On qualitative differential games with two targets

We consider a qualitative differential game between two players, each with their own respective target. A player's objective is to steer the response of a dynamical system under the control of both players into his own target before his opponent can steer it to his. The sufficiency conditions given by Getz and Leitmann (Ref. 2), which ensure termination on a particular target, are improved. The theory is illustrated by a pursuit-evasion problem.     

Online stochastic UAV mission planning with time windows and time-sensitive targets

In this paper we simultaneously consider three extensions to the standard Orienteering Problem (OP) to model characteristics that are of practical relevance in planning reconnaissance missions of Unmanned Aerial Vehicles (UAVs). First, travel and recording times are uncertain. Secondly, the information about each target can only be obtained within a predefined time window. Due to the travel and recording time uncertainty, it is also uncertain whether a target can be reached before the end of its time window. Finally, we consider the appearance of new targets during the flight, so-called time-sensitive targets, which need to be visited immediately if possible. We tackle this online stochastic UAV mission planning problem with time windows and time-sensitive targets using a re-planning approach. To this end, we introduce the Maximum Coverage Stochastic Orienteering Problem with Time Windows (MCS-OPTW). It aims at constructing a tour with maximum expected profit of targets that were already known before the flight. Secondly, it directs the planned tour to predefined areas where time-sensitive targets are expected to appear. We have developed a fast heuristic that can be used to re-plan the tour, each time before leaving a target. In our computational experiments we illustrate the benefits of the MCS-OPTW planning approach with respect to balancing the two objectives: the expected profits of foreseen targets, and expected percentage of time-sensitive targets reached on time. We compare it to a deterministic planning approach and show how it deals with uncertainty in travel and recording times and the appearance of time-sensitive targets.     

目标拦截模拟系统中的造型方法

对目标拦截模拟系统中的造型技术作了研究.包括飞行器造型、地形造型、火焰喷射模拟等.提出了蒙皮技术造型中存在的三个问题及相应改进措施.给出了一个基于蒙皮技术的地形生成新算法.利用嵌套圆台扰动的思想较好地实现了导弹飞行时的火焰喷射模拟.     

有理曲线和曲面的分片多项式逼近

本文利用摄动的思想,以摄动有理曲线（曲面）的系数的无穷模作为优化目标,给出了用多项式曲线（曲面）逼近有理曲线（曲面）的一种新方法．同以前的各种方法相比,该方法不仅收敛而且具有更快的收敛速度,并且可以与细分技术相结合,得到有理曲线与曲面的整体光滑、分片多项式的逼近．     

An equitable DEA-based approach for assigning fixed resources along with targets

A typical problem in organization management is how to divide a fixed resource along with a target among decision making units (DMUs) of an organization equitably. By using the data envelopment analysis technique, this paper concerns the problem from the perspective of efficiency analysis and proposes a new sharing model. In the proposed method, the fixed resource and target are divided among DMUs such that the efficiencies of DMUs remain unchanged after assigning the fixed cost and target. The proposed method is unit-invariant; it eliminates resource waste and target insufficiency brought by slacks. Also, every DMU is assigned a positive resource and a positive target under this method. Two corresponding algorithms are designed to yield a unique allocation. The proposed approach can be developed under both constant returns to scale and variable returns to scale. Two examples are presented to illustrate the validity and superiorities of our method.     

Suboptimal target control for hybrid automata using model predictive control

In this paper, a computationally efficient controller is proposed for the target control problem when the system is modelled by hybrid automata. The design is carried out in two stages. First, we compute off-line the shortest switching path which has the minimum discrete cost from an initial set to the given target set. Next, a controller is derived which successfully drives the system from any given initial state in the initial set to the target set while minimizing a cost function. The model predictive control (MPC) technique is used when the current state is not within a guard set, otherwise the mixed-integer predictive control (MIPC) technique is employed. An on-line, semi-explicit control algorithm is derived by combining these two techniques. When the system is subject to additive bounded disturbance, it is shown that the proposed on-line control algorithm holds if tighter constraints on the original nominal state and controller are imposed. Finally, as an application of the proposed control procedure, the high-speed and energy-saving control problem of the CPU processing is considered.     

Numerical solution of singular boundary value problems using Green’s function and improved decomposition method

In this work, an effective technique for solving a class of singular two point boundary value problems is proposed. This technique is based on the Adomian decomposition method (ADM) and Green’s function. The technique relies on constructing Green’s function before establishing the recursive scheme for the solution components. In contrast to the existing recursive schemes based on ADM, the proposed recursive scheme avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients. The approximate solution is obtained in the form of series with easily calculable components. For the completeness, the convergence and error analysis of the proposed scheme is supplemented. Moreover, the numerical examples are included to demonstrate the accuracy, applicability, and generality of the proposed scheme. The results reveal that the method is very effective, straightforward, and simple.     

Vector assignment problems: a general framework

We present a general framework for vector assignment problems. In such problems one aims at assigning n input vectors to m machines such that the value of a given target function is minimized. While previous approaches concentrated on simple target functions such as max–max, the general approach presented here enables us to design a polynomial time approximation scheme (PTAS) for a wide class of target functions. In particular, thanks to a novel technique of preprocessing the input vectors, we are able to deal with nonmonotone target functions. Such target functions arise in vector assignment problems in the context of video transmission and broadcasting.     

On the semi-discretization of optimal control problems for networks of elastic strings: global optimality systems and domain decomposition

We consider a star-graph as an examplary network, with elastic strings stretched along the edges. The network is allowed to perform out-of-the plane displacements. We consider such networks as being controlled at its simple nodes via Dirichlet conditions. The objective is to steer given initial data to final target data in a given time T with minimal control costs. This problem is discussed in the continuous as well as in the discrete case. We discuss an iterative domain decomposition technique and its discrete analogue. We prove convergence and show some numerical results.     

二维序贯均匀等距设计对跳比单调函数类的有效性

把序贯的思想和均匀设计相结合,提出的“序贯均匀设计”,其目的在于解决多维空间上快速选优问题。已经证明了二维序贯均匀设计对旋转单调函数类的有效性。本文进一步证明了“二维序贯均匀等距设计”对跳比单调函数类的有效性。     

Control and identification of chaotic systems by altering their energy

We developed the control technique for (non)linear oscillators when repellors are stabilized by adjusting the system to energy levels corresponding to their stable counterparts. The technique does not require knowledge of the system equations. Two control strategies are possible. Following the first one, we simply test the systems by changing the feedback strength. This strategy does not require any computation of the control signal, and, hence, can be useful for control as well as identification of unknown systems. If the desired target can be identified (say, from the system time series), one can use another strategy based on goal-oriented control of the desired target. We analyze how the perturbation shape can be tuned so as to preserve the system natural response and discuss how to calculate the minimal strength of the perturbation required for stabilization of a priori chosen orbit. Generally, the control represents addition of an extra nonlinear damping to the system. In two limits of the perturbation slope, it manifests itself in (i) changing the oscillator natural damping; (ii) suppressing (enhancing) the external driving force. In the case of large deviations between phases of the chaotic oscillator and the driving force, only first scenario holds. Generalization of the technique to the case of oscillator networks and 3D autonomous dynamical systems is considered.     

About an Optimal Visiting Problem

In this paper we are concerned with the optimal control problem consisting in minimizing the time for reaching (visiting) a fixed number of target sets, in particular more than one target. Such a problem is of course reminiscent of the famous “Traveling Salesman Problem” and brings all its computational difficulties. Our aim is to apply the dynamic programming technique in order to characterize the value function of the problem as the unique viscosity solution of a suitable Hamilton–Jacobi equation. We introduce some “external” variables, one per target, which keep in memory whether the corresponding target is already visited or not, and we transform the visiting problem in a suitable Mayer problem. This fact allows us to overcome the lacking of the Dynamic Programming Principle for the originary problem. The external variables evolve with a hysteresis law and the Hamilton–Jacobi equation turns out to be discontinuous     

DETERMINATION OF EFFICIENT RANGE OF TARGET LEVELS IN MULTIPLE OBJECTIVE PLANNING

This paper describes a nonlinear programming model combined with a binary search technique that systematically searches for the minimum value of a given objective within the nondominated solution set. The procedure provides a way of determining the range of efficient target levels for any multiobjective planning problem using information contained in the pay-off table. The method is illustrated using a numerical example.     

Solution of fractional differential equations by using differential transform method

In this study, we implement a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equations. Theorems that never existed before are introduced with their proofs. Also numerical examples are carried out for various types of problems, including the Bagley–Torvik, Ricatti and composite fractional oscillation equations for the application of the method. The results obtained are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, accurate and easy to apply.     

On the Chebyshev spectral continuous time approximation for constant and periodic delay differential equations

In this paper, the approximation technique proposed in Breda et al. (2005) [1] for converting a linear system of constant-coefficient delay differential equations (DDEs) into a system of ordinary differential equations (ODEs) using pseudospectral differencing is extended to linear and nonlinear systems of DDEs with time-periodic coefficients. The Chebyshev spectral continuous time approximation (ChSCTA) technique is used to study the stability of first and second-order constant coefficient DDEs, a delayed system with a cubic nonlinearity and parametric sinusoidal excitation, the delayed Mathieu’s equation, and delayed systems with two fixed delays. In all the examples, the stability and time response obtained from ChSCTA show good agreement with either analytical results, or the results obtained before by other reliable approximation methods. The “spectral accuracy” convergence behavior of Chebyshev spectral collocation shown in Trefethen (2000) [2] which the proposed technique possesses is compared to the convergence properties of finite difference-based continuous time approximation for constant-coefficient DDEs proposed recently in Sun (2009) [3] and Sun and Song (2009) [4].     

Stochastic Networks: Admission and Routing Using Penalty Functions

We propose an admission and routing control policy for a network of service facilities in a stochastic setting in order to maximize a long run average reward. Queueing and reneging before entering the network is allowed; we introduce orbiting as an approximation to the queueing. Once a customer has entered the network, it incurs no more waiting. Our control policy is easy to implement and we prove that it performs well in steady state as long as the capacity request sizes are relatively small compared to the capacity of the service facilities. The policy is a target tracking policy: a linear program provides a target operating point and an exponential penalty function is used to translate the optimal deterministic point into a feasible admission and routing policy. This translation essentially transforms the admission and routing control problem into a problem of load balancing via the construction of fictitious systems. Simulation studies are included to illustrate that our policy also performs well when request sizes are moderate or large with respect to the capacity.     

Neuro-fuzzy technique for navigation of multiple mobile robots

In this paper, navigation techniques for several mobile robots are investigated in a totally unknown environment. In the beginning, Fuzzy logic controllers (FLC) using different membership functions are developed and used to navigate mobile robots. First a fuzzy controller has been used with four types of input members, two types of output members and three parameters each. Next two types of fuzzy controllers have been developed having same input members and output members with five parameters each. Each robot has an array of sensors for measuring the distances of obstacles around it and an image sensor for detecting the bearing of the target. It is found that the FLC having Gaussian membership function is best suitable for navigation of multiple mobile robots. Then a hybrid neuro-fuzzy technique has been designed for the same problem. The neuro-fuzzy technique being used here comprises a neural network, which is acting as a pre processor for a fuzzy controller. The neural network considered for neuro-fuzzy technique is a multi-layer perceptron, with two hidden layers. These techniques have been demonstrated in simulation mode, which depicts that the robots are able to avoid obstacles and reach the targets efficiently. Amongst the techniques developed neuro-fuzzy technique is found to be most efficient for mobile robots navigation. Experimental verifications have been done with the simulation results to prove the authenticity of the developed neuro-fuzzy technique.     

Employment of neural network and rough set in meta-learning

The selection of the optimal ensembles of classifiers in multiple-classifier selection technique is un-decidable in many cases and it is potentially subjected to a trial-and-error search. This paper introduces a quantitative meta-learning approach based on neural network and rough set theory in the selection of the best predictive model. This approach depends directly on the characteristic, meta-features of the input data sets. The employed meta-features are the degree of discreteness and the distribution of the features in the input data set, the fuzziness of these features related to the target class labels and finally the correlation and covariance between the different features. The experimental work that consider these criteria are applied on twenty nine data sets using different classification techniques including support vector machine, decision tables and Bayesian believe model. The measures of these criteria and the best result classification technique are used to build a meta data set. The role of the neural network is to perform a black-box prediction of the optimal, best fitting, classification technique. The role of the rough set theory is the generation of the decision rules that controls this prediction approach. Finally, formal concept analysis is applied for the visualization of the generated rules.     

The characteristics of proton and induced neutron-emulsion high energy interactions

We used the technique of the separation of Coulomb and diffraction dissociation of incident heavy ion to select the events due to induced neutron from ¹⁶O leaving sub-oxygen nucleus to break-up. The characteristics of these events of neutron emulsion collisions are displayed and compared with that obtained from incident proton at the same energy.

The studied interactions are classified according to the type of target nucleus (H, CNO and AgBr) by using the method of separation. Cascade-evaporation model (CEM) calculations are taken into account and compared with that obtained from the interactions of induced neutron from ¹⁶O (4.5 A GeV/c) with emulsion nuclei and with the results of incident proton at the same target and energy. CEM can describe the distributions of proton and neutron interactions. It is conjuctured that it may be possible to develop a similar theoretical model based on the modern methods of nonlinear dynamics, neural network and complexity [Randomness and Undecidability in Physics, World Scientific, Singapore, 1993].     

On the minimality of search paths under absolutely continuous univariate distributions

The linear search problem is concerned with the search for a target located randomly on a line. The target being sought for might be on either side of some starting point. A searcher makes for the target with an upper bound on his speed, using a continuous search path in which he changes his direction many times before reaching his goal. The minimality of average distance (time) from the starting point upon reaching the target is the measure of optimality of search paths. We have obtained sufficient conditions that guarantee the minimality of such search paths whenever the target has an absolutely continuous distribution.

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Zusammenfassung Ein Objekt, das sich in zufälliger Position auf einer Strecke befindet, soll gesucht werden; der Startpunkt liegt im Inneren der Strecke. Für die Bewegungsgeschwindigkeit bei der Suche ist eine obere Schranke gegeben; der Suchpfad muß stetig sein, wobei beliebig viele Richtungsänderungen zugelassen sind. Das Ziel ist die Minimierung der erwarteten Zeit bis zum Erreichen des Objekts. Unter der Voraussetzung einer absolut stetigen Verteilung für die Position des Objekts werden hinreichende Bedingungen für die Optimalität eines Suchpfades angegeben.