2,764 research outputs found
Different Approaches on Stochastic Reachability as an Optimal Stopping Problem
Reachability analysis is the core of model checking of time systems. For
stochastic hybrid systems, this safety verification method is very little supported mainly
because of complexity and difficulty of the associated mathematical problems. In this
paper, we develop two main directions of studying stochastic reachability as an optimal
stopping problem. The first approach studies the hypotheses for the dynamic programming
corresponding with the optimal stopping problem for stochastic hybrid systems.
In the second approach, we investigate the reachability problem considering approximations
of stochastic hybrid systems. The main difficulty arises when we have to prove the
convergence of the value functions of the approximating processes to the value function
of the initial process. An original proof is provided
Dynamic Management of Portfolios with Transaction Costs under Tychastic Uncertainty.
We use in this chapter the viability/capturability approach for studying the problem of dynamic valuation and management of a portfolio with transaction costs in the framework of tychastic control systems (or dynamical games against nature) instead of stochastic control systems. Indeed, the very definition of the guaranteed valuation set can be formulated directly in terms of guaranteed viable-capture basin of a dynamical game. Hence, we shall ācomputeā the guaranteed viable-capture basin and find a formula for the valuation function involving an underlying criterion, use the tangential properties of such basins for proving that the valuation function is a solution to Hamilton-Jacobi-Isaacs partial differential equations. We then derive a dynamical feedback providing an adjustment law regulating the evolution of the portfolios obeying viability constraints until it achieves the given objective in finite time. We shall show that the PujalāSaint-Pierre viability/capturability algorithm applied to this specific case provides both the valuation function and the associated portfolios.dynamic games; dynamic valuation; tychastic control systems; management of portfolio;
Controlled diffusion processes
This article gives an overview of the developments in controlled diffusion
processes, emphasizing key results regarding existence of optimal controls and
their characterization via dynamic programming for a variety of cost criteria
and structural assumptions. Stochastic maximum principle and control under
partial observations (equivalently, control of nonlinear filters) are also
discussed. Several other related topics are briefly sketched.Comment: Published at http://dx.doi.org/10.1214/154957805100000131 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Cloud-Based Centralized/Decentralized Multi-Agent Optimization with Communication Delays
We present and analyze a computational hybrid architecture for performing
multi-agent optimization. The optimization problems under consideration have
convex objective and constraint functions with mild smoothness conditions
imposed on them. For such problems, we provide a primal-dual algorithm
implemented in the hybrid architecture, which consists of a decentralized
network of agents into which centralized information is occasionally injected,
and we establish its convergence properties. To accomplish this, a central
cloud computer aggregates global information, carries out computations of the
dual variables based on this information, and then distributes the updated dual
variables to the agents. The agents update their (primal) state variables and
also communicate among themselves with each agent sharing and receiving state
information with some number of its neighbors. Throughout, communications with
the cloud are not assumed to be synchronous or instantaneous, and communication
delays are explicitly accounted for in the modeling and analysis of the system.
Experimental results are presented to support the theoretical developments
made.Comment: 8 pages, 4 figure
On Singular Control Problems with State Constraints and Regime-Switching: A Viscosity Solution Approach
This paper investigates a singular stochastic control problem for a
multi-dimensional regime-switching diffusion process confined in an unbounded
domain. The objective is to maximize the total expected discounted rewards from
exerting the singular control. Such a formulation stems from application areas
such as optimal harvesting multiple species and optimal dividends payments
schemes in random environments. With the aid of weak dynamic programming
principle and an exponential transformation, we characterize the value function
to be the unique constrained viscosity solution of a certain system of coupled
nonlinear quasi-variational inequalities. Several examples are analyzed in
details to demonstrate the main results
A unified framework for hybrid control : b background, model, and theory
Caption title. "April 1994: Revised June 1994."Includes bibliographical references (p. 24-25).Supported by the Army Research Office and the Center for Intelligent Control Systems. DAAL03-92-G-0164 DAAL03-92-G-0115Michael S. Branicky, Vivek S. Borkar, Sanjoy K. Mitter
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