Abstract

This research aims to introduce an analytical solution to the routing problem of Networked Multi-Agent Systems (NMAS) by taking advantage of control theory machinery. Routing problem can be defined as that of finding a route for messages among networked agents by adjusting the output flow of each link according to the traffic information of the network, such that some objective functions are minimized. In this research, a new objective function, namely worst-case queueing length is introduced based on which a novel routing methodology is presented. The propagating, transmitting and processing delays are inevitable characteristics of the queueing dynamics which is considered in the model of the network. The proposed dynamic optimization problem is formulated as a feedback control problem. First, a centralized [Special characters omitted.] optimal control scheme is proposed which can maintain a robust performance of the routing strategy in the presence of multiple and unknown time-varying delays for a fixed network topology. The routing problem is formulated as an [Special characters omitted.] optimal control problem for a time-delayed system. The resulting optimization problem is then recast as a minimization problem involving Linear Matrix Inequality (LMI) constraints. The physical constraints are also formulated as LMI feasibility conditions. The proposed centralized routing scheme is then reformulated in a decentralized framework. This modification yields an algorithm that, obtains the "fastest route", provides robustness against multiple unknown time-varying delays, and enhances the scalability of the algorithm to large scale traffic networks. By stochastically changing the network topology due to the nodes' mobility the overall network model is described by a Markovian jump process. The proposed Markovian jump dynamics can also support changing number of nodes due to adding new nodes to the network or deleting them because of their low energy or faults/failures. The resulting problem which involves Markovian jump dynamics due to the time-varying delays appearing in control is more challenging to solve. The problem is further complicated by the fact that the interconnected terms also change at each switching mode. To stabilize this system, an [Special characters omitted.] controller is presented for the Markovian jump system for mode-dependent interconnected terms. Finally, the LMIs corresponding to the associated physical constrains are properly modified for the mobile networks.