Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$ -Nash Equilibria
01 Sep 2007-IEEE Transactions on Automatic Control (Institute of Electrical and Electronics Engineers (IEEE))-Vol. 52, Iss: 9, pp 1560-1571
TL;DR: A state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv-Nash equilibrium property and a stability property of the mass behavior is established.
Abstract: We consider linear quadratic Gaussian (LQG) games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs. A state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv-Nash equilibrium property. A stability property of the mass behavior is established, and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques.
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TL;DR: In this article, the authors reviewed some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006 and proposed several promising research directions along with some open problems that are deemed important for further investigations.
Abstract: This paper reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles, and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations.
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TL;DR: In this paper, the authors reviewed some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006, and proposed several promising research directions along with some open problems that are deemed important for further investigations.
Abstract: This article reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, task assignment, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations.
1,655 citations
TL;DR: The McKean-Vlasov NCE method presented in this paper has a close connection with the statistical physics of large particle systems: both identify a consistency relationship between the individual agent at the microscopic level and the mass of individuals at the macroscopic level.
Abstract: We consider stochastic dynamic games in large population conditions where multiclass agents are weakly coupled via their individual dynamics and costs. We approach this large population game problem by the so-called Nash Certainty Equivalence (NCE) Principle which leads to a decentralized control synthesis. The McKean-Vlasov NCE method presented in this paper has a close connection with the statistical physics of large particle systems: both identify a consistency relationship between the individual agent (or particle) at the microscopic level and the mass of individuals (or particles) at the macroscopic level. The overall game is decomposed into (i) an optimal control problem whose Hamilton-Jacobi-Bellman (HJB) equation determines the optimal control for each individual and which involves a measure corresponding to the mass effect, and (ii) a family of McKean-Vlasov (M-V) equations which also depend upon this measure. We designate the NCE Principle as the property that the resulting scheme is consistent (or soluble), i.e. the prescribed control laws produce sample paths which produce the mass effect measure. By construction, the overall closed-loop behaviour is such that each agent’s behaviour is optimal with respect to all other agents in the game theoretic Nash sense.
1,195 citations
01 Jan 2011
TL;DR: Conceptual frameworks for actively involving highly distributed loads in power system control actions and some of the challenges to achieving a load control scheme that balances device- level objectives with power system-level objectives are discussed.
Abstract: This paper discusses conceptual frameworks for actively involving highly distributed loads in power system control actions. The context for load control is established by providing an overview of system control objectives, including economic dispatch, automatic generation control, and spinning reserve. The paper then reviews existing initiatives that seek to develop load control programs for the provision of power system services. We then discuss some of the challenges to achieving a load control scheme that balances device-level objectives with power system-level objectives. One of the central premises of the paper is that, in order to achieve full responsiveness, direct load control (as opposed to price response) is required to enable fast time scale, predictable control opportunities, especially for the provision of ancillary services such as regulation and contingency reserves. Centralized, hierarchical, and distributed control architectures are discussed along with benefits and disadvantages, especially in relation to integration with the legacy power system control architecture. Implications for the supporting communications infrastructure are also considered. Fully responsive load control is illustrated in the context of thermostatically controlled loads and plug-in electric vehicles.
1,105 citations
01 Oct 2006
TL;DR: In this article, the authors considered a large population game with weakly coupled agents and proposed the so-called Nash Certainty Equivalence (NCE) principle, which leads to a decentralized control synthesis.
Abstract: We consider stochastic dynamic games in large population conditions where multiclass agents are weakly coupled via their individual dynamics and costs. We approach this large population game problem by the so-called Nash Certainty Equivalence (NCE) Principle which leads to a decentralized control synthesis. The McKean-Vlasov NCE method presented in this paper has a close connection with the statistical physics of large particle systems: both identify a consistency relationship between the individual agent (or particle) at the microscopic level and the mass of individuals (or particles) at the macroscopic level. The overall game is decomposed into (i) an optimal control problem whose Hamilton-Jacobi-Bellman (HJB) equation determines the optimal control for each individual and which involves a measure corresponding to the mass effect, and (ii) a family of McKean-Vlasov (M-V) equations which also depend upon this measure. We designate the NCE Principle as the property that the resulting scheme is consistent (or soluble), i.e. the prescribed control laws produce sample paths which produce the mass effect measure. By construction, the overall closed-loop behaviour is such that each agent’s behaviour is optimal with respect to all other agents in the game theoretic Nash sense.
986 citations
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"Large-Population Cost-Coupled LQG P..." refers methods in this paper
...Instead of a direct continuum population modeling, we induce a probability distribution on a parameter space via empirical statistics; this approach avoids certain measurability difficulties arising in continuum population modeling [ 19 ]....
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