scholarly journals Utilisation de densites des premier passage en commande optimale stochastique

1988 ◽  
Vol 20 (1) ◽  
pp. 231-234 ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Optimal Control ◽  
Gaussian Processes ◽  
Mathematical Expectation ◽  
First Time

A theorem that gives the optimal control of Gaussian processes using the mathematical expectation of a function of the time and the place where the uncontrolled processes hit the boundary of the stopping region for the first time is proved. The result obtained in this note is an extension of a theorem due to Whittle.

scholarly journals Utilisation de densites des premier passage en commande optimale stochastique

1988 ◽  
Vol 20 (01) ◽  
pp. 231-234
Author(s):  
Mario Lefebvre
Keyword(s):  
Optimal Control ◽  
Gaussian Processes ◽  
Mathematical Expectation ◽  
First Time

A theorem that gives the optimal control of Gaussian processes using the mathematical expectation of a function of the time and the place where the uncontrolled processes hit the boundary of the stopping region for the first time is proved. The result obtained in this note is an extension of a theorem due to Whittle.

Commande optimale du processus de wiener

1989 ◽  
Vol 26 (1) ◽  
pp. 50-57 ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Optimal Control ◽  
Wiener Process ◽  
Mathematical Expectation ◽  
Optimal Value ◽  
The Moment ◽  
First Time

The problem of the optimal control of the Wiener process in Rn is considered. The optimal value of the control is obtained from the mathematical expectation of a quantity defined in terms of the moment and the place where the uncontrolled process hits the boundary of the continuation region for the first time. Explicit results are presented.

Commande optimale du processus de wiener

1989 ◽  
Vol 26 (01) ◽  
pp. 50-57
Author(s):  
Mario Lefebvre
Keyword(s):  
Optimal Control ◽  
Wiener Process ◽  
Mathematical Expectation ◽  
Optimal Value ◽  
The Moment ◽  
First Time

The problem of the optimal control of the Wiener process in Rn is considered. The optimal value of the control is obtained from the mathematical expectation of a quantity defined in terms of the moment and the place where the uncontrolled process hits the boundary of the continuation region for the first time. Explicit results are presented.

scholarly journals Power-to-Syngas: A Parareal Optimal Control Approach

2021 ◽  
Vol 9 ◽  
Author(s):  
Andrea Maggi ◽  
Dominik Garmatter ◽  
Sebastian Sager ◽  
Martin Stoll ◽  
Kai Sundmacher
Keyword(s):  
Optimal Control ◽  
Water Gas Shift ◽  
Control Approach ◽  
Renewable Power ◽  
Reverse Water Gas Shift ◽  
Time Modeling ◽  
Continuous Adjoint Method ◽  
Continuous Adjoint ◽  
Water Gas ◽  
First Time

A chemical plant layout for the production of syngas from renewable power, H2O and biogas, is presented to ensure a steady productivity of syngas with a constant H2-to-CO ratio under time-dependent electricity provision. An electrolyzer supplies H2 to the reverse water-gas shift reactor. The system compensates for a drop in electricity supply by gradually operating a tri-reforming reactor, fed with pure O2 directly from the electrolyzer or from an intermediate generic buffering device. After the introduction of modeling assumptions and governing equations, suitable reactor parameters are identified. Finally, two optimal control problems are investigated, where computationally expensive model evaluations are lifted viaparareal and necessary objective derivatives are calculated via the continuous adjoint method. For the first time, modeling, simulation, and optimal control are applied to a combination of the reverse water-gas shift and tri-reforming reactor, exploring a promising pathway in the conversion of renewable power into chemicals.

scholarly journals Optimization of two opposing neutron beams parameters in dynamical (B/Gd) neutron cancer therapy

2019 ◽  
Vol 5 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Nassar H. S. Haidar
Keyword(s):  
Optimal Control ◽  
Cancer Therapy ◽  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Pareto Optimal ◽  
Control Vector ◽  
Relative Time ◽  
Neutron Beams ◽  
Utility Index ◽  
First Time

We demonstrate how the therapeutic utility index and the ballistic index for dynamical neutron cancer therapy (NCT) with two opposing neutron beams form a nonlinear optimization problem. In this problem, the modulation frequencies ω and ϖ of the beams and the relative time advance ε are the control variables. A Pareto optimal control vector ω* = (ω*, ϖ*, ε*) for this problem is identified and reported for the first time. The utility index is shown to be remarkably periodically discontinuous in ε, even in the neighborhood of ε*.

scholarly journals The Optimal Control of Government Stabilization Funds

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1975
Author(s):  
Abel Cadenillas ◽  
Ricardo Huamán-Aguilar
Keyword(s):  
Optimal Control ◽  
Public Debt ◽  
Government Programs ◽  
Fund Manager ◽  
Running Cost ◽  
The Difference ◽  
The Government ◽  
The One ◽  
First Time

We study the optimal control of a government stabilization fund, which is a mechanism to save money during good economic times to be used in bad economic times. The objective of the fund manager is to keep the fund as close as possible to a predetermined target. Accordingly, we consider a running cost associated with the difference between the actual fiscal fund and the fund target. The fund manager exerts control over the fund by making deposits in or withdrawals from the fund. The withdrawals are used to pay public debt or to finance government programs. We obtain, for the first time in the literature, the optimal band for the government stabilization fund. Our results are of interest to practitioners. For instance, we find that the higher the volatility, the larger the size of the optimal band. In particular, each country and state should have its own optimal fund band, in contrast to the “one-size-fits-all” approach that is often used in practice.

A Novelty in Blahut-Arimoto T ype Algorithms: Optimal Control over Noisy Commu nication Channels

2020 ◽  
Author(s):  
Makan Zamanipour
Keyword(s):  
Optimal Control ◽  
Channel Coding ◽  
Joint Source Channel Coding ◽  
Mathematical Expressions ◽  
Type Algorithm ◽  
Theoretic Problem ◽  
Probability Mass ◽  
Information Constraints ◽  
First Time ◽  
Mass Functions

A probability-theoretic problem under information constraints for the concept of optimal control over a noisy-memoryless channel is considered. For our \textit{Observer-Controller} block, i.e., the lossy joint-source-channel-coding (JSCC) scheme, after providing the relative mathematical expressions, we propose a \textit{Blahut-Arimoto}-type algorithm $-$ which is, to the best of our knowledge, for the first time. The algorithm efficiently finds the probability-mass-functions (PMFs) required for .......................................

scholarly journals OPTIMAL DESIGN OF BOREHOLES TRAJECTORIES

2021 ◽  
Vol 1 (48) ◽  
pp. 109-116
Author(s):  
Gulyayev V ◽  
◽  
Shlyun N ◽  
Keyword(s):  
Optimal Control ◽  
Nonlinear Programming ◽  
Trajectory Optimization ◽  
Oil And Gas ◽  
Total Curvature ◽  
Objective Functions ◽  
Gas Wells ◽  
Well Trajectory ◽  
Complex Constraints ◽  
First Time

The problem of optimizing the trajectories of deep curved oil and gas wells, in which the total curvature of the well and its length is minimized, is discussed. For the first time, a discrete-continuum model of the well geometry was proposed, based on the method of projection of a gradient on the hyperplane of linearized constraints, a method was developed for minimizing the corresponding target functionals, which would reduce the risks of emergency drilling situations. An algorithm for reducing the problem of nonlinear optimal control to the problem of nonlinear programming is shown. Such a transition is achieved by approximating the well trajectories with a system of cubic splines, analytically integrating differential equations in separate sections of the trajectory, and further applying the methods of nonlinear programming theory. The considered approach is more algorithmic and allows solving problems of well trajectory optimization under more complex constraints. KEYWORDS: WELL TRACKING, OPTIMAL CONTROL PROBLEM, OBJECTIVE FUNCTIONS, NONLINEAR PROGRAMMING.

scholarly journals Learning Environmental Field Exploration with Computationally Constrained Underwater Robots: Gaussian Processes Meet Stochastic Optimal Control

Sensors ◽  
2019 ◽  
Vol 19 (9) ◽  
pp. 2094 ◽  
Author(s):  
Daniel Andre Duecker ◽  
Andreas Rene Geist ◽  
Edwin Kreuzer ◽  
Eugen Solowjow
Keyword(s):  
Optimal Control ◽  
Path Planning ◽  
Gaussian Processes ◽  
Stochastic Optimal Control ◽  
Markov Random Fields ◽  
Computational Cost ◽  
Real Field ◽  
Underwater Robots ◽  
Exploration Process ◽  
Belief Models

Autonomous exploration of environmental fields is one of the most promising tasks to be performed by fleets of mobile underwater robots. The goal is to maximize the information gain during the exploration process by integrating an information-metric into the path-planning and control step. Therefore, the system maintains an internal belief representation of the environmental field which incorporates previously collected measurements from the real field. In contrast to surface robots, mobile underwater systems are forced to run all computations on-board due to the limited communication bandwidth in underwater domains. Thus, reducing the computational cost of field exploration algorithms constitutes a key challenge for in-field implementations on micro underwater robot teams. In this work, we present a computationally efficient exploration algorithm which utilizes field belief models based on Gaussian Processes, such as Gaussian Markov random fields or Kalman regression, to enable field estimation with constant computational cost over time. We extend the belief models by the use of weighted shape functions to directly incorporate spatially continuous field observations. The developed belief models function as information-theoretic value functions to enable path planning through stochastic optimal control with path integrals. We demonstrate the efficiency of our exploration algorithm in a series of simulations including the case of a stationary spatio-temporal field.

scholarly journals О размере множества произведения множеств рациональных чисел

2020 ◽  
Vol 21 (1) ◽  
pp. 357-363
Author(s):  
Юрий Николаевич Штейников
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper Bound ◽  
Mathematical Expectation ◽  
Lower Estimate ◽  
Main Tool ◽  
Rational Numbers ◽  
Prime Numbers ◽  
Random Subset ◽  
First Time

For the first time  in the article [1] was established non-trivial lower bounds on the size of the set of products of rational numbers, the numerators and denominators of which are limited to a certain quantity $Q$. Roughly speaking, it was shown that the size of the product deviates from the maximum by no less than $$\exp \Bigl\{(9 + o(1)) \frac{\log Q}{\sqrt{\log{\log Q}}}\Bigl\}$$ times. In the article [7], the index of $ \log{\log Q} $ was improved from $ 1/2 $ to $ 1 $, and the proof of the main result on the set of fractions was fundamentally different. This proof, its argument was based on the search for a special large subset of the original set of rational numbers, the set of numerators and denominators of which were pairwise mutually prime numbers. The main tool was the consideration of random subsets. A lower estimate was obtained for the mathematical expectation of the size of this random subset. There, it was possible to obtain an upper bound for the multiplicative energy of the considered set. The lower bound for the number of products and the upper bound for the multiplicative energy of the set are close to optimal results. In this article, we propose the following scheme. In general, we follow the scheme of the proof of the article [1], while modifying some steps and introducing some additional optimizations, we also improve the index from $1/2$ to $1-\varepsilon$ for an arbitrary positive $\varepsilon>0$.

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