The interaction of interest-coupled decision-makers and the uncertainty of individual behavior are prominent characteristics of multiagent systems (MAS). How to break through the framework of conventional control theory, which aims at single decision-maker and single decision objective, and to extend the methodology and tools in the stochastic adaptive control theory to analyze MAS are of great significance. In this paper, a preliminary exploration is made in this direction, and the decentralized control problem is considered for large population stochastic MAS with coupled cost functions. Different from the deterministic discounted costs in the existing differential game models, a time-averaged stochastic cost function is adopted for each agent. The decentralized control law is constructed based on the state aggregation method and tracking-like quadratic optimal control. By using probability limit theory, the stability and optimality of the closed-loop system are analyzed. The main contributions of this paper include the following points. 1) The concepts of asymptotic Nash-equilibrium in probability and almost surely, respectively, are introduced and the relationship between these concepts is illuminated, which provide necessary tools for analyzing the optimality of the decentralized control laws. 2) The closed-loop system is shown to be almost surely uniformly stable, and bounded independently of the number of agents N . 3) The population state average (PSA) is shown to converge to the infinite population mean (IPM) trajectory in the sense of both L2-norm and time average almost surely, as N increases to infinity. 4) The decentralized control law is designed and shown to be almost surely asymptotically optimal; the cost of each agent based on local measurements converges to that based on global measurements almost surely, as N increases to infinity.

/pdf/asymptotically-optimal-decentralized-control-for-large-112xc5h4ib.pdf

Asymptotically Optimal Decentralized Control for Large Population Stochastic Multiagent Systems

Cloud computing is an emerging paradigm which allows the on-demand delivering of software, hardware, and data as services. As cloud-based services are more numerous and dynamic, the development of efficient service provisioning policies become increasingly challenging. Game theoretic approaches have shown to gain a thorough analytical understanding of the service provisioning problem.In this paper we take the perspective of Software as a Service (SaaS) providers which host their applications at an Infrastructure as a Service (IaaS) provider. Each SaaS needs to comply with quality of service requirements, specified in Service Level Agreement (SLA) contracts with the end-users, which determine the revenues and penalties on the basis of the achieved performance level. SaaS providers want to maximize their revenues from SLAs, while minimizing the cost of use of resources supplied by the IaaS provider. Moreover, SaaS providers compete and bid for the use of infrastructural resources. On the other hand, the IaaS wants to maximize the revenues obtained providing virtualized resources. In this paper we model the service provisioning problem as a Generalized Nash game, and we propose an efficient algorithm for the run time management and allocation of IaaS resources to competing SaaSs.

/pdf/a-game-theoretic-formulation-of-the-service-provisioning-2f10h62ifv.pdf

A game theoretic formulation of the service provisioning problem in cloud systems

https://www-sop.inria.fr/members/Eitan.Altman/PAPERS/tania-routing-2links.pdf

Routing into Two Parallel Links

Typical congestion control algorithms for high speed networks include local flow controllers at the bottleneck nodes. In this paper an H/sup /spl infin// based controller is developed for rate feedback in a single bottleneck network. The rates can be assigned to the sources only after a certain transmission delay. Controller design specifications for this time delay system include "fairness" to multiple users, "usage" optimization, and minimization of the transients in the queue length. Stability robustness against uncertainties in time delays is also considered. By a simple algebra the problem is transformed to an H/sup /spl infin// control of a plant with a time delay, and it is solved by using an algorithm developed earlier for this class of problems.

On rate-based congestion control in high speed networks: design of an H/sup /spl infin// based flow controller for single bottleneck

In this contribution, a new method to design multi-loop control systems with several controllers is proposed. Controllers are assumed to be players of a cooperative dynamic game, whose solution is obtained by multi-objective optimization (MOO). The MOO problem is solved by applying a genetic algorithm and the final solution is found from an optimal Pareto set. As illustrative example, the control system design of a reverse osmosis desalination plant is used. Simulation results are satisfactory and show that in many cases, as for example this desalination plant, multi-loop control with several controllers, which have been obtained by join multi-objective optimization, perform as good as more complex controllers but with less implementation effort.

A New Approach to Design Multi-loop Control Systems with Multiple Controllers

Flow and congestion control allow the users of a telecommunication network to regulate the traffic they send into the network according to the quality of service that they require. The flow control may be performed by the network, as is the case in ATM networks, or by the users themselves, as is the case in the Internet (TCP/IP). We consider in this paper both cases using optimal control techniques. For the first case, we obtain a formulation of a dynamic team problem. The second case is handled by dynamic non-cooperative game techniques. We establish the existence and uniqueness of a Nash equilibrium, and compute the corresponding performance measures and (dynamic) equilibrium policies. We further show that when the users update their policies in a greedy manner, not knowing a priori the utilities of the other players, their policies converge to the Nash equilibrium.

Multi-user rate-based flow control: distributed game-theoretic algorithms

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Multi-user rate-based flow control: distributed game-theoretic algorithms