Achieving Convex Optimization Within Prescribed Time for Networked Euler-Lagrange Systems: A Novel Adaptive
IEEE Transactions on Cybernetics
|October 2, 2025
Summary
This study introduces adaptive controllers for prescribed-time distributed convex optimization in networked Euler-Lagrange systems. It ensures faster convergence than existing methods for complex network optimization problems.
Area of Science:
- Control Systems Engineering
- Networked Systems
- Optimization Theory
Background:
- Networked Euler-Lagrange systems (NELSs) present challenges in distributed optimization.
- Existing methods often rely on asymptotic or finite-time convergence, which can be insufficient.
- Distributed convex optimization (DCO) is crucial for coordinated control in NELSs.
Purpose of the Study:
- To address the prescribed-time distributed convex optimization (DCO) problem for NELSs.
- To develop novel adaptive controllers for achieving convergence within a specific time frame.
- To enhance system performance beyond traditional asymptotic or finite-time stabilization.
Main Methods:
- Construction of auxiliary systems utilizing local gradient information and inter-agent communication.
- Reformulation of the DCO problem as a prescribed-time stabilization task.
- Development of a prescribed-time small-gain criterion for system analysis.
- Design of adaptive prescribed-time local tracking controllers with time-varying gains.
- Application of Lyapunov functions and prescribed-time mapping for stability analysis.
Main Results:
- A novel prescribed-time small-gain criterion is proposed for interconnected systems.
- Adaptive prescribed-time local tracking controllers are designed for NELS subsystems.
- Prescribed-time convergence is achieved using time-varying gains approaching infinity at the deadline.
- Prescribed-time stability of the closed-loop system and boundedness of internal signals are proven.
- Theoretical results are validated via a numerical example.
Conclusions:
- The proposed approach effectively solves the prescribed-time DCO problem for NELSs.
- The novel small-gain criterion offers enhanced stability analysis for interconnected systems.
- Adaptive controllers provide a robust solution for achieving rapid convergence in networked optimization.
- This work advances control strategies for systems requiring timely optimization outcomes.
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