- The paper introduces a novel framework to accurately reconstruct dynamic topologies using interval aggregation and persistent excitation.
- It utilizes a projection-based dissimilarity measure with agglomerative clustering to reliably group intervals into distinct modes amid rapid switching.
- Numerical results show estimation errors from 10⁻¹¹ to 10⁻⁷, demonstrating robust topology recovery in complex, dynamic multi-agent environments.
Topology Estimation in Open Multi-Agent Systems with Fast Switching
Introduction
The paper "Topology Estimation for Open Multi-Agent Systems" (2604.13628) investigates the identification problem of interaction topologies in OMAS (open multi-agent systems), where both node sets and agent interactions can change rapidly. Unlike conventional systems, OMAS features frequent arrivals and departures of agents, as well as fast switching between interaction modes, presenting substantial challenges for topology reconstruction. Existing solutions generally assume either slowly-varying topologies or fixed/monotonically expanding node sets, which are not suitable for highly dynamic and structurally evolving OMAS.
The primary objective is to accurately reconstruct the sequence of underlying connectivity matrices for each time interval, given only observed outputs, applied controls, and a sequence of switching events. Each mode corresponds to a distinct weighted, directed network topology, and switches are triggered by agent arrivals, departures, or changes in interactions (including edge creation/removal and weight adjustment). Critically, the approach must handle intervals characterized by short dwell times and limited excitation, which preclude reliable direct identification.
Methodology
Interval Aggregation and Persistent Excitation
The proposed framework advances the state-of-the-art by introducing two key mechanisms:
- Aggregation Over Multiple Intervals: Rather than relying on single-interval estimates, which are unreliable under short dwell time, topology estimation for each mode is achieved by aggregating filtered data from all intervals where the mode is active, thereby accumulating sufficient excitation for robust identification.
- Projection-Based Dissimilarity Measure: A novel distance criterion is developed based on the consistency properties of local least-squares operators and their excitation subspaces. This projection-based measure enables clustering of time segments into modes without requiring accurate topology estimates at each segment, thereby remaining resilient to sparse observations and rapidly fluctuating agent participation.
Algorithmic Structure
Three core algorithms are introduced:
- Algorithm 1: Estimates the connectivity matrix for each interval using auxiliary system excitation and Runge-Kutta-based numerical integration, provided the filtered state meets the persistent excitation criterion.
- Algorithm 2: Aggregates topology information across all intervals of a mode, mitigating the limitations of short dwell times by summing filtered matrices. Unique recovery of the mode's topology is guaranteed if cumulative excitation is sufficient.
- Algorithm 3: Implements agglomerative clustering of time segments using the projection-based dissimilarity measure, thereby grouping intervals by latent modes and assembling unified datasets for reliable topology identification.
The theoretical guarantees leverage properties of persistently exciting signals, excitation-preserving filters, and cumulative excitation criteria, providing rigorous conditions for exact topology recovery under bounded-state and Hurwitz connectivity assumptions.
Numerical Results
Simulation results substantiate the efficacy of the proposed framework. A synthetic OMAS scenario is presented, involving an eight-agent network with subsequent expansion to ten agents and frequent switching among five distinct modes. The interval-wise trajectories are clustered using agglomerative methods based on the projection-based measure. Estimation errors for connectivity matrices are verified to be on the order of 10−11 to 10−7 across all modes, confirming the analytical guarantees and robustness of the approach. The clustering of time segments is shown to be mode-consistent, and the aggregation step produces accurate topology reconstruction for each identified mode.
Implications and Future Directions
The methodology enables practical topology identification in OMAS under conditions of rapid and irregular switchings and dynamic agent sets, which were previously intractable for segment-wise identification strategies. The projection-based dissimilarity represents a technically rigorous approach to mode clustering, with provable resilience in settings of sparse excitation and short time intervals.
Practical implications extend to engineered, biological, and social systems, where interaction networks are often latent and nonstationary, and where real-time topology inference is essential for monitoring, control, and coordination.
Theoretically, the framework shifts the focus from segment-wise identification to cluster-wise aggregation, opening new avenues for scalable online identification and decentralized mode assignment. Future research should address clustering algorithms that do not require pre-specification of mode count, enabling automated, unsupervised mode discovery. Further, additional relaxation of dwell time requirements may broaden applicability to even more rapidly evolving networks, including those with non-Markovian switching and unobservable change points.
Conclusion
The paper provides a systematic solution for topology estimation in OMAS with dynamic node sets and fast switching interactions. By combining interval aggregation, projection-based clustering, and excitation-preserving filters, robust recovery of latent interaction topologies is achieved regardless of short segment durations. The theoretical guarantees and empirical validations highlight the scalability and resilience of the proposed framework, setting the foundation for topology identification in a wide range of dynamic multi-agent networks.