Optimal Control of a Ship for Collision Avoidance Maneuvers

We consider a ship subject to kinematic, dynamic, and moment equations and steered via rudder under the assumptions that the rudder angle and rudder angle time rate are subject to upper and lower bounds. We formulate and solve four Chebyshev problems of optimal control, the optimization criterion being the maximization with respect to the state and control history of the minimum value with respect to time of the distance between two identical ships, one maneuvering and one moving in a predetermined way.Problems P1 and P2 deal with collision avoidance maneuvers without cooperation, while Problems P3 and P4 deal with collision avoidance maneuvers with cooperation. In Problems P1 and P3, the maneuvering ship must reach the final point with a given lateral distance, zero yaw angle, and zero yaw angle time rate. In Problems P2 and P4, the additional requirement of quasi-steady state is imposed at the final point.The above Chebyshev problems, transformed into Bolza problems via suitable transformations, are solved via the sequential gradient-restoration algorithm in conjunction with a new singularity avoiding transformation which accounts automatically for the bounds on rudder angle and rudder angle time rate.The optimal control histories involve multiple subarcs along which either the rudder angle is kept at one of the extreme positions or the rudder angle time rate is held at one of the extreme values. In problems where quasi-steady state is imposed at the final point, there is a higher number of subarcs than in problems where quasi-steady state is not imposed; the higher number of subarcs is due to the additional requirement that the lateral velocity and rudder angle vanish at the final point.     

Flocking and collision avoidance of a Cucker-Smale type system with singular weights

The dynamical behavior of a flock model with a singular communication rate and extra interaction terms is investigated in this paper. A rigorous theoretical proof of collision avoidance between any two agents is obtained which guarantees the existence of global solutions. Moreover, a sufficient condition for the existence of time-asymptotic flocking is also acquired and numerical simulations verified these results which show that a compact equilibrium configuration may emerge.     

A Nonlinear Problem Associated to the Motion of a Membrane

A nonlinear model associated to the motion of a membrane is considered as limit of a sequence of approximate models, for which a global existence and uniqueness theorem can be proved. The paper investigates the relationship between the solutions of the real and approximate models.     

An approach to modelling industrial unit processes: application to a spiral concentrator for minerals

A suite of computer models which simulate process operations in common use in the minerals processing industry is being developed. Application of the models is described with reference to a particular process device, the spiral concentrator. The paper sets out to explain the basic strategy behind the unit process modelling approach and discusses in detail the overall model structure adopted. The model aims to provide a set of equations, with sufficient physical significance to give a reasonable fit to any specific data set, and which can be systematically adjusted (through auxiliary models, user judgement and experience) to provide meaningful performance predictions over a broad range of operating conditions. The approach is thought to be applicable to a wide variety of processes. The model has been tested using a variety of ores, separated on plant-scale equipment and practical examples are given. The scope and limitations of the method are reported, drawing on the results of parallel experimental work. The extent to which this kind of approach can be used as a predictive tool in process design applications and in the day-to-day running of mineral processing plant is discussed.     

Mathematical analysis of the MPS MX missile system

A model for the cost optimization analysis of the multiple protective shelter (MPS) MX missile system is developed. Because many of the components of the system have never been built before and an enemy's capabilities are hard to predict, parametric analysis has been carried out to understand more about the system design.     

The diffusion dynamics of choice: From durable goods markets to fashion first names

Goods, styles, ideologies are adopted by society through various mechanisms. In particular, adoption driven by innovation is extensively studied by marketing economics. Mathematical models are currently used to forecast sales of innovative goods. Inspired by the theory of diffusion processes developed for marketing economics, we propose a modelling framework for the mechanism of fashion, which we apply to first names. Analyses of French, Dutch, and US national databases validate our modelling approach for thousands of first names, covering, on average, more than 50% of the yearly incidence in each database. In these cases, it is thus possible to study how first names become popular and when they run out of fashion. Furthermore, we uncover a clear distinction between popularity and fashion: less popular names, typically not included in studies of fashion, may be driven by fashion, as well. © 2016 The Authors Complexity Published byWiley Periodicals, Inc. Complexity 21: 362–369, 2016     

一种惩罚机制下一次性n人囚徒困境的合作性

为解决一次性n人囚徒困境中局中人如何走出困境的问题,引进了背叛惩罚函数及其严厉度和参与人的背叛愿意度等概念,并用数学论证法证明了如下结果:(1)参与人的背叛愿意度都不超过1.(2)背叛愿意度越大,这个参与人越愿意背叛;(3)背叛愿意度为0零时,这个参与人是否背叛其赢得一样;(4)当背叛愿意度取负数时,其绝对值越大,参与人的合作积极性越大.得到博弈结果的判定法:(1)计算各参与人的背叛愿意度.(2)若至少有一个参与人愿意背叛,则全体参与人都背叛.(3)若全体参与人都愿意合作,则合作成功.例子表明,本结果在理论上可有效地解决中局中人如何走出困境和在给定惩罚机制下博弈结果的预测问题.     

Use of stochastic control theory to model a forest management system

A forest management problem due to Hellman has been modelled as a stochastic control problem with one state variable (inventory level) and one control variable (consumption rate of wood by the factories). The stochastic process governing the evolution of the inventory level is transformed into an Itô stoachastic differential equation by approximating the compound Poisson process of wood arrivals into the depot as a Wiener process. The resulting stochastic control problem is solved by using the Hamilton-Jacobi-Bellman equation of stochastic dynamic programming. Two numerical examples illustrate the results.     

A two-period supply contract model for a decentralized assembly system

Supply contract helps in coordinating the supply of quantities from different suppliers in order to meet the demand for a product. In this paper, supply contract models are developed by considering an assembly system operated under a centralized and a decentralized control modes. The centralized control mode considers a single decision maker and offers a global optimal solution. However, the decentralized control mode considers each player in the contract as a decision maker and offers local optimal solutions based on the production and cost characteristics of each player. Such local optimal solutions are adjusted through coordinating parameters to obtain global optimal solutions. If a contract developed for a decentralized control mode achieves the global optimal solution, then the supply chain (or channel) is said to be coordinated.     

A new approach to fuzzy wavelet system modeling

In this paper, we propose simple but effective two different fuzzy wavelet networks (FWNs) for system identification. The FWNs combine the traditional Takagi–Sugeno–Kang (TSK) fuzzy model and discrete wavelet transforms (DWT). The proposed FWNs consist of a set of if–then rules and, then parts are series expansion in terms of wavelets functions. In the first system, while the only one scale parameter is changing with it corresponding rule number, translation parameter sets are fixed in each rule. As for the second system, DWT is used completely by using wavelet frames. The performance of proposed fuzzy models is illustrated by examples and compared with previously published examples. Simulation results indicate the remarkable capabilities of the proposed methods. It is worth noting that the second FWN achieves high function approximation accuracy and fast convergence.     

Existence of solutions to a phase transition model with microscopic movements

We prove the existence of weak solutions for a 3D phase change model introduced by Michel Frémond in (Non‐smooth Thermomechanics. Springer: Berlin, 2002) showing, via a priori estimates, the weak sequential stability property in the sense already used by the first author in (Comput. Math. Appl. 2007; 53 :461–490). The result follows by passing to the limit in an approximate problem obtained adding a superlinear part (in terms of the gradient of the temperature) in the heat flux law. We first prove well posedness for this last problem and then—using proper a priori estimates—we pass to the limit showing that the total energy is conserved during the evolution process and proving the non‐negativity of the entropy production rate in a suitable sense. Finally, these weak solutions turn out to be the classical solution to the original Frémond's model provided all quantities in question are smooth enough. Copyright © 2008 John Wiley & Sons, Ltd.     

不确定需求下的企业最优外汇持有量模型研究

把外汇作为存货看待,考虑了外汇的持有成本、转换成本、汇率风险,外汇存款利率以及利息税率等因素,通过建立数学模型来研究不确定需求下的企业最优外汇持有量问题.     

Thermodynamics of multi-temperature fluids with applications to turbulence modelling

The thermodynamics of a fluid with several distinct temperatures is considered. The balance laws are studied and a set of linear constitutive equations is derived; equations of motion are obtained and discussed. The application of the developed theory to turbulence modelling is studied and results are shown to be consistent with the one-equation models of turbulence. The thermodynamics of turbulence is also briefly discussed.     

Sensitivity analysis of parameter combinations

For models frequently encountered in system dynamics a method is derived to find the direction in which the parameter vectors should be perturbed, by a given magnitude, so as to maximize the disturbance to the solution trajectory. The method is thus useful for analysing the effects of a combination of parameter changes on a system. The method also yields an ordering of the parameters with respect to their sensitivity.     

Non-existence of positive solution to a quasilinear elliptic system and blow-up estimates for a reaction-diffusion system

IntroductionIn these years, the reaction-diffusion systems of Fujita typea5 ttell as the related elliptic systemt'ith fl g RN, Tnl. n1 3 0, i = 1, 2. \vere studied by' a nu111ber of authors. The probiemsconcerning system (l) inc1ude globa1 existence and g1obal existen(.e numbers. b1ow-up. bloxv-uprates, and blow-up sets. uniqueness or nonuniqueness. et('. FOr s}'stem (2) there are problemssuch as existence or non-existence. uniqueness or nonllniqueI1ess. and so ol1. 1Ieanwhile. itseems that…     

A mathematical programming model applied to the study of water markets within the Spanish agricultural sector

Spanish irrigated agriculture uses about 80% of all the nation's available water resources. The need to increase the economic efficiency of current uses of water in the agricultural sector is perceived as the top priority of the country's national water policy. In Spain surface water is centrally allocated among competing users based on allocation criteria dictated by the Water Law. The complete absence of price or market signals is a major obstacle to induce irrigators to use water more efficiently. Water markets within the agricultural sector is a promising, though scarcely analyzed in Spain, solution to increase its economic efficiency. This research is an attempt to evaluate probable water transfers among farmers and irrigation districts as well as water price equilibria resulting from different water market arrangements. Three interconnected mathematical programming models permit the simulation of water use at the farm level and water market arrangements in the Guadalquivir Valley (Spain). Results show that water markets would be highly dependent on the level of transaction costs and on the relative reductions of water allotments due to nonoverlapping drought cycles among water districts.