Solution approximation in a minimax control problem for a singularly perturbed system with delay

We consider a control problemwith a minimax criterion for a singularly perturbed system with delay. We propose a procedure for constructing an initial approximation to control in the minimax control problem.     

Real-time calculation of the current state estimates for a class of delay systems

The linear optimal observation problem is examined for one type of nonstationary delay system with an uncertainty in the initial state. A fast implementation of the dual method is proposed for calculating estimates of the initial state. This implementation is based on the quasi-reduction of the fundamental matrix of solutions to the mathematical model of delay systems. It is shown that an iteration step of the dual method only requires that auxiliary systems of ordinary differential equations be integrated on small time intervals. An algorithm is described for the real-time calculation of current state estimates. The results are illustrated by the optimal observation problem for a third-order stationary delay system.     

A method of solving boundary-value problems for a non-linear control system allowing for delay in the control action

An algorithm is developed for constructing a control function that guarantees that a wide class of non-linear control systems, described by ordinary differential equations, is transferred from an initial state into a specified final state, allowing for constraints on the system and a delay in the control signal. A constructive criterion is found for the choice of the final states and the value of the delay in the control signal for which the above transfer is possible. An interorbital flight problem is studied as an example and is modelled numerically.     

Optimal control problem with phase constraints for a linear system of equations with delay

The optimal control problem for a linear system of differential equations with delay for which the initial function on the initial set is the control function is considered. Phase constraints with variable times are imposed on the trajectory of the object. Necessary optimality conditions of controls in admissible classes are obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 12, pp. 1647–1652, December, 1991.     

On the existence of an optimal element for a delay control problem

The existence theorems of the optimal element are proved for a nonlinear control problem with constant delay in phase coordinates and with general functional. Here element implies the collection of delay parameter and initial function, initial moment and vector, control and finally moment.     

Real-time calculation of current optimal feedbacks for a delay system

A linear optimal control problem for a nonstationary system with a single delay state variable is examined. A fast implementation of the dual method is proposed in which a key role is played by a quasi-reduction of the fundamental matrices of solutions to the homogeneous part of the delay models under analysis. As a result, an iteration step of the dual method involves only the integration of auxiliary systems of ordinary differential equations over short time intervals. A real-time algorithm is described for calculating optimal feedback controls. The results are illustrated by the optimal control problem for a second-order stationary system with a fixed delay.     

一类非线性系统的时滞相关H∞控制

本文研究一类非线性控制系统的时滞相关日。控制问题．首先通过构造恰当的Lyapunov泛函,设计非线性H∞控制器,得到了该类非线性控制系统渐近稳定的一个充分条件．其次通过建立具有线性矩阵不等式（LMI）约束的凸优化问题,得到了该类非线性系统的时滞相关H∞性能的一个充分条件．MATLAB仿真验证了本文方法的可行性．     

一类带小时滞的非线性快慢系统的渐近解

研究了一类带小时滞的非线性快慢系统的初始值问题,在一定假设条件下,利用奇异摄动理论和校正函数法构造了该问题的形式渐近解,并利用微分不等式理论证明了渐近解的一致有效性.最后进行了算例分析,结果显示时滞能对快慢系统产生重要影响,并表明所述摄动方法是一个行之有效的近似解析方法.从而,可以利用得到的渐近解对系统的动力学行为进行更深层次地分析与研究.     

具无穷时滞竞争扩散系统周期解的唯一性

研究了一类具有无穷时滞竞争扩散模型的周期解问题,采用了上下解的方法,获得了周期解的存在唯一性,并给出了解的渐近性态.     

On scheduling a multiclass queue with abandonments under general delay costs

We consider a multiclass queueing system with abandonments and general delay costs. A system manager makes dynamic scheduling decisions to minimize long-run average delay and abandonment costs. We consider the three types of delay cost: (i) linear, (ii) convex, and (iii) convex–concave, where the last one corresponds to settings where customers may have a particular deadline in mind but once that deadline passes there is increasingly little difference in the added delay. The dynamic control problem for the queueing system is not tractable analytically. Therefore, we consider the system in the conventional heavy traffic regime and study the approximating Brownian control problem (BCP). We observe that the approximating BCP does not admit a pathwise solution due to abandonments. In particular, the celebrated cμ rule and its extension, the generalized cμ rule, which is asymptotically optimal under convex delay costs with no abandonments, are not optimal in this case. Consequently, we solve the associated Bellman equation, which yields a dynamic index policy (derived from the value function) as the optimal control for the approximating BCP. Interpreting that control in the context of the original queueing system, we propose practical policies for each of the three cases considered and demonstrate their effectiveness through a simulation study.     

一类滞后生态微分方程的初值问题

对一般的滞后系统，人们采用了将滞后变量ｘ（ｔ－１）用一个Ｈｅｒｍｉｔｅ插值多项式来处理，从而把滞后系统转化为常微分方程系统来求其数值解（见文［２］，［３］）．本文根据［２］中的表Ⅰ选用了一个带有五次Ｈｅｒｍｉｔｅ插值多项式的四阶Ｒｕｎｇｅ－Ｈｕｔａ法来求两个常见的滞后初值问题．     

Digital Stabilizer Design for a Switched Linear Control Delay System

The problem of designing a digital controller stabilizing a continuous-time switched linear control delay system is studied. The approach to stabilization successively includes the construction of a continuous-time–discrete-time closed-loop system with a digital controller, the transition to its discrete-time model, and the construction of a discrete-time controller by simultaneous stabilization methods.     

ASYMPTOTIC BEHAVIOUR OF A DIFFUSION SYSTEM WITH TIME DELAY IN POPULATION DYNAMICS

ＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＵＲＯＦＡＤＩＦＦＵＳＩＯＮＳＹＳＴＥＭＷＩＴＨＴＩＭＥＤＥＬＡＹＩＮＰＯＰＵＬＡＴＩＯＮＤＹＮＡＭＩＣＳＤｉｎｇＣｈｏｎｇｗｅｎ(丁崇文）（ＦｕｊｉａｎＥｄｕｃａｔｉｏｎａｌＣｏｌｌｅｇｅ，福建教育学院，邮编：３５?..     

时滞广义时变系统的容许性分析与镇定

研究了时滞广义时变系统的容许性与镇定性问题.首先,基于广义Lyapunov不等式、线性矩阵不等式和受限等价方法,建立时滞广义时变系统的Lyapunov不等式,将时滞广义时变系统的容许性问题转化为求解时滞广义时变系统的Lyapunov不等式问题,得到了系统容许的充分条件.然后,根据充分条件进一步研究了时滞广义时变系统的镇定问题,给出了状态反馈镇定器的设计方法.最后,通过数值算例验证了所得结论的有效性.     

Optimal control of switched systems with time delay

In this note, we develop a computational method for solving an optimal control problem which is governed by a switched dynamical system with time delay. Our approach is to parameterize the switching instants as a new parameter vector to be optimized. Then, we derive the required gradient of the cost function which is obtained via solving a number of delay differential equations forward in time. On this basis, the optimal control problem can be solved as a mathematical programming problem.     

One control problem of a pencil of trajectories

A linear control problemwith a nonsingleton initial set is dealt with. For this problem,we consider the problem of transforming this initial set along trajectories of a linear controlled system into some fixed terminal set in a finite time using a single control. Various aspects of this control problem are studied using the machinery of support functions.     

The optimization of a guaranteed result with a delay in the control

The problem of feedback control with a quality index in the form of the Euclidean norm of a set of deviations of the trajectory of motion of the system from the origin of coordinates at specified instants of time is considered for a linear dynamical system that is subjected to the effects of noise and contains a delay in the control element. A procedure for calculating the value of the optimal guaranteed result based on the recursive construction of upper convex hulls of auxiliary functions is given. A method for shaping the controlling actions that guarantee the achievement of this result is described.     

A Stochastic Maximum Principle for a Markov Regime-Switching Jump-Diffusion Model with Delay and an Application to Finance

We study a stochastic optimal control problem for a delayed Markov regime-switching jump-diffusion model. We establish necessary and sufficient maximum principles under full and partial information for such a system. We prove the existence–uniqueness theorem for the adjoint equations, which are represented by an anticipated backward stochastic differential equation with jumps and regimes. We illustrate our results by a problem of optimal consumption problem from a cash flow with delay and regimes.     

Numerical Leak Detection in a Pipeline Network of Complex Structure with Unsteady Flow

An inverse problem for a pipeline network of complex loopback structure is solved numerically. The problem is to determine the locations and amounts of leaks from unsteady flow characteristics measured at some pipeline points. The features of the problem include impulse functions involved in a system of hyperbolic differential equations, the absence of classical initial conditions, and boundary conditions specified as nonseparated relations between the states at the endpoints of adjacent pipeline segments. The problem is reduced to a parametric optimal control problem without initial conditions, but with nonseparated boundary conditions. The latter problem is solved by applying first-order optimization methods. Results of numerical experiments are presented.     

Stability of traveling waves in a monostable delayed system without quasi-monotonicity

This paper is concerned with traveling waves of a monostable reaction–diffusion system with delay and without quasi-monotonicity. When the initial perturbation around the traveling wave is suitably small in a weighted norm, the exponential stability of all traveling wave solutions for the system with delay is proved by the weighted energy method.