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"... A rigid interval graph is an interval graph which has only one clique tree. In 2009, Panda and Das show that all connected unit interval graphs are rigid interval graphs. Generalizing the two classic graph search algorithms, Lexicographic BreadthFirst Search (LBFS) and Maximum Cardinality Search (M ..."
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Cited by 88 (6 self)
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A rigid interval graph is an interval graph which has only one clique tree. In 2009, Panda and Das show that all connected unit interval graphs are rigid interval graphs. Generalizing the two classic graph search algorithms, Lexicographic BreadthFirst Search (LBFS) and Maximum Cardinality Search (MCS), Corneil and Krueger propose in 2008 the socalled Maximal Neighborhood Search (MNS) and show that one sweep of MNS is enough to recognize chordal graphs. We develop the MNS properties of rigid interval graphs and characterize this graph class in several different ways. This allows us obtain several linear time multisweep MNS algorithms for recognizing rigid interval graphs and unit interval graphs, generalizing a corresponding 3sweep LBFS algorithm for unit interval graph recognition designed by Corneil in 2004. For unit interval graphs, we even present a new linear time 2sweep MNS certifying recognition algorithm. Submitted:
Achieving Pareto Optimality Through Distributed Learning
, 2012
"... We propose a simple payoffbased learning rule that is completely decentralized, and that leads to an efficient configuration of actions in any nperson finite strategicform game with generic payoffs. The algorithm follows the theme of exploration versus exploitation and is hence stochastic in natu ..."
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Cited by 19 (5 self)
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We propose a simple payoffbased learning rule that is completely decentralized, and that leads to an efficient configuration of actions in any nperson finite strategicform game with generic payoffs. The algorithm follows the theme of exploration versus exploitation and is hence stochastic in nature. We prove that if all agents adhere to this algorithm, then the agents will select the action profile that maximizes the sum of the agents ’ payoffs a high percentage of time. The algorithm requires no communication. Agents respond solely to changes in their own realized payoffs, which are affected by the actions of other agents in the system in ways that they do not necessarily understand. The method can be applied to the optimization of complex systems with many distributed components, such as the routing of information in networks and the design and control of wind farms. The proof of the proposed learning algorithm relies on the theory of large deviations for perturbed Markov chains.
Designing Games for Distributed Optimization
"... Abstract — The central goal in multiagent systems is to design local control laws for the individual agents to ensure that the emergent global behavior is desirable with respect to a given system level objective. Ideally, a system designer seeks to satisfy this goal while conditioning each agent’s c ..."
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Cited by 12 (2 self)
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Abstract — The central goal in multiagent systems is to design local control laws for the individual agents to ensure that the emergent global behavior is desirable with respect to a given system level objective. Ideally, a system designer seeks to satisfy this goal while conditioning each agent’s control law on the least amount of information possible. Unfortunately, there are no existing methodologies for addressing this design challenge. The goal of this paper is to address this challenge using the field of game theory. Utilizing game theory for the design and control of multiagent systems requires two steps: (i) defining a local objective function for each decision maker and (ii) specifying a distributed learning algorithm to reach a desirable operating point. One of the core advantages of this game theoretic approach is that this two step process can be decoupled by utilizing specific classes of games. For example, if the designed objective functions result in a potential game then the system designer can utilize distributed learning algorithms for potential games to complete step (ii) of the design process. Unfortunately, designing agent objective functions to meet objectives such as locality of information and efficiency of resulting equilibria within the framework of potential games is fundamentally challenging and in many case impossible. In this paper we develop a systematic methodology for meeting these objectives using a broader framework of games termed state based potential games. State based potential games is an extension of potential games where an additional state variable is introduced into the game environment hence permitting more flexibility in our design space. Furthermore, state based potential games possess an underlying structure that can be exploited by distributed learning algorithms in a similar fashion to potential games hence providing a new baseline for our decomposition. I.
Game Theory and Distributed Control
, 2012
"... Game theory has been employed traditionally as a modeling tool for describing and influencing behavior in societal systems. Recently, game theory has emerged as a valuable tool for controlling or prescribing behavior in distributed engineered systems. The rationale for this new perspective stems fro ..."
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Cited by 3 (1 self)
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Game theory has been employed traditionally as a modeling tool for describing and influencing behavior in societal systems. Recently, game theory has emerged as a valuable tool for controlling or prescribing behavior in distributed engineered systems. The rationale for this new perspective stems from the parallels between the underlying decision making architectures in both societal systems and distributed engineered systems. In particular, both settings involve an interconnection of decision making elements whose collective behavior depends on a compilation of local decisions that are based on partial information about each other and the state of the world. Accordingly, there is extensive work in game theory that is relevant to the engineering agenda. Similarities notwithstanding, there remain important differences between the constraints and objectives in societal and engineered systems that require looking at game theoretic methods from a new perspective. This chapter provides an overview of selected recent developments of game theoretic methods in this role as a framework for distributed control in engineered systems.
Information Management in the Smart Grid: A Learning Game Approach
, 2013
"... In this article, the smart grid is modeled as a decentralized and hierarchical network, made of three categories of agents: producers, providers and microgrids. To optimize their decisions concerning the energy prices and the traded quantities of energy, the agents need to forecast the energy produc ..."
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In this article, the smart grid is modeled as a decentralized and hierarchical network, made of three categories of agents: producers, providers and microgrids. To optimize their decisions concerning the energy prices and the traded quantities of energy, the agents need to forecast the energy productions and the demand of the microgrids. The biases resulting from the decentralized learning might create imbalances between demand and supply, leading to penalties for the providers and for the producers. We determine analytically prices that provide to the producers a guarantee to avoid such penalties, reporting all the risk on the providers. Additionally, we prove that collaborative learning, through a grand coalition of providers where information is shared and forecasts aligned on a single value, minimizes their average risk. Simulations, run on a toy network, lead us to observe that the convergence rates of the collaborative learning strategy are clearly superior to rates resulting from distributed learning, using external and internal regret minimization.
Distributed Learning in the Smart Grid
, 2013
"... Abstract—In this article, the smart grid is modeled as a decentralized and hierarchical network, made of three categories of agents: producers, providers and microgrids. To optimize their decisions concerning the energy prices and the traded quantities of energy, the agents need to forecast the ener ..."
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Abstract—In this article, the smart grid is modeled as a decentralized and hierarchical network, made of three categories of agents: producers, providers and microgrids. To optimize their decisions concerning the energy prices and the traded quantities of energy, the agents need to forecast the energy productions and the demand of the microgrids. The biases resulting from the decentralized learning might create imbalances between demand and supply, leading to penalties for the providers and for the producers. We determine analytically prices that provide to the producers a guarantee to avoid such penalties, reporting all the risk on the providers. Additionally, we prove that collaborative learning, through a grand coalition of providers where information is shared and forecasts aligned on a single value, minimizes their average risk. Simulations, run on a toy network, lead us to observe that the convergence rates of the collaborative learning strategy are clearly superior to rates resulting from distributed learning, using external and internal regret minimization.
Constrained Distributed Optimization Based on Population Dynamics
"... Abstract—This paper proposes a novel methodology for solving constrained optimization problems in a distributed way, inspired by population dynamics and adding dynamics to the population masses. The proposed methodology divides the problem into smaller problems, whose feasible regions vary over time ..."
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Abstract—This paper proposes a novel methodology for solving constrained optimization problems in a distributed way, inspired by population dynamics and adding dynamics to the population masses. The proposed methodology divides the problem into smaller problems, whose feasible regions vary over time achieving an agreement to solve the global problem. The methodology also guarantees attraction to the feasible region and allows to have few changes in the decisionmaking design, when the network suffers the addition or removal of nodes. Simulation results are presented in order to illustrate several cases. I.
Author manuscript, published in "ValueTools 2012, Cargèse: France (2012)" Distributed Learning in Hierarchical Networks
, 2012
"... Abstract—In this article, we propose distributed learning based approaches to study the evolution of a decentralized hierarchical system, an illustration of which is the smart grid. Smart grid management requires the control of nonrenewable energy production and the integration of renewable energie ..."
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Abstract—In this article, we propose distributed learning based approaches to study the evolution of a decentralized hierarchical system, an illustration of which is the smart grid. Smart grid management requires the control of nonrenewable energy production and the integration of renewable energies which might be highly unpredictable. Indeed, their production levels rely on uncontrolable factors such as sunshine, wind strength, etc. First, we derive optimal control strategies on the nonrenewable energy productions and compare competitive learning algorithms to forecast the energy needs of the end users. Second, we introduce an online learning algorithm based on regret minimization enabling the agents to forecast the production of renewable energies. Additionally, we define organizations of the market promoting collaborative learning which generate higher performance for the whole smart grid than full competition.
Game Theory and Distributed Control
, 2012
"... Game theory has been employed traditionally as a modeling tool for describing and influencing behavior in societal systems. Recently, game theory has emerged as a valuable tool for controlling or prescribing behavior in distributed engineered systems. The rationale for this new perspective stems fro ..."
Abstract
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Game theory has been employed traditionally as a modeling tool for describing and influencing behavior in societal systems. Recently, game theory has emerged as a valuable tool for controlling or prescribing behavior in distributed engineered systems. The rationale for this new perspective stems from the parallels between the underlying decision making architectures in both societal systems and distributed engineered systems. In particular, both settings involve an interconnection of decision making elements whose collective behavior depends on a compilation of local decisions that are based on partial information about each other and the state of the world. Accordingly, there is extensive work in game theory that is relevant to the engineering agenda. Similarities notwithstanding, there remain important differences between the constraints and objectives in societal and engineered systems that require looking at game theoretic methods from a new perspective. This chapter provides an overview of selected recent developments of game theoretic methods in this role as a framework for distributed control in engineered systems.
Evolutionarygamebased
"... dynamical tuning for multiobjective model predictive control J. BarreiroGomez, C. OcampoMartinez and N. Quijano Abstract Model predictive control (MPC) is one of the most used optimizationbased control strategies for largescale systems, since this strategy allows to consider a large number of s ..."
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dynamical tuning for multiobjective model predictive control J. BarreiroGomez, C. OcampoMartinez and N. Quijano Abstract Model predictive control (MPC) is one of the most used optimizationbased control strategies for largescale systems, since this strategy allows to consider a large number of states and multiobjective cost functions in a straightforward way. One of the main issues in the design of multiobjective MPC controllers, which is the tuning of the weights associated to each objective in the cost function, is treated in this work. All the possible combinations of weights within the cost function affect the optimal result in a given Pareto front. Furthermore, when the system has timevarying parameters, e.g., periodic disturbances, the appropriate weight tuning might also vary over time. Moreover, taking into account the computational burden and the selected sampling time in the MPC controller design, the computation time to find a suitable tuning is limited. In this regard, the development of strategies to perform a dynamical tuning in function of the system conditions potentially