Corpus ID: 220935989

Quantifying and managing uncertainty in piecewise-deterministic Markov processes

@article{Cartee2020QuantifyingAM,
  title={Quantifying and managing uncertainty in piecewise-deterministic Markov processes},
  author={Elliot Cartee and Antonio Farah and A. Nellis and Jacob Van Hook and A. Vladimirsky},
  journal={arXiv: Optimization and Control},
  year={2020}
}
In piecewise-deterministic Markov processes (PDMP) the state of a finite-dimensional system evolves dynamically, but the evolutive equation may change randomly as a result of discrete switches. A running cost is integrated along the corresponding piecewise-deterministic trajectory up to the termination to produce the cumulative cost of the process. We address three natural questions related to uncertainty in cumulative cost of PDMP models: (1) how to compute the Cumulative Distribution Function… Expand
2 Citations
Optimal Path-Planning with Random Breakdowns
We propose a model for path-planning based on a single performance metric that accurately accounts for the the potential (spatially inhomogeneous) cost of breakdowns and repairs. These randomExpand
Stochastic Optimal Control of a Sailboat
In match race sailing, competitors must steer their boats upwind in the presence of unpredictably evolving weather. Combined with the tacking motion necessary to make upwind progress, this makes itExpand

References

SHOWING 1-10 OF 41 REFERENCES
Deterministic control of randomly-terminated processes
We consider both discrete and continuous "uncertain horizon" deterministic control processes, for which the termination time is a random variable. We examine the dynamic programming equations for theExpand
Control of piecewise-deterministic processes via discrete-time dynamic programming
TLDR
It is shown that an optimal stationary policy exists in relaxed controls under certain continuity assumptions and that a discounted infinite horizon control problem can be reformulated as a discrete-time Markov decision problem. Expand
Optimal control of piecewise deterministic markov process
The trajectories of piecewise deterministic Markov processes are solutions of an ordinary (vector)differential equation with possible random jumps between the different integral curves. BothExpand
Piecewise-Deterministic Optimal Path Planning
We consider piecewise-deterministic optimal control problems in which the environment randomly switches among several deterministic modes, and the goal is to optimize the expected cost up to theExpand
Probabilistic planning with non-linear utility functions and worst-case guarantees
TLDR
This work provides a Dynamic Programming algorithm to compute the optimal policy, and introduces an admissible heuristic to effectively prune the search space and uses a stochastic shortest path problem on large real-world road networks to demonstrate the practical applicability of this method. Expand
Controlled Markov processes and viscosity solutions
This book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. The authors approach stochastic control problemsExpand
Piecewise deterministic Markov processes applied to fatigue crack growth modelling
In this paper, we use a particular piecewise deterministic Markov process (PDMP) to model the evolution of a degradation mechanism that may arise in various structural components, namely, the fatigueExpand
Threshold dynamics and ergodicity of an SIRS epidemic model with Markovian switching
Abstract This work studies the threshold dynamics and ergodicity of a stochastic SIRS epidemic model with the disease transmission rate driven by a semi-Markov process. The semi-Markov process usedExpand
A dynamic contagion process
We introduce a new point process, the dynamic contagion process, by generalising the Hawkes process and the Cox process with shot noise intensity. Our process includes both self-excited andExpand
AN EFFICIENT METHOD FOR MULTIOBJECTIVE OPTIMAL CONTROL AND OPTIMAL CONTROL SUBJECT TO INTEGRAL CONSTRAINTS
We introduce a new and efficient numerical method for mul- ticriterion optimal control and single criterion optimal control under in- tegral constraints. The approach is based on extending the stateExpand
...
1
2
3
4
5
...