multi-Lane Mixed-Autonomy Traffic

Sirui Li·Roy Dong·Cathy Wu

View original source ↗Read source document ↗Export metadata ↓

Abstract

Autonomous vehicles (AVs) hold vast potential to enhance transportation systems by reducing congestion, improving safety, and lowering emissions. AV controls lead to emergent traffic phenomena; one such intriguing phenomenon is traffic breaks (rolling roadblocks), where a single AV efficiently stabilizes multiple lanes through frequent lane switching, similar to the highway patrolling officers weaving across multiple lanes during difficult traffic conditions. While previous theoretical studies focus on single-lane mixed-autonomy systems, this work proposes a stability analysis framework for multi-lane systems under AV controls. Casting this problem into the hybrid system paradigm, the proposed analysis integrates continuous vehicle dynamics and discrete jumps from AV lane-switches. Through examining the influence of the lane-switch frequency on the system's stability, the analysis offers a principled explanation to the traffic break phenomena, and further discovers opportunities for less-intrusive traffic smoothing by employing less frequent lane-switching. The analysis further facilitates the design of traffic-aware AV lane-switch strategies to enhance system stability. Numerical analysis reveals a strong alignment between the theory and simulation, validating the effectiveness of the proposed stability framework in analyzing multi-lane mixed-autonomy traffic systems.

Explore related subjects

eess.SY cs.SY

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Sirui Li, Roy Dong, Cathy Wu. 2024-10-10. Hybrid System Stability Analysis of Multi-Lane Mixed-Autonomy Traffic. https://arxiv.org/abs/2310.07689

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Co-Investment with Payoff-Sharing Mechanism for Cooperative Decision-Making in Network Design Games

Network-based systems are inherently interconnected, with the design and performance of subnetworks being interdependent. However, the decisions of self-interested operators may lead to suboptimal outcomes for users and the overall system. This paper explores cooperative mechanisms that can simultaneously benefit both operators and users. We address this challenge using a game-theoretical framework that integrates both non-cooperative and cooperative game theory. In the non-cooperative stage, we propose a network design game in which subnetwork decision-makers strategically design local infrastructures. In the cooperative stage, co-investment with payoff-sharing mechanism is developed to enlarge collective benefits and fairly distribute them. To demonstrate the effectiveness of our framework, we conduct case studies on the Sioux Falls network and real-world public transport networks in Zurich and Winterthur, Switzerland. Our evaluation considers impacts on environmental sustainability, social welfare, and economic efficiency. The proposed framework provides a foundation for improving interdependent networked systems by enabling strategic cooperation among self-interested operators.

eess.SY↗

arXiv2026

Generalizable Optimal Control with Transformers: One Policy Across Diverse Systems

Classical optimal control designs a separate controller for each plant. Even for the Linear Quadratic Regulator (LQR), every new model must be identified and its Riccati equation re-solved. We ask whether a single learned policy can instead serve an entire family of systems, and we show that one transformer can. We train the policy to imitate optimal LQR state feedback across a collection of heterogeneous Multiple-Input, Multiple-Output (MIMO) Linear Time-Invariant (LTI) systems that differ in their state and input dimensions and in their cost objectives. A shared representation lets the same parameters control every member of the family. It combines system-wise standardization, zero-padding and masking across dimensions, and an explicit encoding of the cost matrices. At run time, the policy maps a short window of recent states and the specified cost to a control action. It uses no plant matrices and identifies the dynamics implicitly from the state history. We evaluate on $28$ simulated systems over $9{,}675$ closed-loop rollouts, and no unstable rollout was observed in any of them. On the systems seen during training, it attains a median relative sub-optimality of $0.022\%$, even under parameter perturbations of up to $\pm10\%$. It transfers to unseen systems with lightweight fine-tuning, reaching a median sub-optimality of $0.19\%$. These results support transformers as generalizable near-optimal controllers for structured families of linear systems.

eess.SY↗

arXiv2026

Two-Timescale Asymptotic Simulations of Hybrid Inclusions with Applications to Stochastic Hybrid Optimization

Convergence properties of model-free two-timescale asymptotic simulations of singularly perturbed hybrid inclusions are developed. A hybrid inclusion combines constrained differential and difference inclusions to capture continuous (flow) and discrete (jump) dynamics, respectively. Sufficient conditions are established under which sequences of iterates and step sizes constitute a two-timescale asymptotic simulation of such a system, with limiting behavior characterized via weakly invariant and internally chain-transitive sets of an associated boundary layer and reduced system. To illustrate the applicability of these results, conditions are given under which a two-timescale stochastic approximation of a hybrid optimization algorithm asymptotically recovers the behavior of its deterministic counterpart.

eess.SY↗