17 research outputs found
Differential games described by infinite system of differential equations
No full textDifferent approaches have been used by many researchers to solve control problems for parabolic and hyperbolic partial differential equations. Some of these problems can be reduced to the ones described by infinite systems of ordinary differential equations by using the decomposition method. Therefore there is a significant relationship between control problems described by partial differential equations and those described by infinite system of differential equations.
We study three types of infinite systems. The first is infinite systems of first order differential equations. The second system is infinite system of second order differential equations and the third system is infinite system of 2-systems of first order
differential equations.
In this thesis, we study the uniqueness and existence theorems for all systems then
we study control and differential game problems. For the first system, we study a pursuit game of one pursuer and one evader and evasion differential game of one evader from infinitely many pursuers in the case of integral constraints. For the second system, we study an evasion differential game of one evader from finite number of pursuers in the case of geometric constraints and for the third system, we study a control problem
Pursuit and evasion differential games in Hilbert Space
No full textWe consider pursuit and evasion differential game problems described by an infinite system of differential equations with countably many Pursuers in Hilbert space. Integral constraints are imposed on the controls of players. In this paper an attempt has been made to solve an evasion problem under the condition that the total resource of the Pursuers is less then that of the Evader and a pursuit problem when the total resource of the Pursuers greater than that of the Evader. The strategy of the Evader is constructe
Average-based intervals and frequency density-based intervals in forecasting tuberculosis cases in Sabah
No full textInitially, time series models were used to forecast the number of students enrolled in the University of Alabama in 1993. Forecasting is one of the branches of fuzzy sets theory. As time goes on, these models are being used to make predictions of stock prices, weather, road accidents, and several other models. In this paper, we compare two different approaches in determining the suitable length of intervals to increase the accuracy of forecasting in fuzzy time series. The methods proposed are the average-based intervals and frequency-density-based partitioning. The results showed that the average-based intervals have higher accuracy in forecasting the number of cases compared to frequency-density-based intervals
Interval estimation of forecasting value by using trapezoidal fuzzy number
No full textOne of the major highlights of the fuzzy time series forecasting model is that it only provides one single point forecasted value, as in the traditional time series methods. One of the major highlights of the fuzzy time series forecasting model is that it only provides one single point forecasted value, as in the traditional time series methods. Besides, most of the models use triangular fuzzy numbers in their methods. The aim of this paper is to show that the forecasted value will be a trapezoidal fuzzy number in interval form instead of a single-point value. In our case, we applied tuberculosis cases collected in Sabah to examine this method. Two numerical data sets from the whole tuberculosis data set were used to illustrate the chosen methods
A differential game of evasion from many pursuers
No full textThis paper considers a game problem with many pursuers described by infinite systems of differential equations of second order. On the controls of players geometric constraints are imposed. The aim of the pursuers is to capture the evader,while the aim of the evader is the opposite. The theorem on evasion is proved in this paper
Differential Game for an Infinite System of Two-Block Differential Equations
No full textWe present a pursuit differential game for an infinite system of two-block differential equations in Hilbert space l2. The pursuer and evader control functions are subject to integral constraints. The differential game is said to be completed if the state of the system falls into the origin of l2 at some finite time. The purpose of the pursuer is to bring the state of the controlled system to the origin of the space l2, whereas the evader’s aim is to prevent this. For the optimal pursuit time, we obtain an equation and construct the optimal strategies for the players
Implementation of Revised Heuristic Knowledge in Average-based Interval for Fuzzy Time Series Forecasting of Tuberculosis Cases in Sabah
No full textFuzzy time series forecasting is one method used to forecast in certain reality problems. The research on fuzzy time series forecasting has been increased due to its capability in dealing with vagueness and uncertainty. In this paper, we are dealing with implementation of revised heuristic knowledge to basic average-based interval and showing that these models forecast better than the basic one. We suggest three different lengths of interval, size 5, size 10 and size 20 to be used in comparing these models of average-based interval, average-based interval with implementation of heuristic knowledge and, average-based interval with implementation of revised heuristic knowledge. These models applied to forecast the number of tuberculosis cases reported monthly in Sabah starting from January 2012 until December 2019. A few numerical examples are shown as well. The performances of evaluations are shown by comparison on the values obtained by Mean Square error (MSE) and Root Mean Square Error (RMSE)
Differential games with many pursuers when evader moves on the surface of a cylinder
No full textWe study a pursuit differential game with many Pursuers when the Evader moves on the surface of a given cylinder. Maximal speeds of all players are equal. We consider two cases: in the first case, the Pursuers move arbitrarily without phase constraints; and in the second case, the Pursuers move on the surface of the cylinder. In both cases, we give necessary and sufficient conditions to complete the pursuit. In addition, in the second case, we show that pursuit differential game on a cylinder are equivalent to a differential game on the plane with many groups of Pursuers where each group consists of infinite number of pursuers having the same control parameter.
References Isaacs, R. Differential Games. A Mathematical Theory with Applications to Warfare and Pursuit, Control, and Optimization. New York: Wiley, 1963. Petrov, N. N. A problem of group pursuit with phase constraints. J. Appl. Math. Mech. 1988, 52, No 6, 1030--1033. Petrosyan, L. A. Survival differential game with many participants. Dokl. Akad. Nauk USSR. 1965, 161, No 2, 285--287. Petrosyan, L. S. Differentsial'nye igry presledovaniya (Pursuit Differential Games). Leningrad (SPb): Leningr.State Univ(SPbSU), 1977. Pshennichnyi, B. N. Simple pursuit of several targets. Kibernetika. 1976, No 3, 145--146. Chernous'ko, F. L. A problem of evasion of several pursuers. J. Appl. Maths Mechs.1976, 40, No 1, 14--24. Ivanov R. P. Simple pursuit-evasion on a compact. Dokl. Akad. Nauk SSSR. 1980, 254, No 6, 1318--1321. Melikyan, A. A. and Ovakimyan, N. V. Singular trajectories in the problem of simple pursuit on a manifold. J. Appl. Math. Mech. 1991, 55, No 1, 42--48. Melikyan, A. A. and Ovakimyan, N. V. Differential Games of Simple Pursuit and Approach on Manifolds. Institute of Mechanics, National Academy of Sciences of Armenia. Yerevan. Preprint, 1993. Kuchkarov, A. Sh. The problem of optimal approach in locally euclidean spaces. Automation and Remote Control. 2007, 68, No 6, 974-978. Kuchkarov, A. Sh. A simple pursuit--evasion problem on a ball of a Riemannian manifold. Mathematical Notes. 2009, 85, No 2, 190--197. Azamov, A. On a problem of escape along a prescribed curve. J. Appl. Math. Mech. 1982, 46, No 4, 553--555. Kuchkarov, A. Sh. and Rikhsiev, B. B. on the solution of a pursuit problem with phase constraints. Automation and Remote Control. 2001, 62, No 8, 1259--1262. Ibragimov G. I. A game problem on a closed convex set. Siberian advances in mathematics., 2002, 12, No 3, 16--31. Nikulin, V. V. and Shafarevich, I. R. Geometriya i Gruppy (Geometric and Groups). Moscow: Nauka, 1983
Optimal pursuit time in differential game for an infinite system of differential equations
No full textWe consider a differential game of one pursuer and one evader. The game is described by an infinite system of first order differential equations. Control functions of the players are subject to coordinate-wise integral constraints. Game is said to be completed if each component of state vector equal to zero at some unspecified time. The pursuer tries to complete the game and the evader pursues the opposite goal. A formula for optimal pursuit time is found and optimal strategies of players are constructed
A Systematic Review on the Advancement in the Study of Fuzzy Variational Problems
No full textThe study of fuzzy variational problems has received significant attention over the past decade due to its successful applications in numerous fields, such as image segmentation and optimal control theory. The fuzzy Euler-Lagrange equations provide the necessary optimality conditions for solving fuzzy variational problems explicitly and have been studied under several differentiability conditions. In this paper, we provide a systematic review to recap the history of variational principle in the calculus of variations and compare it with the existing techniques in the fuzzy setting. We begin with the preliminary concepts and definitions of fuzzy theory and scrutinize the Euler-Lagrange’s strategy via systematically searched studies concerning fuzzy variational problems to highlight the importance of improving the existing methods. Finally, we set up the main open problems regarding the limitations of the current approaches, shedding light on future directions
