Search results for "Stochastic control"
showing 10 items of 11 documents
Dynamic Demand and Mean-Field Games
2017
Within the realm of smart buildings and smart cities,\ud dynamic response management is playing an ever-increasing\ud role thus attracting the attention of scientists from different\ud disciplines. Dynamic demand response management involves a\ud set of operations aiming at decentralizing the control of loads\ud in large and complex power networks. Each single appliance\ud is fully responsive and readjusts its energy demand to the\ud overall network load. A main issue is related to mains frequency\ud oscillations resulting from an unbalance between supply and\ud demand. In a nutshell, this paper contributes to the topic by\ud equipping each signal consumer with strategic insight. In particu…
Advanced stochastic control systems with engineering applications
2014
1 School of Astronautics, Harbin Institute of Technology, Harbin, Heilongjiang, China 2 School of Electrical and Electronic Engineering, The University of Adelaide, SA 5005, Australia 3 Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway 4 Institute of Automation and Complex Systems, University of Duisburg-Essen, Duisburg, Germany 5 College of Automation, Chongqing University, Chongqing 400044, China
Robust linear quadratic mean-field games in crowd-seeking social networks.
2013
We consider a social network where opinions evolve following a stochastic averaging process under the influence of adversarial disturbances. We provide a robust mean-field game model in the spirit of H∞-optimal control, establish existence of a mean-field equilibrium, and analyze its stochastic stability.
Stochastic acceleration in generalized squared Bessel processes
2015
We analyze the time behavior of generalized squared Bessel processes, which are useful for modeling the relevant scales of stochastic acceleration problems. These nonstationary stochastic processes obey a Langevin equation with a non-Gaussian multiplicative noise. We obtain the long-time asymptotic behavior of the probability density function for non-Gaussian white and colored noise sources. We find that the functional form of the probability density functions is independent of the statistics of the noise source considered. Theoretical results are in good agreement with those obtained by numerical simulations of the Langevin equation with pulse noise sources.
A Fokker–Planck control framework for multidimensional stochastic processes
2013
AbstractAn efficient framework for the optimal control of probability density functions (PDFs) of multidimensional stochastic processes is presented. This framework is based on the Fokker–Planck equation that governs the time evolution of the PDF of stochastic processes and on tracking objectives of terminal configuration of the desired PDF. The corresponding optimization problems are formulated as a sequence of open-loop optimality systems in a receding-horizon control strategy. Many theoretical results concerning the forward and the optimal control problem are provided. In particular, it is shown that under appropriate assumptions the open-loop bilinear control function is unique. The res…
On stability and dissipativity of stochastic nonlinear systems
2012
Input-to-state stability of nonlinear control system is described in several different manners, and has been a central concept since the equivalences among them were verified. In this paper, a framework of stability and dissipativity for stochastic control systems is constructed on the maximal existence interval of behaviors (states and external inputs), by the aid of stochastic Barbalat lemma and stochastic dissipativity. The main work consists of three aspects. First, input-to-state stability and robust stability are extended to the stochastic case, and several criteria are established. Second, two forms of dissipativity and their criteria are presented. Third, the key relations among the…
Solving fully randomized first-order linear control systems: Application to study the dynamics of a damped oscillator with parametric noise under sto…
2022
[EN] This paper is devoted to study random linear control systems where the initial condition, the final target, and the elements of matrices defining the coefficients are random variables, while the control is a stochastic process. The so-called Random Variable Transformation technique is adapted to obtain closed-form expressions of the probability density functions of the solution and of the control. The theoretical findings are applied to study the dynamics of a damped oscillator subject to parametric noise.
European Option Pricing and Hedging with Both Fixed and Proportional Transaction Costs
2003
Abstract In this paper we provide a systematic treatment of the utility based option pricing and hedging approach in markets with both fixed and proportional transaction costs: we extend the framework developed by Davis et al. (SIAM J. Control Optim., 31 (1993) 470) and formulate the option pricing and hedging problem. We propose and implement a numerical procedure for computing option prices and corresponding optimal hedging strategies. We present a careful analysis of the optimal hedging strategy and elaborate on important differences between the exact hedging strategy and the asymptotic hedging strategy of Whalley and Wilmott (RISK 7 (1994) 82). We provide a simulation analysis in order …
American Option Pricing and Exercising with Transaction Costs
2005
In this paper we examine the problem of finding the reservation option prices and corresponding exercise policies of American options in a market with proportional transaction costs using the utility based approach proposed by Davis and Zariphopoulou (1995). We present a model where the option holder has a constant absolute risk aversion. We discuss the numerical algorithm and propose a new characterization of the option holder's value function. We suggest original discretization schemes for computing reservation prices and exercise policies of American options. The discretization schemes are implemented for the cases of American put and call options. We present the study of the optimal tra…
Stochastic Control Problems
2003
The general theory of stochastic processes originated in the fundamental works of A. N. Kolmogorov and A. Ya. Khincin at the beginning of the 1930s. Kolmogorov, 1938 gave a systematic and rigorous construction of the theory of stochastic processes without aftereffects or, as it is customary to say nowadays, Markov processes. In a number of works, Khincin created the principles of the theory of so-called stationary processes.