Distributed Optimal Resource Allocation Control for Heterogeneous Linear Multiagent Systems

This article investigates the continuous-time optimal distributed coordination problem with resource allocation constraints for general linear multiagent systems. The study is conducted over a connected undirected graph. By integrating the tracking controller design with global resource allocation optimization, fully distributed state-feedback controllers are proposed to solve optimization problems with output-based local objective functions. The dynamics of the entire multiagent system are well studied at the equilibrium point, which solves the optimal resource allocation and keeps system stable at the same time. The characteristics of the stable states are extracted as additional optimization constraints. By transferring the output-based optimization problem of general linear dynamics systems to a combination of a state-based optimization problem of single-integrator dynamics systems and a state tracking problem, the state equation of the system dynamics can be simplified through appropriate transformation, thereby decreasing the difficulty that brings to the performance index optimization, eliminating assumptions about the structure of the system state matrices, and achieving output stability and performance optimality simultaneously. The team performance, formed by a sum of privately known convex local objective functions and a demand for the total resource, is optimized in a fully distributed fashion. Sufficient conditions are given to ensure that the multiagent system with the proposed algorithms can reach the optimal resource allocation. Numerical simulations are provided to verify the feasibility of the controllers.