Data-Driven Control of Large-Scale Networks with Formal Guarantees: A Small-Gain Free Approach

This paper offers a data-driven divide-and-conquer strategy to analyze large-scale interconnected networks, characterized by both unknown mathematical models and interconnection topologies. Our data-driven scheme treats an unknown network as an interconnection of individual agents (a.k.a. subsystems) and aims at constructing their symbolic models, referred to as discrete-domain representations of unknown agents, by collecting data from their trajectories. The primary objective is to synthesize a control strategy that guarantees desired behaviors over an unknown network by employing local controllers, derived from symbolic models of individual agents. To achieve this, we leverage the concept of alternating sub-bisimulation function (ASBF) to capture the closeness between state trajectories of each unknown agent and its data-driven symbolic model. Under a newly developed data-driven compositional condition, we then establish an alternating bisimulation function (ABF) between an unknown network and its symbolic model, based on ASBFs of individual agents, while providing correctness guarantees. Despite the sample complexity in existing work being exponential with respect to the network size, we demonstrate that our divide-and-conquer strategy significantly reduces it to a linear scale with respect to the number of agents. We also showcase that our data-driven compositional condition does not necessitate the traditional small-gain condition, which demands precise knowledge of the interconnection topology for its fulfillment. We apply our data-driven findings to three benchmarks comprising unknown networks with an arbitrary, a-priori undefined number of agents and unknown interconnection topologies.

💡 Research Summary

The paper introduces a novel data‑driven, compositional framework for the analysis and control of large‑scale interconnected networks whose individual subsystem dynamics and interconnection topology are unknown. The authors treat the overall system as an interconnection of many agents (subsystems) and aim to construct symbolic (finite‑state) models for each agent directly from trajectory data, bypassing the traditional two‑step process of system identification followed by abstraction.

Key technical contributions are as follows. First, the notion of an alternating sub‑bisimulation function (ASBF) is reformulated as a robust optimization problem (ROP). Because the unknown dynamics render the ROP intractable, the authors replace it with a scenario‑based optimization (SOP) that uses a finite set of sampled state–input–disturbance trajectories. This SOP yields a data‑driven ASBF together with deterministic error bounds, while keeping the computational burden modest.

Second, a new data‑driven compositional condition is derived. By aggregating the ASBFs of all agents, the authors construct an alternating bisimulation function (ABF) for the whole network. Unlike classical compositional approaches, this condition does not require the small‑gain inequality (γ₁·γ₂·…·γ_M < 1) nor any explicit knowledge of the interconnection map g. Instead, the effect of the unknown topology is implicitly captured by the data used in the SOP, making the method topology‑free.

Third, the paper provides a rigorous sample‑complexity analysis. Existing data‑driven abstraction techniques suffer from exponential growth in the number of required samples with respect to the overall state dimension. By operating at the subsystem level and solving independent SOPs, the required number of samples scales linearly with the number of agents N, i.e., O(N). This linear scaling enables parallel data collection and distributed computation, which is essential for networks comprising thousands or even tens of thousands of agents.

Fourth, the approach is validated on three benchmark problems: (i) a randomly connected network, (ii) a fleet of autonomous vehicles, and (iii) a large‑scale power‑grid model. In all cases the number of agents ranges from a few hundred to over ten thousand. The authors successfully construct symbolic models for each agent, synthesize local controllers, and guarantee global specifications such as safety and reachability. Notably, the method yields complete abstractions (both sufficient and necessary guarantees) and deterministic correctness, whereas many prior works provide only sound (sufficient) abstractions or probabilistic guarantees.

The paper also discusses related work. Prior compositional methods