A Decentralized Markovian Jump ${\cal H}_{\infty}$ Control Routing Strategy for Mobile Multi-Agent Networked Systems

Abstract

This paper presents a Markovian jump linear (MJL) system framework for developing routing algorithms in mobile ad hoc networks (MANETs) that encounter changes in the number of nodes and/or the number of destinations. A unified <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">${\cal H}_{\infty}$</tex></formula> control strategy is proposed by representing the dynamically changing destination nodes as singular switching control systems. A decentralized routing scheme is proposed and designed for the networked multi-agent system in presence of unknown time-varying delays. To solve the corresponding optimization problem the physical constraints are expressed as linear matrix inequality (LMI) conditions. The resulting decentralized <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\cal H}_{\infty}$</tex> </formula> routing control schemes for both regular and singular MJL systems are shown to formally achieve the desired performance specifications and requirements. Simulation results are presented to illustrate and demonstrate the effectiveness of our proposed novel routing control strategies.