The distributed biased min-consensus protocol revisited: pre-specified finite time control strategies and small-gain based analysis

Yuanqiu Mo; He Wang

Home/Archive/arXiv

arXiv · 2405.08599

The distributed biased min-consensus protocol revisited: pre-specified finite time control strategies and small-gain based analysis

Yuanqiu Mo·He Wang

View original source ↗Read source document ↗Export metadata ↓

Abstract

Unlike the classical distributed consensus protocols enabling the group of agents as a whole to reach an agreement regarding a certain quantity of interest in a distributed fashion, the distributed biased min-consensus protocol (DBMC) has been proven to generate advanced complexity pertaining to solving the shortest path problem. As such a protocol is commonly incorporated as the first step of a hierarchical architecture in real applications, e.g., robots path planning, management of dispersed computing services, an impedance limiting the application potential of DBMC lies in, the lack of results regarding to its convergence within a user-assigned time. In this paper, we first propose two control strategies ensuring the state error of DBMC decrease exactly to zero or a desired level manipulated by the user, respectively. To compensate the high feedback gains incurred by these two control strategies, this paper further investigates the nominal DBMC itself. By leveraging small gain based stability tools, this paper also proves the global exponential input-to-state stability of DBMC, outperforming its current stability results. Simulations have been provided to validate the efficacy of our theoretical result.

Explore related subjects

eess.SY cs.SY math.OC

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Yuanqiu Mo, He Wang. 2024-05-14. The distributed biased min-consensus protocol revisited: pre-specified finite time control strategies and small-gain based analysis. https://arxiv.org/abs/2405.08599

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

KEEP EXPLORING

Related papers

arXiv2026

Ensuring Stability of Non-Minimal Modes in Input-Output Data-Driven Representation

Many recent data-driven control approaches for linear time-invariant systems are based on output trajectory prediction using input-output data matrices. The system dynamics described by this predictor, which we refer to as the input-output data-driven representation, yields non-unique autoregressive with exogenous inputs (ARX) models having possibly unstable non-minimal modes. In this note, we show that the stability of these non-minimal modes is ensured by a certain choice of ARX model, which coincides with the minimum-norm least-squares predictor using the Moore-Penrose inverse of the data matrix. This stability guarantee holds regardless of the underlying system's stability. Moreover, the stability persists under sufficiently small noise in data when a suitably truncated Moore-Penrose inverse is used. Consequently, the ARX model need not be reduced to the true system order in order to avoid unstable additional modes.

eess.SY↗

arXiv2026

Optimization-Based Formation Flight on Libration Point Orbits

A model predictive control (MPC) framework is developed for station-keeping in spacecraft formation flight along libration point orbits. At each control period, the MPC policy solves a multi-vehicle optimal control problem (MVOCP) that tracks a reference trajectory, while enforcing path constraints on the relative motion of the formation. The control policy makes use of a limited set of control nodes consistent with operational constraints that allow only a small number of maneuver opportunities per revolution. To promote recursive feasibility, path constraints are progressively tightened across the prediction horizon. An isoperimetric reformulation of the constraints is used to prevent inter-sample violations. The resulting MVOCP is a nonconvex program, which is solved via sequential convex programming. The proposed approach is evaluated in a high-fidelity ephemeris model under uncertainties for a formation along the near-rectilinear halo orbit (NRHO), and subject to path constraints on inter-spacecraft separation and relative Sun phase angle. The results demonstrate maintenance of a spacecraft formation that satisfies the path constraints with realistic cumulative propellant consumption.

eess.SY↗

arXiv2026

Certificates Synthesis for A Class of Observational Properties in Stochastic Systems: A Unified Approach

In this paper, we investigate the probabilistic formal verification of stochastic dynamical systems over continuous state spaces. Motivated by problems in state estimation and information-flow security, we introduce the notion of observational properties, which characterize the inferences an external observer can draw from system outputs. These properties are formulated as probabilistic hyperproperties based on HyperLTL over finite traces, yielding a unified framework that subsumes several existing notions studied separately in the literature. We reduce the verification problem to reachability analysis over an augmented structure that integrates the system dynamics with an automaton representation of the specification. Building on this construction, we develop stochastic barrier certificates that provide probabilistic guarantees for property satisfaction while avoiding explicit state-space discretization. The effectiveness of the proposed framework is demonstrated through a case study.

eess.SY↗