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1
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Cooperative driving at isolated intersections based on the optimal minimization of the maximum exit time

100%
Wu J., Abbas-Turki A., Perronnet F.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 4
773-785
EN
Traditional traffic control systems based on traffic light have achieved a great success in reducing the average delay of vehicles or in improving the traffic capacity. The main idea of these systems is based on the optimization of the cycle time, the phase sequence, and the phase duration. The right-of-ways are assigned to vehicles of one or several movements for a specific time. With the emergence of cooperative driving, an innovative traffic control concept, Autonomous Intersection Management (AIM), has emerged. In the framework of AIM, the right-of-way is customized on the measurement of the vehicle state and the traffic control turns to determine the passing sequence of vehicles. Since each vehicle is considered individually, AIM faces a combinatorial optimization problem. This paper proposes a dynamic programming algorithm to find its optimal solution in polynomial time. Experimental results obtained by simulation show that the proper arrangement of the vehicle passing sequence can greatly improve traffic efficiency at intersections.
2
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Viscosity solutions of the Isaacs equation οn an attainable set

100%
Zaremba L. S.
Applicationes Mathematicae
|
1993-1995
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tom 22
|
nr 2
181-192
EN
We apply a modification of the viscosity solution concept introduced in [8] to the Isaacs equation defined on the set attainable from a given set of initial conditions. We extend the notion of a lower strategy introduced by us in [17] to a more general setting to prove that the lower and upper values of a differential game are subsolutions (resp. supersolutions) in our sense to the upper (resp. lower) Isaacs equation of the differential game. Our basic restriction is that the variable duration time of the game is bounded above by a certain number T>0. In order to obtain our results, we prove the Bellman optimality principle of dynamic programming for differential games.
3
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On infinite horizon active fault diagnosis for a class of non-linear non-Gaussian systems

100%
Punčochář I., Šimandl M.
International Journal of Applied Mathematics and Computer Science
|
2014
|
tom 24
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nr 4
795-807
EN
The paper considers the problem of active fault diagnosis for discrete-time stochastic systems over an infinite time horizon. It is assumed that the switching between a fault-free and finitely many faulty conditions can be modelled by a finite-state Markov chain and the continuous dynamics of the observed system can be described for the fault-free and each faulty condition by non-linear non-Gaussian models with a fully observed continuous state. The design of an optimal active fault detector that generates decisions and inputs improving the quality of detection is formulated as a dynamic optimization problem. As the optimal solution obtained by dynamic programming requires solving the Bellman functional equation, approximate techniques are employed to obtain a suboptimal active fault detector.
4
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Parallel dynamic programming algorithms: Multitransputer systems

88%
Sadecki J.
International Journal of Applied Mathematics and Computer Science
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2002
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tom 12
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nr 2
241-255
EN
The present paper discusses real parallel computations. On the basis of a selected group of dynamic programming algorithms, a number of factors affecting the efficiency of parallel computations such as, e.g., the way of distributing tasks, the interconnection structure between particular elements of the parallel system or the way of organizing of interprocessor communication are analyzed. Computations were implemented in the parallel multitransputer SUPER NODE 1000 system using from 5 to 50 transputers.
5
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An adaptive multi-spline refinement algorithm in simulation based sailboat trajectory optimization using onboard multi-core computer systems

88%
Dębski R.
International Journal of Applied Mathematics and Computer Science
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2016
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tom 26
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nr 2
351-365
EN
A new dynamic programming based parallel algorithm adapted to on-board heterogeneous computers for simulation based trajectory optimization is studied in the context of “high-performance sailing”. The algorithm uses a new discrete space of continuously differentiable functions called the multi-splines as its search space representation. A basic version of the algorithm is presented in detail (pseudo-code, time and space complexity, search space auto-adaptation properties). Possible extensions of the basic algorithm are also described. The presented experimental results show that contemporary heterogeneous on-board computers can be effectively used for solving simulation based trajectory optimization problems. These computers can be considered micro high performance computing (HPC) platforms-they offer high performance while remaining energy and cost efficient. The simulation based approach can potentially give highly accurate results since the mathematical model that the simulator is built upon may be as complex as required. The approach described is applicable to many trajectory optimization problems due to its black-box represented performance measure and use of OpenCL.
6
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An autonomous vehicle sequencing problem at intersections: A genetic algorithm approach

88%
Yan F., Dridi M., El Moudni A.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
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nr 1
183-200
EN
This paper addresses a vehicle sequencing problem for adjacent intersections under the framework of Autonomous Intersection Management (AIM). In the context of AIM, autonomous vehicles are considered to be independent individuals and the traffic control aims at deciding on an efficient vehicle passing sequence. Since there are considerable vehicle passing combinations, how to find an efficient vehicle passing sequence in a short time becomes a big challenge, especially for more than one intersection. In this paper, we present a technique for combining certain vehicles into some basic groups with reference to some properties discussed in our earlier works. A genetic algorithm based on these basic groups is designed to find an optimal or a near-optimal vehicle passing sequence for each intersection. Computational experiments verify that the proposed genetic algorithms can response quickly for several intersections. Simulations with continuous vehicles are carried out with application of the proposed algorithm or existing traffic control methods. The results show that the traffic condition can be significantly improved by our algorithm.
7
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(s,S)-type policy for a production inventory problem with limited backlogging and with stockouts

88%
Rempała R.
Applicationes Mathematicae
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1996-1997
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tom 24
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nr 3
343-354
EN
A production inventory problem with limited backlogging and with stockouts is described in a discrete time, stochastic optimal control framework with finite horizon. It is proved by dynamic programming methods that an optimal policy is of (s,S)-type. This means that in every period the policy is completely determined by two fixed levels of the stochastic inventory process considered.
8
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Efficient list cost coloring of vertices and/or edges of bounded cyclicity graphs

88%
Giaro K., Kubale M.
Discussiones Mathematicae Graph Theory
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2009
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tom 29
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nr 2
361-376
EN
We consider a list cost coloring of vertices and edges in the model of vertex, edge, total and pseudototal coloring of graphs. We use a dynamic programming approach to derive polynomial-time algorithms for solving the above problems for trees. Then we generalize this approach to arbitrary graphs with bounded cyclomatic numbers and to their multicolorings.
9
Content available remote

An algorithm for construction of ε-value functions for the Bolza control problem

75%
Jacewicz E.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 2
391-428
EN
The problem considered is that of approximate numerical minimisation of the non-linear control problem of Bolza. Starting from the classical dynamic programming method of Bellman, an ε-value function is defined as an approximation for the value function being a solution to the Hamilton-Jacobi equation. The paper shows how an ε-value function which maintains suitable properties analogous to the original Hamilton-Jacobi value function can be constructed using a stable numerical algorithm. The paper shows the numerical closeness of the approximate minimum to the infimum of the Bolza functional.
10
Content available remote

A method for constructing ε-value functions for the Bolza problem of optimal control

75%
Pustelnik J.
International Journal of Applied Mathematics and Computer Science
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2005
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tom 15
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nr 2
177-186
EN
The problem considered is that of approximate minimisation of the Bolza problem of optimal control. Starting from Bellman's method of dynamic programming, we define the ε-value function to be an approximation to the value function being a solution to the Hamilton-Jacobi equation. The paper shows an approach that can be used to construct an algorithm for calculating the values of an ε-value function at given points, thus approximating the respective values of the value function.
11

Adaptive control for sequential design

63%
Gautier R., Pronzato L.
Discussiones Mathematicae Probability and Statistics
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2000
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tom 20
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nr 1
97-114
EN
The optimal experiment for estimating the parameters of a nonlinear regression model usually depends on the value of these parameters, hence the problem of designing experiments that are robust with respect to parameter uncertainty. Sequential designpermits to adapt the experiment to the value of the parameters, and can thus be considered as a robust design procedure. By designing theexperiments sequentially, one introduces a feedback of information, and thus dynamics, into the design procedure. Several sequential schemes, corresponding to different control policies, are considered. The optimal one corresponds to closed-loop control, and is solution of a stochastic dynamic-programming problem, which is extremely difficult to solve. A suboptimal strategy is proposed, which relies ona normal approximation of the future posterior of θ, independent of future observations. The design criterion obtained involves several mathematical expectations, which are approximated by Laplace method. Finally, stochastic approximation algorithms are also suggested to determine (sub)optimal sequential experiments without having to compute expectations.
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