K一致圆形与渐近非扩张型映象的不动点

本文在k一致圆形Banach空间中证明了连续渐近非扩张型映象不动点的存在性。这一结果推广了Gocbcl-Kirk,Kirk,俞鑫泰—戴兴德等人的结果。本文还在K-致圆形且满足Opial条件的Banach空间中证明了渐近非扩张(型)映象Picard逐次迭代序列的弱收敛性。     

具有正负系数的二阶非线性中立型方程的非振动准则

中立型泛函微分方程的振动性在理论和应用中有着重要意义。本文研究了一类具有正负系数的二阶非线性中立型时滞泛函微分方程的振动性,利用Banach空间的压缩映象原理和一些分析技巧,建立了该方程非振动的一些新的准则,并给出了定理应用的例子。所得结论推广和改进了现有文献中的一系列结果。     

共振条件下 $p$-Laplacian 方程三点边值问题的可解性

运用紧向量场方程的解集连通理论和常序上下解方法,对共振条件下 $p$-Laplacian 方程三点边值问题进行了研究,其中的非线性项连续,将所研究的问题改写成定义在某个 Banach 空间上的泛函方程,继而获得解的存在性结果。     

Banach空间中二阶周期边值问题的解

本文研究Banach空间中弱拓扑下二阶周期边值问题的解。在上解小于等于下解的假设条件下证明了二阶周期边值问题解的存在性。     

Banach空间中二阶微分方程的无穷边值问题

利用Monch不动点定理研究了Banach空间中一类无穷区间上的二阶微分方程的边值问题，在比较弱的条件下得到了解的存在性。     

修理工可单重休假带有一个冷贮备部件并联系统的适定性

本文运用线性算子半群理论研究修理工可单重休假的带有一个冷贮备部件的Gaver并联可修系统的适定性问题．文中假定部件的工作时间服从指数分布,修理时间和修理工的休假时间均服从一般连续分布．通过对描述该系统行为的偏微分方程组的规范化,并引入系统的状态空间,主算子及其定义域,我们将该系统方程转化成Banach空间中的抽象的Cauchy问题．然后,运用泛函分析中的Hille-Yosida定理、Phillips定理与Fattorini定理,我们证明了该系统存在唯一的、满足概率性质的正时间依赖解．     

基于二阶矩阵微分方程的机械振动系统线性二次型调节器设计

本文讨论机械振动系统线性二次型状态调节器（LQR）问题，直接针对系统二阶运动微分方程，性能指标为一个依赖于二阶导数的泛函。由欧拉-拉格朗日方程得出一个系统矩阵增广的二阶线性微分方程，指出该方程稳定的特征对就是最优控制振动系统闭环特征对，并给出求解最优控制状态反馈矩阵的方法，另外，由本文方法还可得出基于速度和加速度反馈的最优控制反馈矩阵。这里不涉及求解代数矩阵Riccati方程。     

复对合Banach代数态的刻划

Gaur(1998)提出并利用g-有界泛函刻划任意复合对Banach代数，但对这类泛函的性质刻划甚少，详细讨论了其具有一些重要性质。     

Orlicz空间中一个最优控制问题

本文对于一个分布参数系统的最优边界控制问题,借助于Orlicz空间,讨论了最优控制的唯一存在性,并给出最优控制的判别条件。 考虑分布参数系统[1]     

物理空间下转子轴承系统电磁阻尼器的最优控制研究

本文研究电磁阻尼器对转子轴承系统的最优控制规律。首先给出受电磁阻尼器控制的一般多自由度转子轴承系统的振动方程，在此基础上直接在物理空间求出强迫响应和最优控制电流，并导出部分响应可观察时的激振力估计。本文的研究及提出的最优控制规律，利用稳态响应的特点，物理概念明确，且计算简捷。计算机仿真表明，采用本文提出的最优控制规律，可获得较好的控制效果。     

Melnikov’s method for controlled stochastic oscillations of a rocking block with fractional derivative

The problem of controlling a rocking block with fractional dissipation so as to prevent it from leaving a prescribed set of bounded oscillations has a number of interesting applications in many scientific and technological fields. This work develops an analytical framework to describe the influence of control on the behavior of a fractionally dissipative rocking block subject to random acceleration of the ground. Control equations are developed and control strategies leading to optimal suppression of instability are asymptotically described under the assumptions of weak dissipation along with a small energy noise. Under these assumptions, the behavior of the block is interpreted as weakly perturbed rocking oscillations close to a generic periodic solution, and the Melnikov approximations are considered as the necessary conditions of instability. The stochastic Melnikov criterion derived in this paper allows for an approximate calculation of an upper bound to the overturning probability as well as to the representation of an optimal control strategy. The Melnikov criterion for stochastic rocking oscillations in the presence of convenient control strategies are derived explicitly for the first time, using an extension of the Melnikov theory to a model with fractional derivative.     

A convenient solver for solving optimal control problems

Abstract

This paper focuses on the development of a solver for solving optimal control problems. A developed numerical optimal control module integrated with the Sequential Quadratic Programming method is introduced. An optimal control problem solver based on the proposed method is implemented to solve optimal control problems efficiently in engineering applications. In addition, a systematic procedure for solving optimal control problems by using the optimal control problem solver is also proposed. A time‐optimal benchmark problem presented in the literature is used to illustrate for the capability and facility of solving optimal control problems. The numerical results demonstrate the proposed method and the procedure suggested in this paper are helpful to engineers in solving optimal control problems in a systematic and efficient manner.     

Parametric optimal control of uncertain systems under an optimistic value criterion

It is well known that the optimal control of a linear quadratic model is characterized by the solution of a Riccati differential equation. In many cases, the corresponding Riccati differential equation cannot be solved exactly such that the optimal feedback control may be a complex time-oriented function. In this article, a parametric optimal control problem of an uncertain linear quadratic model under an optimistic value criterion is considered for simplifying the expression of optimal control. Based on the equation of optimality for the uncertain optimal control problem, an approximation method is presented to solve it. As an application, a two-spool turbofan engine optimal control problem is given to show the utility of the proposed model and the efficiency of the presented approximation method.     

A SINGULAR-ARC APPROXIMATION TO A DYNAMIC SAILPLANE FLIGHT PATH OPTIMIZATION PROBLEM

A dynamic sailplane performance problem is investigated using optimal control theory. The problem is to minimize the total flight time between successive thermals subject to zero altitude loss. From the original nonlinear optimal control problem, a singular linear/quadratic problem is derived and solved.

A relationship between the original optimal control problem and a certain parameter optimization problem is explored, and it is shown that the solution to this parameter optimization provides a lower bound for the minimum flight time of the original optimal control problem. The parameter optimization solution is adopted as the reference trajectory for the linear/quadratic problem. Finally, the linear/quadratic problem is shown to provide a good approximation to the original optimal control problem at a small fraction of the computing cost.     

Calculation of optimum feedback gains for output constrained regulators

A new and a simple algorithm for approximate calculation of optimal output-constrained feedback regulators is presented. computational simplicity is achieved by using properties of weakly coupled linear systems. The algorithm has been shown to be very effective in solving high dimensional control problems.     

Optimal minimum variance‐entropy control of tumour growth processes based on the Fokker–Planck equation

The authors demonstrated an optimal stochastic control algorithm to obtain desirable cancer treatment based on the Gompertz model. Two external forces as two time‐dependent functions are presented to manipulate the growth and death rates in the drift term of the Gompertz model. These input signals represent the effect of external treatment agents to decrease tumour growth rate and increase tumour death rate, respectively. Entropy and variance of cancerous cells are simultaneously controlled based on the Gompertz model. They have introduced a constrained optimisation problem whose cost function is the variance of a cancerous cells population. The defined entropy is based on the probability density function of affected cells was used as a constraint for the cost function. Analysing growth and death rates of cancerous cells, it is found that the logarithmic control signal reduces the growth rate, while the hyperbolic tangent–like control function increases the death rate of tumour growth. The two optimal control signals were calculated by converting the constrained optimisation problem into an unconstrained optimisation problem and by using the real–coded genetic algorithm. Mathematical justifications are implemented to elucidate the existence and uniqueness of the solution for the optimal control problem.Inspec keywords: optimal control, genetic algorithms, cancer, Fokker‐Planck equation, cellular biophysics, stochastic systems, probability, tumours, entropy, medical control systemsOther keywords: cancer treatment, Gompertz model, time‐dependent functions, process input signals, external treatment agents, tumour growth rate, constrained optimisation problem, cost function, cancerous cells population, probability density function, logarithmic control signal, Fokker‐Planck equation, tumour growth process, optimal control signals, optimal control problem, optimal minimum variance‐entropy control, optimal stochastic control algorithm, tumour death rates, hyperbolic tangent‐like control function, unconstrained optimisation problem, real‐coded genetic algorithm     

A two-phase computational scheme for solving bang-bang control problems

This paper focuses on numerical methods for solving time-optimal control problems using discrete-valued controls. A numerical Two-Phase Scheme, which combines admissible optimal control problem formulation with enhanced branch-and-bound algorithms, is introduced to efficiently solve bang-bang control problems in the field of engineering. In Phase I, the discrete restrictions are relaxed, and the resulting continuous problem is solved by an existing optimal control solver. The information on switching times obtained in Phase I is then used in Phase II wherein the discrete-valued control problem is solved using the proposed algorithm. Two numerical examples, including a third-order system and the F-8 fighter aircraft control problem, are presented to demonstrate the use of this proposed scheme. Comparing to STC and CPET methods proposed in the literature, the proposed scheme provides a novel method to find a different switching structure with a better minimum time for the F-8 fighter jet control problem.     

Calculation of the diffusion coefficient in a heated turbulent medium using optimisation techniques

With a view to measuring the temperature fluctuations in a heated turbulent air stream, the latter is traversed by a laser beam perpendicular to the flow. The ultimate aim is to access the temperature fluctuations along the laser’s path starting from the luminous dot projected by the laser on to a position probe placed at the stream output. Our initial task is to demonstrate that by solving an optimal control problem, it is possible to calculate the variable diffusion coefficient along the beam trajectory. The optimal control problem considered here is formulated in terms of a nonlinear system whose dynamics are described by a mathematical model developed with the Einstein-Fokker-Plank-Kolmogorov equation as starting-point, and where the control action is assumed given by the diffusion coefficient. A fresh approach to solving the problem based on the decomposition-co-ordination principle is introduced in order to solve the corresponding optimal control problem, i.e. to calculate the diffusion coefficient which meets required objectives.     

Computational method for optimal machine scheduling problem with maintenance and production

This paper considers an optimal scheduling problem of maintenance and production for a machine. Firstly, the problem is formulated as a stochastic switched impulsive optimal control problem. However, there exists the stochastic disturbance in this model. Thus, it is difficult to solve the problem by conventional optimisation techniques. To overcome this difficulty, the stochastic switched impulsive optimal control problem is transformed into a deterministic switched impulsive optimal control problem with continuous state inequality constraints. Then, by combining a time-scaling transformation, a second-order smoothing technique and a penalty function method, an improved Newton algorithm is developed for solving this problem. Convergence results indicate that the algorithm is globally convergent with quadratic rate. Finally, two numerical examples are provided to illustrate the effectiveness of the developed algorithm.     

航天器太阳帆板伸展过程最优控制的粒子群优化算法

讨论航天器太阳帆板伸展过程中航天器姿态运动的最优控制问题。利用多体动力学方法导出带太阳帆板航天器姿态运动方程。在系统角动量为零的情况下,带太阳帆板航天器系统的姿态运动控制问题可转化为无漂移系统的非完整运动规划问题。在非完整运动规划中引入粒子群优化算法,通过控制太阳帆板伸展运动可同时获得航天器姿态的期望位形。数值仿真表明,该方法对太阳帆板伸展过程中航天器主体姿态控制是有效的。