1,309 research outputs found
On gradual-impulse control of continuous-time Markov decision processes with multiplicative cost
In this paper, we consider the gradual-impulse control problem of
continuous-time Markov decision processes, where the system performance is
measured by the expectation of the exponential utility of the total cost. We
prove, under very general conditions on the system primitives, the existence of
a deterministic stationary optimal policy out of a more general class of
policies. Policies that we consider allow multiple simultaneous impulses,
randomized selection of impulses with random effects, relaxed gradual controls,
and accumulation of jumps. After characterizing the value function using the
optimality equation, we reduce the continuous-time gradual-impulse control
problem to an equivalent simple discrete-time Markov decision process, whose
action space is the union of the sets of gradual and impulsive actions
Numerical method for impulse control of Piecewise Deterministic Markov Processes
This paper presents a numerical method to calculate the value function for a
general discounted impulse control problem for piecewise deterministic Markov
processes. Our approach is based on a quantization technique for the underlying
Markov chain defined by the post jump location and inter-arrival time.
Convergence results are obtained and more importantly we are able to give a
convergence rate of the algorithm. The paper is illustrated by a numerical
example.Comment: This work was supported by ARPEGE program of the French National
Agency of Research (ANR), project "FAUTOCOES", number ANR-09-SEGI-00
Average Continuous Control of Piecewise Deterministic Markov Processes
This paper deals with the long run average continuous control problem of
piecewise deterministic Markov processes (PDMP's) taking values in a general
Borel space and with compact action space depending on the state variable. The
control variable acts on the jump rate and transition measure of the PDMP, and
the running and boundary costs are assumed to be positive but not necessarily
bounded. Our first main result is to obtain an optimality equation for the long
run average cost in terms of a discrete-time optimality equation related to the
embedded Markov chain given by the post-jump location of the PDMP. Our second
main result guarantees the existence of a feedback measurable selector for the
discrete-time optimality equation by establishing a connection between this
equation and an integro-differential equation. Our final main result is to
obtain some sufficient conditions for the existence of a solution for a
discrete-time optimality inequality and an ordinary optimal feedback control
for the long run average cost using the so-called vanishing discount approach.Comment: 34 page
Maintenance optimization with piecewise deterministic Markov processes
International audienc
Piecewise deterministic Markov process for condition-based imperfect maintenance models
In this paper, a condition-based imperfect maintenance model based on
piecewise deterministic Markov process (PDMP) is constructed. The degradation
of the system includes two types: natural degradation and random shocks. The
natural degradation is deterministic and can be nonlinear. The damage increment
caused by a random shock follows a certain distribution, and its parameters are
related to the degradation state. Maintenance methods include corrective
maintenance and imperfect maintenance. Imperfect maintenance reduces the
degradation degree of the system according to a random proportion. The
maintenance action is delayed, and the system will suffer natural degradations
and random shocks while waiting for maintenance. At each inspection time, the
decision-maker needs to make a choice among planning no maintenance, imperfect
maintenance and perfect maintenance, so as to minimize the total discounted
cost of the system. The impulse optimal control theory of PDMP is used to
determine the optimal maintenance strategy. A numerical study dealing with
component coating maintenance problem is presented. Relationship with optimal
threshold strategy is discussed. Sensitivity analyses on the influences of
discount factor, observation interval and maintenance cost to the discounted
cost and optimal actions are presented.Comment: 34 pages, 28 figure
- …