Multi-Agent Consensus Based Distributed Optimization over Undirected Networks with Time Varying Cost Function Using Dynamic Inversion
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Authors
Keshani, Ali
Date
2024-08-01
Type
thesis
Language
eng
Keyword
Distributed optimization , Dynamic inversion , Multi-agent systems , PI-consensus
Alternative Title
Abstract
This research aims to address the challenging problem of distributed optimization over an undirected network of agents, concerning minimization of a global objective function formed by the sum of local convex time-varying cost functions possessed by each agent. Due to the decentralized nature of the optimization process, a number of local problems arise when each agent in the network is tasked with minimizing its own cost function. However, these local problems are interconnected through the network structure, as agents exchange information and collaborate to reach a consensus on the optimal solution.
To solve this problem, we develop a consensus approach which implements a dynamic inversion method to enhance computational efficiency and ensure convergence towards an optimal solution. By utilizing this method, we can use an estimation of the inverse of local Hessian matrices that bypasses the need for explicit calculations. We demonstrate that the proposed technique significantly reduces the computational cost while preserving the accuracy of the optimization process.
Furthermore, this approach has been coupled with a PI-based consensus algorithm which acts as a control mechanism, ensuring that all agents converge to a common solution that minimizes the global cost function. This integration enhances the convergence properties of the consensus approach, promoting effective collaboration among the distributed agents.
Mathematical foundation of our method has been rigorously established, providing theoretical evidence for its functionality and convergence guarantees. In addition, we conducted a comprehensive numerical analysis and simulation study, demonstrating the performance and effectiveness of our method in solving the distributed optimization problem over an arbitrary undirected network.