The averaging principle for perturbations of continuous timecontrol problems with fast controlled jump parametersRachid

نویسندگان

  • Rachid El Azouzi
  • Eitan Altman
  • Vladimir Gaitsgory
چکیده

We consider a class of singularly perturbed zero-sum diier-ential games with piecewise deterministic dynamics, where the changes from one structure (for the dynamics) to another are governed by a nite-state Markov process. Player 1 controls the continuous dynamics, whereas Player 2 controls the rate of transition for the nite-state Markov process; both have access to the states of both processes. Player 1 wishes to minimize a given quantity. For player 2, we consider two possible scenarios: one in which it wishes to minimize the same quantity (team framework), and one in which it wishes to maximize it (zero sum game). The transition rates of the Markov process are fast, of the order of 1==. To solve the above problem, we use the dynamic programming approach. In particular, we study the asymptotic properties of the underlying system for suuciently small. The viscosity solution method is employed to verify the convergence of the value function, which allows us to obtain the convergence in a general setting and helps us to characterize the structure of the limit system. We apply this to the special case of linear quadratic games with jump parameters , which allows us to obtain an explicit solution for the limiting problem.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Comparison of the immediate and delayed effects of two dry needle methods fast in fast out and winding in gastrocnemius muscle trigger points on lower extremity function and pain in non-professional athletes: A randomized controlled clinical trial

Introduction: The objective of this study was to compare two methods of dry needle treatment in active trigger points of Gastrocnemius muscle on pain and height jump in non-professional athletes. Materials and Methods: Forty male athletes were selected with active trigger points in each Gastrocnemius muscle. Relatively, subjects were assigned randomly in two conventional dry needle piston metho...

متن کامل

Averaging in Dynamical Systems: Some Classical and New Results

The averaging setup arises in the study of perturbations of parametric families of dynamical systems when parameters start changing slowly in time. This situation arises in perturbations of Hamiltonian systems when integrals of motion, e.g. energy, start changing slowly, i.e. we arrive at a double scale system with fast motions along constant energy manifolds of the unperturbed system and with ...

متن کامل

An Averaging Principle for Fast Degrees of Freedom Exhibiting Long-Term Correlations

This article is concerned with the averaging principle and its extensions for stochastic dynamical systems with fast and slow degrees of freedom. It is demonstrated how the “conventional” averaging principle results from asymptotic multiscale analysis, how one can construct an indicator for its (in-)appropriateness, and how, if inappropriate, it may be extended into an improved approximation. T...

متن کامل

Averaging and Large Deviation Principles for Fully–coupled Piecewise Deterministic Markov Processes and Applications to Molecular Motors

We consider Piecewise Deterministic Markov Processes (PDMPs) with a finite set of discrete states. In the regime of fast jumps between discrete states, we prove a law of large number and a large deviation principle. In the regime of fast and slow jumps, we analyze a coarse–grained process associated to the original one and prove its convergence to a new PDMP with effective force fields and jump...

متن کامل

Voltage Regulation of DC-DC Series Resonant Converter Operating in Discontinuous Conduction Mode: The Hybrid Control Approach

Dynamic modeling and control of dc-dc series resonant converter (SRC) especially when operating in discontinuous conduction mode (DCM) is still a challenge in power electronics. Due to semiconductors switching, SRC is naturally represented as a switched linear system, a class of hybrid systems. Nevertheless, the hybrid nature of the SRC is commonly neglected and it is modeled as a purely contin...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007