4,246 research outputs found
Singularly perturbed forward-backward stochastic differential equations: application to the optimal control of bilinear systems
We study linear-quadratic stochastic optimal control problems with bilinear
state dependence for which the underlying stochastic differential equation
(SDE) consists of slow and fast degrees of freedom. We show that, in the same
way in which the underlying dynamics can be well approximated by a reduced
order effective dynamics in the time scale limit (using classical
homogenziation results), the associated optimal expected cost converges in the
time scale limit to an effective optimal cost. This entails that we can well
approximate the stochastic optimal control for the whole system by the reduced
order stochastic optimal control, which is clearly easier to solve because of
lower dimensionality. The approach uses an equivalent formulation of the
Hamilton-Jacobi-Bellman (HJB) equation, in terms of forward-backward SDEs
(FBSDEs). We exploit the efficient solvability of FBSDEs via a least squares
Monte Carlo algorithm and show its applicability by a suitable numerical
example
Adaptive Robust Optimization with Dynamic Uncertainty Sets for Multi-Period Economic Dispatch under Significant Wind
The exceptional benefits of wind power as an environmentally responsible
renewable energy resource have led to an increasing penetration of wind energy
in today's power systems. This trend has started to reshape the paradigms of
power system operations, as dealing with uncertainty caused by the highly
intermittent and uncertain wind power becomes a significant issue. Motivated by
this, we present a new framework using adaptive robust optimization for the
economic dispatch of power systems with high level of wind penetration. In
particular, we propose an adaptive robust optimization model for multi-period
economic dispatch, and introduce the concept of dynamic uncertainty sets and
methods to construct such sets to model temporal and spatial correlations of
uncertainty. We also develop a simulation platform which combines the proposed
robust economic dispatch model with statistical prediction tools in a rolling
horizon framework. We have conducted extensive computational experiments on
this platform using real wind data. The results are promising and demonstrate
the benefits of our approach in terms of cost and reliability over existing
robust optimization models as well as recent look-ahead dispatch models.Comment: Accepted for publication at IEEE Transactions on Power System
Ergodic Mean Field Games with H\"ormander diffusions
We prove existence of solutions for a class of systems of subelliptic PDEs
arising from Mean Field Game systems with H\"ormander diffusion. These results
are motivated by the feedback synthesis Mean Field Game solutions and the Nash
equilibria of a large class of -player differential games
Evolutionary Poisson Games for Controlling Large Population Behaviors
Emerging applications in engineering such as crowd-sourcing and
(mis)information propagation involve a large population of heterogeneous users
or agents in a complex network who strategically make dynamic decisions. In
this work, we establish an evolutionary Poisson game framework to capture the
random, dynamic and heterogeneous interactions of agents in a holistic fashion,
and design mechanisms to control their behaviors to achieve a system-wide
objective. We use the antivirus protection challenge in cyber security to
motivate the framework, where each user in the network can choose whether or
not to adopt the software. We introduce the notion of evolutionary Poisson
stable equilibrium for the game, and show its existence and uniqueness. Online
algorithms are developed using the techniques of stochastic approximation
coupled with the population dynamics, and they are shown to converge to the
optimal solution of the controller problem. Numerical examples are used to
illustrate and corroborate our results
Model of cybersecurity means financing with the procedure of additional data obtaining by the protection side
The article describes the model of cybersecurity means financing strategies of the information object with incomplete information about the financial resources of the attacking side. The proposed model is the core of the module of the developed decision support system in the problems of choosing rational investing variants for information protection and cybersecurity of various information objects. The model allows to find financial solutions using the tools of the theory of multistep games with several terminal surfaces. The authors proposed an approach that allows information security management to make a preliminary assessment of strategies for financing the effective cybersecurity systems. The model is distinguished by the assumption that the protection side does not have complete information, both about the financing strategies of the attacking side, and about its financial resources state aimed at overcoming cybersecurity lines of the information object. At the same time, the protection side has the opportunity to obtain additional information by the part of its financial resources. This makes it possible for the protection side to obtain a positive result for itself in the case when it can not be received without this procedure. The solution was found using a mathematical apparatus of a nonlinear multistep quality game with several terminal surfaces with alternate moves. In order to verify the adequacy of the model there was implemented a multivariate computational experiment. The results of this experiment are described in the article. © 2005 - ongoing JATIT & LL
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