Quasiperiodic motion induced by heterogeneous delays in a simplified internet congestion control model

In this paper, a simplified congestion control model is considered to study the quasiperiodic motion induced by heterogenous time delays. Analysis for the stability of the equilibrium shows that the Hopf bifurcation curves with diverse frequencies may intersect at the so-called non-resonant double Hopf bifurcation point. Choosing the delays as the bifurcation parameters and employing the method of multiple scales, the amplitude–frequency equations or normal form equations are obtained theoretically. Based on these equations, the dynamics near the bifurcation point is classified. The values of the delays for which the quasiperiodic motion exists can be predicted with an acceptable accuracy. This result provides a reference in designing and optimizing the network systems.     

Navigation and control of the motion of a back wheel drive tricycle

This work deals with the guidance and control of the motion of a back wheel drive tricycle. Denote by O the center of mass of the tricycle. Given N points P_i, i = 0,…, N − 1 in the horizontal plane, a finite time interval [0, t_f], and a sequence of times τ₀ = 0 < τ₁ < … < τ_{N −1} = t_f. Based on a dynamical model of the tricycle, and by using the concept of path controllability, control laws are derived for the tricycle's pedalling moment and directional moment such that O will pass through p_j at the time τ_j, j = 0,…, N − 1, respectively.     

Unsteady state fugacity model by a dynamic control system

A continuous time dynamic system of an unsteady state fugacity model is presented. Properties of this model as stability are studied. In order to evaluate numerical results a discretization preserving the stability and yielding the positivity property of the model is used. Finally, algorithms to determine the values of the fugacities, the concentrations and the dissipation time are given. The above study is illustrated with numerical results in a three compartmental environmental system.     

On the dynamic model and motion planning for a spherical rolling robot actuated by orthogonal internal rotors

The paper deals with the dynamics of a spherical rolling robot actuated by internal rotors that are placed on orthogonal axes. The driving principle for such a robot exploits nonholonomic constraints to propel the rolling carrier. A full mathematical model as well as its reduced version are derived, and the inverse dynamics are addressed. It is shown that if the rotors are mounted on three orthogonal axes, any feasible kinematic trajectory of the rolling robot is dynamically realizable. For the case of only two rotors the conditions of controllability and dynamic realizability are established. It is shown that in moving the robot by tracing straight lines and circles in the contact plane the dynamically realizable trajectories are not represented by the circles on the sphere, which is a feature of the kinematic model of pure rolling. The implication of this fact to motion planning is explored under a case study. It is shown there that in maneuvering the robot by tracing circles on the sphere the dynamically realizable trajectories are essentially different from those resulted from kinematic models. The dynamic motion planning problem is then formulated in the optimal control settings, and properties of the optimal trajectories are illustrated under simulation.     

Analysis and approximation of optimal control problems for a simplified Ginzburg-Landau model of superconductivity

Summary. This paper is concerned with optimal control problems for a Ginzburg-Landau model of superconductivity that is valid for high values of the Ginzburg-Landau parameter and high external fields. The control is of Neumann type. We first show that optimal solutions exist. We then show that Lagrange multipliers may be used to enforce the constraints and derive an optimality system from which optimal states and controls may be deduced. Then we define finite element approximations of solutions for the optimality system and derive error estimates for the approximations. Finally, we report on some numerical results. Received May 3, 1994 / Revised version received November 28, 1995     

Trajectory-tracking of 6-RSS Stewart-Gough manipulator by feedback-linearization control using a novel inverse dynamic model based on the force distribution algorithm

ABSTRACT

6-RSS Stewart-Gough parallel manipulator contains six crank-rod limbs connecting the base and moving platforms to each other, forming a 6DOF manipulator. In this paper, we introduce a novel decoupled inverse dynamic model for this manipulator based on the Force Distribution Algorithm. The performance of the proposed model was evaluated in tracking a complex trajectory (of multiple segments with simultaneous translational and rotational motions) using feedback-linearization control in the joint space and compared with that of the Lagrangian inverse dynamic model. Results showed that this model leads to a better performance in feedback-linearization control, especially when the reference trajectory is quantized, and with less calculation burden in comparison with the Lagrangian model. The control system employing both models showed robustness against payload uncertainty on the moving platform (150% of the moving platform’s mass). The performance assessment and the robustness approval were performed in simulation using a Simscape model specifically built for this purpose in the Simulink environment.     

Congestion control using dynamic routing and flow control

In this paper, the congestion control in store and forward computer com-munication networks is studied, the method employed consists of a combination of a dynamic routing policy that minimizes the delay, and buffer nianagement schemes to control the flow of data. Simulation using liner programming has been carried out, under balanced and transient traffic conditions, on a simple 3–node network , the relative merits and drawbacks of each approach are discussed. Irland [2], showed that with static routing, the SQRT scheme improves the switch performance. In this paper it is shown that in the case of dynamic routing, the SQRT is an excellent solution to remedy the performance degradation caused by CP and CS schemes     

Optimal feedback control for a thermoviscoelastic model of Voigt fluid motion

A system of equations describing the motion of viscous fluids with polymer additives is considered. The system involves a temperature-dependent viscosity and a velocity-dependent external force, which is used as a control. The existence of an optimal feedback control for the system is proved.     

Reinsurance control in a model with liabilities of the fractional Brownian motion type

We propose a model for reinsurance control for an insurance firm in the case where the liabilities are driven by fractional Brownian motion, a stochastic process exhibiting long-range dependence. The problem is transformed to a nonlinear programming problem, the solution of which provides the optimal reinsurance policy. The effect of various parameters of the model, such as the safety loading of the reinsurer and the insurer, the Hurst parameter, etc. on the optimal reinsurance program is studied in some detail. Copyright © 2007 John Wiley & Sons, Ltd.     

Optimal control in a model of the motion of a viscoelastic medium with objective derivative

In this paper we consider the Jeffreys model of the motion of a viscoelastic incompressible medium with the Yaumann derivative. Within this model we study the optimal control problem for the right-hand sides of the initial boundary value problem. We prove the existence of the optimal strong solution.     

Optimum control laws in a non-autonomous dynamic model of a gas field

A model of gas field development described as a nonlinear optimum control problem with an infinite planning horizon is considered. The Pontryagin maximum principle is used to solve it. The theorem on sufficient optimumity conditions in terms of constructions of the Pontryagin maximum principles is used to substantiate the optimumity of the extremal solution. A procedure for constructing the optimum solution by dynamic programming is described and is of some methodological interest. The obtained optimum solution is used to construct the Bellman function. Reference is made to a work containing an economic interpretation of the problem.     

A multiattractor model for the dynamic control of companies

The dynamic behaviour of complex human organisations in dynamic environments results from the interplay of multiple agents. In the particular case of a commercial or industrial companies, the agents are for example the shareholders, the customers/consumers, the subcontractors/competitors, the workers/employees etc. The role of the managers is to find and to maintain the adequate balance of resources between various management levels to respond to the conflicting interests of these agents without endangering the viability of the company. A distinction is made between operational, strategic and normative levels. Kolm's triangle is introduced as a convenient representation for making visible the relative strength of the three management levels. In the triangle a stability polygon representing a viability zone is identified and monitored by observing the company's indicators. Failure paths are followed whenever the current representative point in Kolm's triangle shifts towards the boundaries of the stability polygon. Herewith a diagnostic tool is provided to the managers in charge to design control policies preventing such adverse evolution.     

Global optimization using a synchronization of multiple search Points autonomously driven by a chaotic dynamic model

In the present paper, we propose a new multipoint type global optimization model using a chaotic dynamic model and a synchronization phenomenon in nonlinear dynamic systems for a continuously differentiable optimization problem. We first improve the Discrete Gradient Chaos Model (DGCM), which drives each search point’s autonomous movement, based on theoretical analysis. We then derive a new coupling structure called PD type coupling in order to obtain stable synchronization of all search points with the chaotic dynamic model in a discrete time system. Finally, we propose a new multipoint type global optimization model, in which each search point moves autonomously by improved DGCM and their trajectories are synchronized to elite search points by the PD type coupling model. The proposed model properly achieves diversification and intensification, which are reported to be important strategies for global optimization in the Meta-heuristics research field. Through application to proper benchmark problems [Liang et al. Novel composition test functions for numerical global optimization. In: Proceedings of Swarm Intelligence Symposium, 2005 (SIS 2005), pp. 68–75 (2005); Liang et al. Nat. Comput. 5(1), 83–96, 2006] (in which the drawbacks of typical benchmark problems are improved) with 100 or 1000 variables, we confirm that the proposed model is more effective than other gradient-based methods.     

利用传递函数——噪声模型表达经济变量间的动态影响机制

传递函数———噪声模型是一类多变量时间序列模型,它在表达系统动态影响机制方面有着独到的优势。本文将这种模型的建模方法应用于经济系统,建立了一个表达产值和出口间动态关系的传递函数———噪声模型。近几个月的实际数据表明模型的拟合是理想的。     

On an optimal control problem in the Voigt model of the motion of a viscoelastic fluid

The external feedback control problem in the Voigt model of the motion of a viscoelastic fluid is investigated. To this end, we prove the existence of weak solutions of the initial-boundary problem with the multi-valued right-hand side in the model considered and show the existence of a solution minimizing a given bounded lower semicontinuous functional. __________ Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 16, Differential and Functional Differential Equations. Part 2, 2006.     

Analysis of a simplified model of drop combustion

Summary A simplified model of drop combustion is studied; its main mathematical difficulty is a nonlinearity which does not satisfy a Lipschitz condition. The existence of a solution is proved and a uniqueness result is given. Moreover, an algorithm is stated and its convergence is proved.Supported by the Fonds National Suisse de la Recherche Scientifique     

Stabilization and control of the motion of a rolling disk

This work deals with the stabilization and control of the motion of a disk rolling on the horizontal plane. It is assumed here that the motion of the disk is controlled by a tilting moment, a directional moment, and a pedalling moment. By using a kind of an inverse control transformation, a control strategy is proposed under which the motion of the disk is stabilized and is able asymptotically to track any given smooth ground trajectory.     

Nonlinear dynamic analysis of viscoelastic beams using a fractional rheological model

The paper presents quasi-static analysis, classical and fractional dynamic analysis of a simply supported viscoelastic beam subjected to uniformly distributed load, where the Riemann–Liouville fractional derivative is of the order ν ∈ (0, 1). A comparative study of the results obtained for a classical and fractional Zener model using the techniques of Laplace transform, Bessel functions theory and binomial series is achieved. The graphic representations show how the existence of fractional derivative in the selected rheological model influences the dynamic response of the structure. This paper provides a theoretical basis for researchers who want to choose a mathematical model that will precisely fit with a particular experimental model.