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Exponential stability of shallow water equations with arbitrary time dependent action

International Journal of Dynamics and Control 2014年第3期2卷 247-253页

作者： Dia, Ben Mansour SRI Center for Uncertainty Quantification in Computational Science and Engineering CEMSE King Abdullah University of Sciences and Technology Thuwal23955-6900 Saudi Arabia

In this paper, we examine an exponential stability result in L2- norm of the classical solution of shallow water equations. By using Riemann analysis with sub-critical flow condition, we show that only one boundary control law suffices to achieve the exponential stability. For that, we provide a sufficient dissipative condition as second order polynomial inequality with respect to the boundary control law which relies on the setting of a non-increasing arbitrary action. © 2014, Springer-Verlag Berlin Heidelberg.

关键词： Equations of motion

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A stochastic maximum principle for risk-sensitive mean-field type control

A stochastic maximum principle for risk-sensitive mean-field...

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作者： Djehiche, Boualem Tembine, Hamidou Tempone, Raul Department of Mathematics KTH Royal Institute of Technology Stockholm100 44 Sweden Center for Interdisciplinary Studies in Security and Privacy Electrical and Computer Engineering Polytechnic School of Engineering New York University NY10003 United States Division of Engineering Saadiyat Island New York University Abu Dhabi Abu Dhabi United Arab Emirates SRI Uncertainty Quantification Center in Computational Science and Engineering CEMSE King Abdullah University of Science and Technology Thuwai Jeddah23955-6900 Saudi Arabia

In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends the risk-sensitive SMP (without mean-field coupling) of Lim and Zhou (2005), derived for feedback (or Markov) type optimal controls, to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. In our approach to the risk-sensitive SMP, the smoothness assumption on the value-function imposed in Lim and Zhou (2005) needs not be satisfied. For a general action space a Peng's type SMP is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type SMP under linear stochastic dynamics with exponential quadratic cost function. Explicit solutions are given for both mean-field free and mean-field models. © 1963-2012 IEEE.

关键词： Maximum principle

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Nonasymptotic mean-field games 19

Nonasymptotic mean-field games

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19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014

作者： Tembine, Hamidou KAUST Strategic Research Initiative Center for Uncertainty Quantification in Computational Science and Engineering CEMSE KAUST Saudi Arabia

ISBN: (纸本)9783902823625

Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networked systems with few entities. In this paper we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through a dynamic auction with asymmetric valuation distributions. © IFAC.

关键词： Game theory

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Cooperative mean-field type games 19

Cooperative mean-field type games

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19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014

作者： Cissé, Abdoul Karim Tembine, Hamidou GrIIsG - ISG International Business School Paris France SRI - Center for Uncertainty Quantification in Computational Science and Engineering CEMSE KAUST Saudi Arabia

ISBN: (纸本)9783902823625

In the standard formulation of a game, a player's payoff function depends on the states and actions of all the players. Yet, real world applications suggest to consider also a functional of the probability measure of states and actions of all the players. In this paper, we consider cooperative mean-field type games in which the state dynamics and the payoffs depend not only on the state and actions but also on their probability measure. We establish stochastic maximum principle and provide a time-dependent payoff allocation procedure for coalitions. The allocated payoff considers not only fairness property but also the cost of making the coalition. Finally, time consistency and subgame perfectness solution concept equations are established. © IFAC.

关键词： Stochastic systems

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Fast distributed strategic learning for global optima in queueing access games 19

Fast distributed strategic learning for global optima in que...

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19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014

作者： Tembine, Hamidou KAUST Strategic Research Initiative Center for Uncertainty Quantification in Computational Science and Engineering CEMSE KAUST Saudi Arabia

ISBN: (纸本)9783902823625

In this paper we examine combined fully distributed payoff and strategy learning (CODIPAS) in a queue-aware access game over a graph. The classical strategic learning analysis relies on vanishing or small learning rate and uses stochastic approximation tool to derive steady states and invariant sets of the underlying learning process. Here, the stochastic approximation framework does not apply due to non-vanishing learning rate. We propose a direct proof of convergence of the process. Interestingly, the convergence time to one of the global optima is almost surely finite and we explicitly characterize the convergence time. We show that pursuit-based CODIPAS learning is much faster than the classical learning algorithms in games. We extend the methodology to coalitional learning and proves a very fast formation of coalitions for queue-aware access games where the action space is dynamically changing depending on the location of the user over a graph. © IFAC.

关键词： Learning algorithms

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Cooperative Mean-Field Type Games

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IFAC Proceedings Volumes 2014年第3期47卷 8995-9000页

作者： Abdoul Karim Cissé Hamidou Tembine GrIIsG - ISG International Business School Paris France SRI – Center for Uncertainty Quantification in Computational Science & Engineering CEMSE KAUST

关键词： Mean-field type cooperation stochastic maximum principle subgame perfection

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Fast Distributed Strategic Learning for Global Optima in Queueing Access Games

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IFAC Proceedings Volumes 2014年第3期47卷 7055-7060页

作者： Hamidou Tembine KAUST Strategic Research Initiative Center for Uncertainty Quantification in Computational Science and Engineering CEMSE KAUST

关键词： Coalitional learning queue access control

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Nonasymptotic Mean-Field Games

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IFAC Proceedings Volumes 2014年第3期47卷 8989-8994页

作者： Hamidou Tembine KAUST Strategic Research Initiative Center for Uncertainty Quantification in Computational Science and Engineering CEMSE KAUST

关键词： non-asymptotic mean-field game theory

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Demand response scheme based on lottery-like rebates 19

Demand response scheme based on lottery-like rebates

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19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014

作者： Schwartz, Galina A. Tembine, Hamidou Amin, Saurabh Sastry, S. Shankar Department of Electrical Engineering and Computer Science University of California BerkeleyCA United States SRI - Center for Uncertainty Quantification in Computational Science Engineering CEMSE KAUST United States Department of Civil and Environmental Engineering Massachusetts Institute of Technology CambridgeMA United States

ISBN: (纸本)9783902823625

In this paper, we develop a novel mechanism for reducing volatility of residential demand for electricity We construct a reward-based (rebate) mechanism that provides consumers with incentives to shift their demand to off-peak time. In contrast to most other mechanisms proposed in the literature, the key feature of our mechanism is its modest requirements on user preferences, i.e., it does not require exact knowledge of user responsiveness to rewards for shifting their demand from the peak to the off-peak time. Specifically, our mechanism utilizes a probabilistic reward structure for users who shift their demand to the off-peak time, and is robust to incomplete information about user demand and/or risk preferences. We approach the problem from the public good perspective, and demonstrate that the mechanism can be implemented via lottery-like schemes. Our mechanism permits to reduce the distribution losses, and thus improve efficiency of electricity distribution. Finally, the mechanism can be readily incorporated into the emerging demand response schemes (e.g., the time-of-day pricing, and critical peak pricing schemes), and has security and privacy-preserving properties. © IFAC.

关键词： Data privacy

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A Stochastic Maximum Principle for Risk-Sensitive Mean-Field-Type Control

A Stochastic Maximum Principle for Risk-Sensitive Mean-Field...

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IEEE Annual Conference on Decision and Control

作者： Boualem Djehiche Hamidou Tembine Raul Tempone Department of Mathematics KTH Royal Institute of Technology Stockholm Sweden SRI Uncertainty Quantification Center in Computational Science and Engineering CEMSE KAUST KSA

ISBN: (纸本)9781467360890

In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle for optimal control of stochastic differential equations of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. For a general action space a Peng's type stochastic maximum principle is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type under linear stochastic dynamics with exponential quadratic cost function. Explicit characterizations are given for both mean-field free and mean-field risk-sensitive models.

关键词： Equations Stochastic processes Optimal control Process control Mathematical model Couplings Yttrium

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