露天矿卡车运输系统最佳调度的数学模型及其数值解法研究

文章分析了目前卡车调度系统的建模情况,应用最佳控制的理论建立了卡车调度系统的数学模型,并结合一简例,分析了数值解法,给出简例的数值解。通过对数值解的分析,说明数学模型和数值解法都是正确的     

Optimal control asymptotics of a magnetohydrodynamic flow

An optimal multiplicative control problem is considered for a one-dimensional magnetohydrodynamic flow between parallel planes (Hartman flow). The external magnetic field is used as a control function. An optimality system is derived, and the asymptotics of an optimal control with respect to a regularization parameter and the Reynolds number are constructed.     

Optimal guaranteed control of linear systems under disturbances

This paper is devoted to the problem of the minimax control of a dynamical system with quadratic performance functional under external disturbances and geometric control constraints. The optimal guaranteed control strategy is obtained in explicit form.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 198–205, August, 1996.This research was supported by the Russian Foundation for Basic Research under grant No. 95-01-000771a.     

Optimal feedback control of bilinear systems

Feedback synthesis of optimal constrained controls for single-input bilinear systems is considered. Quadratic cost functionals (with and without quadratic control penalization) are modified by the inclusion of additional nonnegative state penalizing functions in the respective cost integrands. The latter functions are chosen so as to regularize the problems, in the sense that feedback solutions of particularly simple form are obtained. Finite and infinite time horizon problem formulations are treated, and associated aspects of feedback stabilization of bilinear systems are discussed.     

Optimal control and basic reproduction numbers for a compartmental spatial multipatch dengue model

Dengue is a vector‐borne viral disease increasing dramatically over the past years due to improvement in human mobility. In this work, a multipatch model for dengue transmission dynamics is studied, and by that, the control efforts to minimize the disease spread by host and vector control are investigated. For this model, the basic reproduction number is derived, giving a choice for parameters in the endemic case. The multipatch system models the host movement within the patches, which coupled via a residence‐time budgeting matrix P. Numerical results confirm that the control mechanism embedded in incidence rates of the disease transmission effectively reduces the spread of the disease.     

Optimal control of dengue epidemic outbreaks under limited resources

In this paper, we reflect upon control intervention practices habitually exerted by healthcare authorities in tropical areas that suffer from incidental outbreaks of dengue fever, in particular, the city of Cali, Colombia. Such control interventions, principally based on the insecticide spraying, are carried out sporadically in order to overcome an ongoing epidemic or at least to reduce its size. It is worth pointing out that control actions of this type do not usually account for sufficient budget because epidemic outbreaks are difficult to predict. In practical terms, these occasional control interventions are performed by spraying, as quickly as possible, all existing stock of insecticide (regardless of its lethality) and employing all available manpower. The goal of this paper is to design better strategies for insecticide-based control actions, which are capable of preventing more human infections at no additional cost, and to reveal the obsolescence of current vector eradication practices. Our approach relies on dynamic optimization, where the number of averted human infections is maximized under budget constraint and subject to a simple dengue transmission model amended with one control variable that stands for the insecticide spraying. As a result, we obtain structurally robust control intervention policies that demonstrate better performance and higher resilience to possible budget limitations than traditional modus operandi.     

Optimal control of sea level in a tidal basin by means of the Pontryagin maximum principle

The maximum principle has been applied in optimizing the sea level, induced by a tidal component, in a small basin. The water level control has been simulated by means of gate operations acting at the open mouth of the tidal basin. The main feature of the model is that the control operations do not require complete closure of the basin but only a variable reduction of its mouth. Although the equations describing the dynamics of the basin have been simplified, the results obtained are expected to be of practical use.     

Optimal control of tandem reentrant queues

We consider optimal policies for reentrant queues in which customers may be served several times at the same station. We show that for tandem reentrant queues the last-buffer first-served (LBFS) policy stochastically maximizes the departure process. This revised version was published online in June 2006 with corrections to the Cover Date.     

Optimal intensity control of a multi-class queue

We study a mixed problem of optimal scheduling and input and output control of a single server queue with multi-classes of customers. The model extends the classical optimal scheduling problem by allowing the general point processes as the arrival and departure processes and the control of the arrival and departure intensities. The objective of our scheduling and control problem is to minimize the expected discounted inventory cost over an infinite horizon, and the problem is formulated as an intensity control. We find the well-knownc is the optimal solution to our problem.Supported in part by NSF under grant ECS-8658157, by ONR under contract N00014-84-K-0465, and by a grant from AT&T Bell Laboratories.The work was done while the author was a postdoctoral fellow in the Division of Applied Sciences, Harvard University, Cambridge, Massachusetts 02138.     

Optimal design and control of queues

We have divided this review into two parts. The first part is concerned with the optimal design of queueing systems and the second part deals with the optimal control of queueing systems. The second part, which has the lion’s share of the review since it has received the most attention, focuses mainly on the modelling aspects of the problem and describes the different kinds of threshold (control) policy models available in the literature. To limit the scope of this survey, we decided to limit ourselves to research on papers dealing with the three policies (N, T, and D), where a cost function is designed specifically and optimal thresholds that yield minimum cost are sought.     

Convex-concave utility function: Optimal blood-consumption for vampires

This paper considers an optimal control problem for the dynamics of a predator-prey model. The predator population has to choose the predation intensity over time in a way that maximizes the present value of the utility stream derived by consuming prey. The utility function is assumed to be convex for small levels of consumption and concave otherwise. The problem is solved using the maximum principle and different time patterns of the optimal solution are obtained in the cases of small, medium and high rates of time preference. The model has features of both, convex and concave optimal control problems and therefore phase plane analysis has to be combined with the problem of synthesis of bang-bang, singular and chattering solution pieces.     

Optimal control of an elastic string with viscous damping

We study bilinear optimal control of a wave equation with one spatial dimension. The problem describes oscillations of an elastic string with viscous damping, and the damping coefficient is taken as the control. The objective functional involves driving the state solution close to a desired profile and incurring a cost on the control. The optimal control is characrerized in terms of an optimality system.     

Chaos control and synchronization of fractional order delay‐varying computer virus propagation model

In the present article, the authors have studied the dynamical behavior of delay‐varying computer virus propagation (CVP) model with fractional order derivative, and it is found that the chaotic attractor exists in the considered fractional order system. In order to eliminate the chaotic behavior of fractional order delay‐varying CVP model, feedback controlmethod is used. This article also dealswith the synchronization between controlled and chaotic delay‐varying CVPmodel via active controlmethod. The fractional derivative is described in the Caputo sense. Numerical simulation results are carried out by means of Adams‐Boshforth‐Moultonmethod with the help ofMATLAB, and the results are successfully depicted through graphs .Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal control applied on an HIV‐1 within‐host model

The treatment of human immunodeficiency virus (HIV) remains a major challenge, even if significant progress has been made in infection treatment by ‘drug cocktails’. Nowadays, research trend is to minimize the number of pills taken when treating infection. In this paper, an HIV‐1 within host model where healthy cells follow a simple logistic growth is considered. Basic reproduction number of the model is calculated using next generation matrix method, steady states are derived; their local, as well as global stability, is discussed using the Routh–Hurwitz criteria, Lyapunov functions and the Lozinskii measure approach. The optimal control policy is formulated and solved as an optimal control problem. Numerical simulations are performed to compare several cases, representing a treatment by Interleukin2 alone, classical treatment by multitherapy drugs alone, then both treatments at the same time. Objective functionals aim to (i) minimize infected cells quantity; (ii) minimize free virus particles number; and (iii) maximize healthy cells density in blood. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal control of infinite-dimensional uncertain systems

In this paper, we consider a minimax problem of optimal control for a class of strongly nonlinear uncertain evolution equations on a Banach space. We prove the existence of optimal controls. A nontrivial example of a class of systems governed by a nonlinear partial differential equation with uncertain spatial parameters is presented for illustration.This work was supported in part by the National Science and Engineering Research Council of Canada under Grant No. A7109 and The Engineering Faculty Development Fund, University of Ottawa.The authors would like to thank the anonymous reviewers for their valuable comments and suggestions.     

Optimal control synthesis in therapy of solid tumor growth

A mathematical model of tumor growth therapy is considered. The total amount of a drug is bounded and fixed. The problem is to choose an optimal therapeutic strategy, i.e., to choose an amount of the drug permanently affecting the tumor that minimizes the number of tumor cells by a given time. The problem is solved by the dynamic programming method. Exact and approximate solutions to the corresponding Hamilton-Jacobi-Bellman equation are found. An error estimate is proved. Numerical results are presented.     

Optimal control in a macroeconomic problem

The Pontryagin maximum principle is used to develop an original algorithm for finding an optimal control in a macroeconomic problem. Numerical results are presented for the optimal control and optimal trajectory of the development of a regional economic system. For an optimal control satisfying a certain constraint, an invariant of a macroeconomic system is derived.     

具有年龄结构的种群线性动力系统的最优收获控制问题

§ 1　Introduction and setting of the problemThe optimal control of age-dependent population dynamics has been intensivelystudied in the last two decades and there is now a vast stock of literature on the topic ofoptimal control problems ofage-structured population dynamics.(see [1 -9] ) .To the bestof our knowledge,the works of Brokate[3,4] are the firstto deal with this topic.Since then,many authors devote to the optimal harvesting problem.In this aspect,we refere to thefundamental papers o…     

Optimal control of a signorini contact problem

We are interested in finding the coefficient of friction which leads us to a given displacement on the contact surface between an elastic solid body and a rigid foundation. The mathematical formulation of the problem is an optimal control problem governed by a quasivariational inequality. We obtain an approximative caracterization, by using two families of penalized and regularized problems, for a given optimal control.     

Optimal control problem of a generalized Ginzburg–Landau model equation in population problems

In this paper, we consider the problem for distributed optimal control of the generalized Ginzburg–Landu model equation in population. The optimal control under boundary condition is given, the existence of optimal solution to the equation is proved, and the optimality system is established. Copyright © 2013 John Wiley & Sons, Ltd.