Semiglobal Input-Delay Tolerance Algorithm for Distributed Nonconvex Optimization of Networked Nonlinear Systems
For control systems researchers, this work addresses the challenging coupling between input delays and nonlinear dynamics in distributed optimization, but the semiglobal nature and reliance on the Polyak-Łojasiewicz condition limit its generality.
This paper tackles distributed nonconvex optimization in networked nonlinear systems with input delays, achieving semiglobal convergence to the optimal solution under consensus constraints. The proposed SIDT algorithm is validated on nonlinear systems with input delays.
This paper studies a class of distributed optimization problems in networked nonlinear systems (NNSs) subject to input delays and consensus constraints. It introduces input-delay tolerant semiglobal convergence (IDTSC), meaning that for any prescribed compact initial set there exists an admissible delay bound under which the optimal solution is computed within consensus constraints and all node states converge to the solution. Building on a hierarchical design and input-to-state stability analysis, a new semiglobal input-delay tolerant (SIDT) algorithm is developed that practically achieves IDTSC for distributed optimization under the coupling between input delays and nonlinear dynamics. Further, by relaxing strict convexity requirements through the Polyak-Łojasiewicz condition, the SIDT algorithm broadens its applicability to nonconvex optimization. Finally, numerical experiments corroborate the theory on NNSs with input delays.