Distributed Resource Allocation Algorithm for General Linear Multiagent Systems

Abstract

We focus on the optimal resource allocation problems with global equality constraints and convex function inequality constraints over heterogeneous linear multi-agent systems. The resource allocation problem aims to minimize the total objective function through neighboring information exchange. First, based on the state variable information, Karush-Kuhn-Tucker(KKT) conditions, and proportionalintegral control concept, we propose an initialization-free distributed optimization algorithm, where each agent is driven by the gradient(subgradient) of its local objective function and local constraint convex function. In addition, the penalty factor control parameter is changed adaptively. Next, we propose an output-based distributed optimization algorithm that uses a Luenberger observer when the state variable is not accessible. Based on Lyapunov stability, it is proved that the proposed algorithms converge to the optimal solution of the resource allocation problem. Finally, simulation examples are used to demonstrate the effectiveness of the proposed algorithms.

A Distributed Resource Allocation Algorithm for the General Linear Multiagent Systems

“…Mathematical Problems in Engineering e LaSalle's invariant principle is widely used in the algorithm design of the distributed optimization problem, such as the distributed optimal coordinated problem [9] and distributed optimal resource allocation problem [10,13,14,[16][17][18]27]. erefore, we provide the LaSalle's invariant principle in the following lemma.…”

“…e output variable y i is actually unconstrained in [39]. Although the same problem is solved in [27] under a milder rank condition, the designed algorithm depends on an equality C i B i K i � C i A i , and thus, the designed algorithm can be reduced to a first-order multiagent system. Also because of this equality, the designed algorithm will diverge as time goes to infinity.…”

“…is equality is difficult to hold strictly, and then the small deviations may lead to system divergence. In addition, the event-triggered communication is also not considered in [27].…”

“…Practically, agents' decisions are subject to some local constraints, such as the security considered in robots and the production capacity of the generator in smart grids. Although a novel adaptive distributed algorithm is proposed in [27] based on the Karush-Kuhn-Tucker (KKT) condition, the proposed algorithm tends to diverge as time goes to infinity. In addition, with the continuous expansion of multiagent systems' scale, each agent's communication burden becomes heavier and heavier.…”

Predefined‐time distributed event‐triggered algorithms for resource allocation

“…[30], and the adaptive distributed algorithm for the general linear multi‐agent systems in Ref. [31]. However, all the above continuous‐time algorithms converge to the optimal global solution with an asymptotic or exponential convergence rate.…”