On a team control problem under obstacles

The paper deals with the problem of coordinated goal-oriented target control for a group of control systems that are to realize a joint movement towards a given target set under collision avoidance. The members of the group are obliged to lie inside a virtual ellipsoidal container, which realizes a reference motion while also avoiding external obstacles specified in advance. We describe a general solution scheme based on decomposing the main problem into auxiliary subproblems, for which we indicate solution methods as well as the necessity of coordinating these solutions at the final stage.     

Bipartite flocking for multi-agent systems

This paper addresses the bipartite flock control problem where a multi-agent system splits into two clusters upon internal or external excitations. Using structurally balanced signed graph theory, LaSalle’s invariance principle and Barbalat’s Lemma, we prove that the proposed algorithm guarantees a bipartite flocking behavior. In each of the two disjoint clusters, all individuals move with the same direction. Meanwhile, every pair of agents in different clusters moves with opposite directions. Moreover, all agents in the two separated clusters approach a common velocity magnitude, and collision avoidance among all agents is ensured as well. Finally, the proposed bipartite flock control method is examined by numerical simulations. The bipartite flocking motion addressed by this paper has its references in both natural collective motions and human group behaviors such as predator–prey and panic escaping scenarios.     

On the optimal control of minimum film thickness

The present paper is concerned with the study of controlling the motion of a bearing so that the thin film of lubricant separating it from its container will have the largest possible thickness. Explicit equations are derived, and the control problem is solved explicitly in some simple cases.The authors thank Dr. S. M. Rohde, Manager, Systems Analysis and Simulation Department, General Motors System Engineering Center, for many valuable discussions about this problem.     

Control Problems for a Class of Set Valued Evolutions

The paper studies controllability problems for the reachable set of a differential inclusion. These were originally motivated by models of control of a flock of animals. Conditions are derived for the existence or nonexistence of a strategy which confines the reachable set within a given bounded region, at all sufficiently large times. Steering problems and the asymptotic shape of the reachable set are also investigated.     

微重力环境中摆转运动引起的流体晃动力及力矩

本文以部分充液的贮箱系统作为研究对象，用数值方法计算研究了在扰动力作用下流体系统的晃动力学问题。文中给出了由于系统摆转而在流体中引起的扰动加速度的数学表达式。晃动力的计算是在与贮箱固结在一起的非惯性坐标系中，对依赖于初始与边界条件的三维非稳态偏微分方程组进行数值求解，计算了在伴随系统的摆转运动而在流体中产生的扰动加速度作用下，流体施加于贮箱上的力与力矩的波动规律。     

A numerical investigation of energy dissipation with a shallow depth sloshing absorber

A liquid sloshing absorber consists of a container, partially filled with liquid. The absorber is attached to the structure to be controlled, and relies on the structure’s motion to excite the liquid. Consequently, a sloshing wave is produced at the liquid free surface within the absorber, possessing energy dissipative qualities. The behaviour of liquid sloshing absorbers has been well documented, although their use in structural control applications has attracted considerably less attention.     

The learnable evolution model in agent-based delivery optimization

The learnable evolution model is a stochastic optimization method which employs machine learning to guide the optimization process. LEM3, its newest implementation, combines its machine learning mode with other search operators. The presented research concerns its application within a multi-agent system for autonomous control of container on-carriage operations. Specifically, LEM3 is used by transport management agents that act on behalf of the trucks of a forwarding agency for the planning of individual transport schedules.     

Mean–variance analysis of a single supplier and retailer supply chain under a returns policy

In the literature, most of the supply chain coordinating policies target at improving the supply chain’s efficiency in terms of expected cost reduction or expected profit improvement. However, optimizing the expected performance alone cannot guarantee that the realized performance measure will fall within a small neighborhood of its expected value when the corresponding variance is high. Moreover, it ignores the risk aversion of supply chain members which may affect the achievability of channel coordination. As a result, we carry out in this paper a mean–variance (MV) analysis of supply chains under a returns policy. We first propose an MV formulation for a single supplier single retailer supply chain with a newsvendor type of product. The objective of each supply chain decision maker is to maximize the expected profit such that the standard deviation of profit is under the decision maker’s control. We study both the cases with centralized and decentralized supply chains. We illustrate how a returns policy can be applied for managing the supply chains to address the issues such as channel coordination and risk control. Extensive numerical studies are conducted and managerial findings are proposed.     

弹性振动的闭环系统

细长体的飞行器在飞行中考虑了既有刚性运动又有弹性振动的运动,由于刚性运动对弹性振动的影响,通过安装在飞行器上面的仪表所测得的角速度作为反馈信号输入到控制器,由控制器输出端输出信号到执行机构来实现反馈控制,把刚性运动飞行器、弹性振动飞行器同时考虑作受控对象,这里我们研究了由刚性飞行器、弹性飞行器和控制器三者形成的闭环系统的弹性振动问题,得到了求闭环系统的频率和振型的公式,设计控制器使得闭环系统渐近稳定的条件和能控性、能观测性的条件。     

Capture Conditions in a Pursuit-Evasion Game between Players with Biproper Dynamics<Superscript>1</Superscript>

Capture conditions in a planar pursuit-evasion game between a guided missile and its aerial target, each having either forward control or tail control, are derived analytically. The adversaries closed-loop maneuver dynamics are represented by first-order biproper transfer functions. A distinction is made between open and closed capture zones in the reduced-order game space. It is shown that locating the control surface forward, instead of aft, provides considerable advantages with regard to the existence and size of different capture zones. A new game space decomposition with two singular regions is also presented and the conditions for its existence are given.The author expresses his gratitude to the anonymous reviewers for the thorough reading of the paper and helpful comments.     

A Stackelberg game model for resource allocation in cargo container security

This paper presents a game theoretic model that analyzes resource allocation strategies against an adaptive adversary to secure cargo container transportation. The defender allocates security resources that could interdict an unauthorized weapon insertion inside a container. The attacker observes the defender’s security strategy and chooses a site to insert the weapon. The attacker’s goal is to maximize the probability that the weapon reaches its target. The basic model includes a single container route. The results in the basic model suggest that in equilibrium the defender should maintain an equal level of physical security at each site on the cargo container’s route. Furthermore, the equilibrium levels of resources to interdict the weapon overseas increase as a function of the attacker’s capability to detonate the weapon remotely at a domestic seaport. Investment in domestic seaport security is highly sensitive to the attacker’s remote detonation capability as well. The general model that includes multiple container routes suggests that there is a trade-off between the security of foreign seaports and the physical security of sites including container transfer facilities, container yards, warehouses and truck rest areas. The defender has the flexibility to shift resources between non-intrusive inspections at foreign seaports and physical security of other sites on the container route. The equilibrium is also sensitive to the cost effectiveness of security investments.     

A dual form of Noether's theorem with applications to continuum mechanics

Considering simultaneously the equations of motion of the physical system and of the non-physical adjoint system, we introduce a general form of Noether's theorem by constructing a “dual Lagrangian” functional with a corresponding invariant of motion which preserves its value along the trajectories of combined physical and unphysical systems. The statement of invariance of this functional reduces to the classical statement of Noether's theorem if the system is self-adjoint; some possible generalizations are indicated. Applications to continuum mechanics are discussed within the framework of Noble's dual variational formulation.     

Local well‐posedness for volume‐preserving mean curvature and Willmore flows with line tension

We show the short‐time existence and uniqueness of solutions for the motion of an evolving hypersurface in contact with a solid container driven by the volume‐preserving mean curvature flow (MCF) taking line tension effects on the boundary into account. Difficulties arise due to dynamic boundary conditions and due to the contact angle and the non‐local nature of the resulting second order, nonlinear PDE. In addition, we prove the same result for the Willmore flow with line tension, which results in a nonlinear PDE of fourth order. For both flows we will use a curvilinear cordinate system due to Vogel to write the flows as graphs over a fixed reference hypersurface.     

An approach-evasion differential game: Stochastic guide

An approach-evasion positional differential game is considered for a conflict-controlled motion and a target set within a given set. Use is made of a solution of the associated boundary-value problem for a parabolic equation degenerating as the diffusion term vanishes to a Hamilton-Jacobi type equation, which is typical for techniques in the theory of differential games. Based on this, a control scheme with a stochastic guide is developed.     

Multilevel,threshold-based policies for cargo container security screening systems

To mitigate the threat of nuclear terrorism within the US using nuclear material that has been smuggled into the country, the US Bureau of Customs and Border Protection has expanded its cargo container detection capabilities at ports of entry into the US This paper formulates a risk-based screening framework for determining how to define a primary screening alarm for screening cargo containers given a set of dependent primary screening devices. To do so, this paper proposes two linear programming models for screening cargo containers for nuclear material at port security stations using knapsack problem models. All cargo containers undergo primary screening, where they are screened by a given number of security devices. The objective is to identifying the primary security outcomes that warrant a system alarm for each container risk group such that the system detection probability is maximized, subject to a screening budget. The base model is compared to a second model that explicitly requires a threshold-based policy. The structural properties of the two models are compared, which indicates that all risk groups except at most one have deterministic screening policies. A computational example suggests that the detection probability is not significantly altered by enforcing a threshold policy.     

Optimal investment–reinsurance strategies with state dependent risk aversion and VaR constraints in correlated markets

In this paper, we investigate the optimal time-consistent investment–reinsurance strategies for an insurer with state dependent risk aversion and Value-at-Risk (VaR) constraints. The insurer can purchase proportional reinsurance to reduce its insurance risks and invest its wealth in a financial market consisting of one risk-free asset and one risky asset, whose price process follows a geometric Brownian motion. The surplus process of the insurer is approximated by a Brownian motion with drift. The two Brownian motions in the insurer’s surplus process and the risky asset’s price process are correlated, which describe the correlation or dependence between the insurance market and the financial market. We introduce the VaR control levels for the insurer to control its loss in investment–reinsurance strategies, which also represent the requirement of regulators on the insurer’s investment behavior. Under the mean–variance criterion, we formulate the optimal investment–reinsurance problem within a game theoretic framework. By using the technique of stochastic control theory and solving the corresponding extended Hamilton–Jacobi–Bellman (HJB) system of equations, we derive the closed-form expressions of the optimal investment–reinsurance strategies. In addition, we illustrate the optimal investment–reinsurance strategies by numerical examples and discuss the impact of the risk aversion, the correlation between the insurance market and the financial market, and the VaR control levels on the optimal strategies.     

Modal Coupling for Active Damping of Load Swing of Container Cranes

Oscillation control of container handling is dominated by open-loop or closed-loop control of the crane trolley, which highly effects the crane operator's well-being. An alternative actuating approach is presented using the hoists of the crane system. Simulation and test stand results prove the effect of modal coupling control of container handling and its capability to assure improved work environment conditions for the operator of container cranes. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling and Optimal Receding-horizon Control of Maritime Container Terminals

The main objective of this paper consists in modelling, optimizing, and controlling container transfer operations inside intermodal terminals. More specifically, maritime container terminals are here considered, involving three kinds of transportation modes, i.e., maritime, rail, and road transport. Generally speaking, an intermodal port terminal can be seen as a system of container flows with two interfaces, towards the hinterland and towards the sea, respectively. Moreover, inside a terminal, unloading operations of inbound containers, container storage, and loading operations of outbound containers are carried out. A simple model for maritime container terminals is proposed in this paper. In the model, a system of queues represents the standing of containers and their movements inside the terminal. The dynamic evolutions of these queues are described by discrete-time equations, where the state variables represent the queue lengths and the control variables take into account the utilization of terminal resources such as load/unload handling rates. On the basis of the proposed model, an optimization problem is defined that consists in minimizing the transfer delays of containers in the terminal. The problem is stated as an optimal control problem whose solution is sought by adopting a receding-horizon strategy.      

A heuristic for sea-freight container selection,cargo allocation and cargo orientation

A model is proposed to generate solutions for container selection, for the allocation of cargo to containers, and for cargo orientation within a container. The model is in the form of a mixed integer program with the objective of minimizing the total shipping cost. The practical requirements of loading priority and weight distribution along the main dimension of the container are incorporated into the model. A heuristic solution strategy is proposed and used to control the computation time by pre-setting the search increments. Three case examples are presented. The first and third examples show that the proposed model can produce a better solution than the manual schedulers. The second example is taken from the literature and is compared with the solution generated by the proposed model, demonstrating that the practical considerations incorporated into the model do not necessarily lead to increased shipping costs.     

Motion of a container as a nonholonomous system in a curved section of a horizontal pipeline

The problem of the motion of a container in a curved section of a horizontal pipeline is solved using second-order Lagrange equations in the presence of nonholonous couplings. The special case of the motion of a container in a circular curve is examined.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 90–95, 1987.