Semiglobal Input-Delay Tolerance Algorithm for Distributed Nonconvex Optimization of Networked Nonlinear Systems

2026-06-19 · Source: cs.MA updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems · Depth: Expert, extended

Summary

A novel Semiglobal Input-Delay Tolerant (SIDT) algorithm addresses distributed optimization in networked nonlinear systems (NNSs) subject to input delays and consensus constraints. This algorithm practically achieves Input-Delay Tolerant Semiglobal Convergence (IDTSC), ensuring optimal solutions are computed and node states converge within constraints, given an admissible delay bound tied to the initial condition set. Built on a hierarchical design and input-to-state stability analysis, the SIDT algorithm extends its applicability to nonconvex optimization by leveraging the Polyak-Łojasiewicz (P-Ł) condition, relaxing strict convexity. Numerical experiments on a 5-node NNS with x_dot_i(t) = x_i^2(t) + u_i(t-d) and control parameters vartheta=0.1, varepsilon=11, k_0=0.1 demonstrate its efficacy for both convex (optimal solution x*=-1.47) and nonconvex (optimal solution x*=1.4) problems, with initial radius r=5 and delays up to 0.05 and 0.03 respectively.

Key takeaway

For control engineers designing distributed optimization systems in networked nonlinear environments, you should consider the Semiglobal Input-Delay Tolerant (SIDT) algorithm. It offers a robust solution for both convex and nonconvex problems, even with input delays, by guaranteeing semiglobal convergence within an admissible delay margin. Implement this delay-independent controller to manage physical state regulation and optimization simultaneously, but be mindful that increasing gains or network size can reduce delay tolerance.

Key insights

The SIDT algorithm enables distributed optimization in networked nonlinear systems despite input delays and nonconvexity.

Principles

• Input delays can undermine stability in nonlinear systems.
• Semiglobal convergence links initial conditions to delay tolerance.
• Polyak-Łojasiewicz condition broadens nonconvex applicability.

Method

The SIDT algorithm uses a hierarchical design and input-to-state stability theory. It formulates control inputs based on delayed states, incorporating consensus and gradient terms, and is delay-independent.

In practice

• Apply to sensor networks and robotics.
• Manage economic dispatch in smart grids.
• Use sat_sigma(s) to mitigate chattering.

Topics

• Distributed Optimization
• Networked Nonlinear Systems
• Input Delay Tolerance
• Nonconvex Optimization
• Polyak-Łojasiewicz Condition
• Control Systems

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.MA updates on arXiv.org.