Constrained distributed optimization: A population dynamics approach

Barreiro-Gómez, Julian; Quijano, Nicanor; Ocampo‐Martínez, Carlos

doi:10.1016/j.automatica.2016.02.004

Cited by 56 publications

(50 citation statements)

References 28 publications

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“…In order to perform the partitioning of the system, first it is established a time τ that satisfies Remark 2, which defines when the proper topology is evaluated 3 . Every time τ , the Shapley value Φ( ) of all the players ∈ V is computed by using the low-computational-cost operation with the factor Θ.…”

Section: Partitioning Proceduresmentioning

confidence: 99%

“…For instance in [16], an application of non-cooperative game theory can be found, where a distributed control strategy based on the convergence to a Nash equilibrium is proposed [24]. Furthermore, convergence to Nash equilibrium by using evolutionary-game theory has been used in the design of control and optimization strategies [3][26] [39]. On the other hand, cooperative game theory has been used for example in [6], where a coalitional control approach is introduced, or in [18], where a control scheme considering different network topologies is presented.…”

Section: Introductionmentioning

confidence: 99%

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Non-centralized control for flow-based distribution networks: A game-theoretical insight

Barreiro-Gómez

Ocampo‐Martínez

Quijano

et al. 2017

Journal of the Franklin Institute

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This paper solves a data-driven control problem for a flow-based distribution network with two objectives: a resource allocation and a fair distribution of costs. These objectives represent both cooperation and competition directions. It is proposed a solution that combines either a centralized or distributed cooperative game approach using the Shapley value to determine a proper partitioning of the system and a fair communication cost distribution. On the other hand, a decentralized noncooperative game approach computing the Nash equilibrium is used to achieve the control objective of the resource allocation under a non-complete information topology. Furthermore, an invariant-set property is presented and the closed-loop system stability is analyzed for the non-cooperative game approach. Another contribution regarding the cooperative game approach is an alternative way to compute the Shapley value for the proposed specific characteristic function. Unlike the classical cooperative-games approach, which has a limited application due to the combinatorial explosion issues, the alternative method allows calculating the Shapley value in polynomial time and hence can be applied to large-scale problems.

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Section: Partitioning Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non-centralized control for flow-based distribution networks: A game-theoretical insight

Barreiro-Gómez

Ocampo‐Martínez

Quijano

et al. 2017

Journal of the Franklin Institute

Self Cite

View full text Add to dashboard Cite

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“…Some applications of EGT in engineering problems can be found along different fields. For instance, wind farms control [20], [21], multiple access control for communication systems [22], cyber security [23], combinatorial optimization [24], bandwidth allocation [25], hierarchical frequency control in microgrids [26], dispatch of electric generators [27], building temperature control [28], constrained extremum seeking [29], and control of drinking water networks [30], among others.There are three main advantages of using EGT in engineering problems. The first motivation is that the analogy between games and engineering problems is straightforward in a large variety of cases.…”

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confidence: 99%

“…In this regard, it has been proven that, under certain conditions, the Nash equilibrium satisfies the Karush-KuhnTucker (KKT) first-order conditions of constrained optimization problems [13]. This property has been exploited in many works such as [30], where distributed optimization problems are addressed by using potential games and population dynamics. In [33], a general analysis of statebased potential games is presented and the growing interest in the application of game-theoretic methods to the design and control of multi-agent systems is discussed.…”

mentioning

confidence: 99%

“…In the case of distributed population dynamics, additional conditions are required. These conditions are related to the location of the Nash equilibrium inside the simplex ∆, and the connectivity of the graph that models the strategy-constrained interactions of the individuals within the population.Convergence properties of population games have been exploited in engineering applications during the last few years (see [29], [30] and references therein). This fact is mainly given since there exists an equivalence between the Nash equilibria of a full-potential game and the arguments that maximize its potential function.…”

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confidence: 99%

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The Role of Population Games and Evolutionary Dynamics in Distributed Control Systems: The Advantages of Evolutionary Game Theory

et al. 2017

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Recently, there has been an increasing interest in studying large-scale distributed systems in the control community. Efforts have been invested in developing several techniques wishing to address the main challenges found in this kind of problems, for instance, the amount of information to guarantee the proper operation of the system and the economic costs associated to the required communication structure. Moreover, another issue appears when there is a large amount of required data to control the system. The measuring and transmission processes, and the computation of the control inputs make closed-loop systems suffer from high computational burden.One way to overcome such problems is to consider the use of multi-agent systems framework, which may be cast in game-theoretical terms. Game theory studies interactions between self-interested agents. Particularly, this theory tackles with the problem of interaction between agents using different strategies that wish to maximize their welfares. For instance in [1], the authors provide connections between games, optimization, and learning for signal processing in networks. Other approaches in terms of learning and games can be found in [2]. In [3], distributed computation algorithms are developed based on generalized convex games that do not require full information, and where there is a dynamic change in terms of network topologies. Applications of game theory in control of optical networks and game-theoretic methods for smart grids are described in [4], [5], [6]. Another approach in game theoretical methods is to design protocols or mechanisms that possess some desirable properties [7]. This approach leads to a broad analysis of multi-agent interactions, particularly those involving negotiation and coordination problems [8]. Other game-theoretical applications to engineering are reported in [9].From a game-theoretical perspective, it can be distinguished among three types of games: matrix games, continuous games, and differential/dynamic games (see "The relationship among matricial games, full-potential population games, and resource allocation problems"). In matrix games (that generally use the normal form), individuals play simultaneously and only once, and the decision is mainly based on a static terms. In this case, players or agents are individually treated. Differently, in continuous games, players have infinitely many pure strategies [10], [11]. On the other hand, in dynamic games it is assumed that players can use some type of learning mechanism that allows them to adjust the actions taken based on their past decisions. Basically, it can be said that dynamic games are characterized by three main problems: i) how to model the environment where players interact; ii) how to model the objectives of players; and iii) how to specify the order in which the actions are taken and how much information each player possesses. In this case, it is assumed that there are interactions between large number of agents (which are usually unknown) [12].Among these dynamic game...

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Hybrid online learning control in networked multiagent systems: A survey

Poveda

Benosman

Teel

2018

Adaptive Control & Signal

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This survey paper studies deterministic control systems that integrate three of the most active research areas during the last years: (1) online learning control systems, (2) distributed control of networked multiagent systems, and (3) hybrid dynamical systems (HDSs). The interest for these types of systems has been motivated mainly by two reasons: First, the development of cheap massive computational power and advanced communication technologies, which allows to carry out large computations in complex networked systems, and second, the recent development of a comprehensive theory for HDSs that allows to integrate continuous-time dynamical systems and discrete-time dynamical systems in a unified manner, thus providing a unifying modeling language for complex learning-based control systems. In this paper, we aim to give a comprehensive survey of the current state of the art in the area of online learning control in multiagent systems, presenting an overview of the different types of problems that can be addressed, as well as the most representative control architectures found in the literature. These control architectures are modeled as HDSs, which include as special subsets continuous-time dynamical systems and discrete-time dynamical systems. We highlight the different advantages and limitations of the existing results as well as some interesting potential future directions and open problems. KEYWORDSadaptive control, hybrid dynamical systems, learning, multiagent systems, networked systems 228One of the fields where control systems with learning and adaptation have recently seen increased attention is in the area of networked multiagent systems (MAS), 16,17 which are systems comprised of multiple interacting subsystems, each subsystem having individual dynamics and computational capabilities as well as limited sensing, communication, and actuation. Depending on the structure of the underlying communication graph between the agents of the system, MAS can be centralized or decentralized. In a centralized MAS, there exists one central agent which has access to the state information of all other agents and which is able to compute the control action for all agents of the system. On the other hand, in a decentralized or distributed MAS, agents individually compute their own control signals, which are shared with a subset of the other agents characterized by a communication graph. Figure 1 illustrates three MASs with different communication graphs. Centralized MASs are typically not scalable, and they present the disadvantage of having a single point of failure that could potentially shut down the complete system. 16 Decentralized and distributed systems, on the other hand, are scalable and more robust, and in nonstationary environments, they allow for adaptation and self-organization of the system. 18 Recent technological advances in communication and computation have made MAS ubiquitous, and today, they can be found in several engineering systems such as in power generation and distribution systems, 19-21 teams of ...

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Constrained distributed optimization: A population dynamics approach

Cited by 56 publications

References 28 publications

Non-centralized control for flow-based distribution networks: A game-theoretical insight

Non-centralized control for flow-based distribution networks: A game-theoretical insight

The Role of Population Games and Evolutionary Dynamics in Distributed Control Systems: The Advantages of Evolutionary Game Theory

Hybrid online learning control in networked multiagent systems: A survey

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