Using Viscosity Solution for Approximations in Piecewise Deterministic Control Systems
نویسندگان
چکیده
In 15] a numerical approximation scheme is proposed for the solution of piecewise deterministic control systems (PDCS). This approximation scheme is based on a time discretization which reformulates the original PDCS into a stochastic program. In this paper we prove the convergence of the approximating vector value function to the vector value function of the original PDCS as the discretization's step tends to zero.
منابع مشابه
An Optimal L-minimization Algorithm for Stationary Hamilton-jacobi Equations
We describe an algorithm for solving steady Hamilton-Jacobi equations in dimension one using a L-minimization technique on piecewise linear approximations. The algorithm is proved to have optimal complexity and to give approximations that converge to the viscosity solution of the problem. Numerical results are presented to illustrate the performance of the method.
متن کاملViability, Invariance and Reachability for Controlled Piecewise Deterministic Markov Processes Associated to Gene Networks
We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techni...
متن کاملOptimal Control of Nonlinear Systems with Controlled Transitions
This paper studies the optimum stochastic control problem with piecewise deterministic dynamics. The controls enter through the system dynamics as well as the transitions for the underlying Markov chain process, and are allowed to depend on both the continuous state and the current state of the Markov chain. The paper shows that the feedback optimal control relies on the viscosity solutions of ...
متن کاملAnalytic Solution for Hypersonic Flow Past a Slender Elliptic Cone Using Second-Order Perturbation Approximations
An approximate analytical solution is obtained for hypersonic flow past a slender elliptic cone using second-order perturbation techniques in spherical coordinate systems. The analysis is based on perturbations of hypersonic flow past a circular cone aligned with the free stream, the perturbations stemming from the small cross-section eccentricity. By means of hypersonic approximations for the ...
متن کاملSolution examples of an impulse control problem
Optimal impulse control problems were introduced by Bensoussan and Lions [5] and then formalized by other authors. In the past decades, many studies related to this problem have been reported in [2, 3, 10, 12]. These studies showed the existence of an optimal strategy but it seems that an explicit form of this optimal strategy is often missing. Barles showed in [4] that the optimal cost functio...
متن کاملذخیره 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 1988