6533b839fe1ef96bd12a6697
RESEARCH PRODUCT
Game Theoretic Decentralized Feedback Controls in Markov Jump Processes
Marta ZoppelloFabio BagagioloDario BausoRosario Maggistrosubject
0209 industrial biotechnologyMathematical optimizationDecentralized routing policies; Hysteresis; Inverse control problem; Mean-field games; Optimal control; Control and Optimization; Management Science and Operations Research; Applied MathematicsControl and OptimizationStability (learning theory)02 engineering and technologyManagement Science and Operations ResearchMean-field games01 natural sciencesDecentralized routing policie020901 industrial engineering & automationControl theorySettore MAT/05 - Analisi MatematicaMean-field gameConvergence (routing)0101 mathematicsMean field gamesMathematicsEquilibrium pointSettore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e FinanziarieDecentralized routing policies; Hysteresis; Inverse control problem; Mean-field games; Optimal controlApplied MathematicsHysteresis010102 general mathematics[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Optimal controlOptimal control Mean-field games Inverse control problem Decentralized routing policies HysteresisDecentralised systemOptimal control Mean-field games Inverse control problem Decentralized routing policies HysteresisExpression (mathematics)Optimal controlTheory of computationDecentralized routing policiesHysteresiInverse control problemRouting (electronic design automation)Settore MAT/09 - Ricerca Operativadescription
This paper studies a decentralized routing problem over a network, using the paradigm of mean-field games with large number of players. Building on a state-space extension technique, we turn the problem into an optimal control one for each single player. The main contribution is an explicit expression of the optimal decentralized control which guarantees the convergence both to local and to global equilibrium points. Furthermore, we study the stability of the system also in the presence of a delay which we model using an hysteresis operator. As a result of the hysteresis, we prove existence of multiple equilibrium points and analyze convergence conditions. The stability of the system is illustrated via numerical studies.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-02-10 |