潜射鱼雷命中结果的解析计算方法

为了实现解析计算潜射鱼雷命中结果的目的,采用几何分析法,依据潜射鱼雷弹道过程,建立了鱼雷射击通式,通过分析目标运动要素(航向、速度和距离)与鱼雷命中结果之间的解析关系,建立了鱼雷命中结果的解析计算模型.在此基础上,进一步分析了目标运动要素误差对鱼雷不同制导方式下射击效果的影响.通过实例说明了计算方法的可行性和有效性.     

半线性二阶系统的奇异摄动现象*

本文研究半线性二阶系统的奇异摄动现象,在适当的假设下,借助于构造特殊的不变域,证得向量边值问题解的存在及其当ε→0+时的渐近性质,在这种不变域中解呈现所谓的边界层现象和角层现象.     

约束尺度和算子自适应变化的差分进化算法

由于可行域不连续和函数形式复杂使得许多算法难以有效求解约束优化问题,提出了一种约束尺度和算子自适应变化的差分进化算法.通过统计新个体中可行解和不可行解的数量以自适应调整惩罚系数,使个体能够分布在多个不连续的可行域中,从而找到最优解所在区域.同时,算法还采用了两种不同的差分算子,分别用于局部区域的快速寻优和整个可行域的全局探索.在两种算子的选择上,则根据新个体的存活情况和约束违反情况来自适应调整其选择的概率.最后通过3组标准约束优化问题在10维和30维变量下的测试结果显示:所提算法的性能整体优于对比算法,其平均最优解在10维时至少提升了4.75%.     

基于单纯形方法的双层线性规划全局优化算法

通过分析双层线性规划可行域的结构特征和全局最优解在约束域的极点上达到这一特性,对单纯形方法中进基变量的选取法则进行适当修改后,给出了一个求解双层线性规划局部最优解方法,然后引进上层目标函数对应的一种割平面约束来修正当前局部最优解,直到求得双层线性规划的全局最优解.提出的算法具有全局收敛性,并通过算例说明了算法的求解过程.     

四旋翼飞行器姿态控制方法和实现

研究了小型四旋翼飞行器惯导系统的姿态解算和控制问题.首先,文章采用三阶近似毕卡四元数算法来解决四旋翼飞行器的姿态解算问题,进而将该算法与卡尔曼滤波器相结合,避免了陀螺仪的积分累积误差,有效消除了四旋翼飞行器机体振动引起的传感器测量误差.其次,根据姿态解算得到的姿态角,设计了积分分离PID和串级PID控制器进行姿态控制.最后,将设计的姿态解算算法和姿态控制算法应用到四旋翼飞行器平台上,实现了四旋翼飞行器的姿态控制,验证了文章算法的有效性.     

高阶复线性微分方程解的角域增长性

本文研究了高阶复线性微分方程解在角域上的增长性问题.利用Nevanlinna理论和共形变换的方法,获得了一些使得方程非平凡解在角域上有快速增长的系数条件,这些结果丰富了复方程解在角域上增长性的研究.     

基于Simulink的某动能弹外弹道仿真

为了更加直观简洁地显示出某动能弹的外弹道性能,同时对恒量动能打击武器系统外弹道的研究结论进行进一步的整体分析与评价,利用MATLAB提供的Simulink仿真工具,通过相应模型参数的设定,对Mcro3型高速摄影机测得的着速和降落量及理论解算值进行了外弹道仿真验证.仿真结果与理论解算对比,结果基本一致,满足实际研究的精度要求.     

基于动力系统的线性不等式组的解法

本文提出了一种新的求解线性不等式组可行解的方法-动力系统方法.假设线性不等式组的可行域为非空,在可行域的相对内域上建立一个非线性极值问题,根据对偶关系,得到一个对偶空间的无约束极值问题以及原始、对偶变量之间的简单线性映射关系,进而得到了一个结构简单的动力系统模型.文中主要讨论了动力系统的隐式格式,通过证明模型具有较好的计算稳定性.同时,在寻找不等式组可行解的过程中,定义了穿越方向,这样可以减少计算量.数值实验结果表明此算法是有效的.     

基于种群分类排序的约束优化遗传算法

针对约束优化问题,提出了一类将种群中的个体分类排序的思想.算法的特点在于:先将种群中的解分为可行解和不可行解两类,然后分别按照不同的标准排序.由于很多约束优化问题的最优解位于可行域的边界上或附近,所以排序时并不认为可行解一定优于不可行解.基于此分类排队思想,特别设计了只允许同等级个体进行交叉的新的交叉算子,称之为同等级交叉算子,以及基于一维搜索的变异算子.算法同时采用了保证固定比例不可行解的自适应策略.4个标准测试函数的数值仿真结果验证了算法的有效性.     

利用整点折线边界解一类线性规划问题

线性规划问题中的最优解的常用求法是图象法,如没有特殊要求,最优解一般会在可行域的边界点处取得.但是,对于最优解必须是整数的线性规划问题,有时在原边界处取不到最优解.对于这种情况,现行课本及资料提供的方法,一是以取得非整数最优解的线     

Optimal abort landing trajectories in the presence of windshear

This paper is concerned with optimal flight trajectories in the presence of windshear. The abort landing problem is considered with reference to flight in a vertical plane. It is assumed that, upon sensing that the airplane is in a windshear, the pilot increases the power setting at a constant time rate until maximum power setting is reached; afterward, the power setting is held constant. Hence, the only control is the angle of attack. Inequality constraints are imposed on both the angle of attack and its time derivative.The performance index being minimized is the peak value of the altitude drop. The resulting optimization problem is a minimax problem or Chebyshev problem of optimal control, which can be converted into a Bolza problem through suitable transformations. The Bolza problem is then solved employing the dual sequential gradient-restoration algorithm (DSGRA) for optimal control problems. Numerical results are obtained for several combinations of windshear intensities, initial altitudes, and power setting rates.For strong-to-severe windshears, the following conclusions are reached: (i) the optimal trajectory includes three branches: a descending flight branch, followed by a nearly horizontal flight branch, followed by an ascending flight branch after the aircraft has passed through the shear region; (ii) along an optimal trajectory, the point of minimum velocity is reached at about the time when the shear ends; (iii) the peak altitude drop depends on the windshear intensity, the initial altitude, and the power setting rate; it increases as the windshear intensity increases and the initial altitude increases; and it decreases as the power setting rate increases; (iv) the peak altitude drop of the optimal abort landing trajectory is less than the peak altitude drop of comparison trajectories, for example, the constant pitch guidance trajectory and the maximum angle of attack guidance trajectory; (v) the survival capability of the optimal abort landing trajectory in a severe windshear is superior to that of comparison trajectories, for example, the constant pitch guidance trajectory and the maximum angle of attack guidance trajectory.Portions of this paper were presented at the IFAC 10th World Congress, Munich, Germany, July 27–31, 1987 (Paper No. IFAC-87-9221).This research was supported by NASA Langley Research Center, Grant No. NAG-1-516, by Boeing Commercial Airplane Company (BCAC), and by Air Line Pilots Association (ALPA). Discussions with Dr. R. L. Bowles (NASA-LRC) and Mr. C. R. Higgins (BCAC) are acknowledged.     

Contribution to the propeller aerodynamic interference

Propeller wake can significantly change the flowfield at the downstream lifting surfaces and therefore influence its aerodynamic coefficients. The numerical model of the propeller presented here is using discrete vortices to form vortex sheet that is leaving each blade. Model is also applicable for combination of lifting surface and propeller using undeveloped propeller vortex sheet in determination of aerodynamic interference of the propeller on the downstream lifting surface, wing or tail for small angle of attack. This low computational cost numerical model is suitable for implementation in component build–up method used in preliminary estimation of aerodynamic coefficients for different propeller aircraft configurations.     

Optimal penetration landing trajectories in the presence of windshear

This paper is concerned with optimal flight trajectories in the presence of windshear. The penetration landing problem is considered with reference to flight in a vertical plane, governed by either one control (the angle of attack, if the power setting is predetermined) or two controls (the angle of attack and the power setting). Inequality constraints are imposed on the angle of attack, the power setting, and their time derivatives.The performance index being minimized measures the deviation of the flight trajectory from a nominal trajectory. In turn, the nominal trajectory includes two parts: the approach part, in which the slope is constant; and the flare part, in which the slope is a linear function of the horizontal distance. In the optimization process, the time is free; the absolute path inclination at touchdown is specified; the touchdown velocity is subject to upper and lower bounds; and the touchdown distance is subject to upper and lower bounds.Three power setting schemes are investigated: (S1) maximum power setting; (S2) constant power setting; and (S3) control power setting. In Scheme (S1), it is assumed that, immediately after the windshear onset, the power setting is increased at a constant time rate until maximum power setting is reached; afterward, the power setting is held constant; in this scheme, the only control is the angle of attack. In Scheme (S2), it is assumed that the power setting is held at a constant value, equal to the prewindshear value; in this scheme, the only control is the angle of attack. In Scheme (S3), the power setting is regarded as a control, just as the angle of attack.Under the above conditions, the optimal control problem is solved by means of the primal sequential gradient-restoration algorithm (PSGRA). Numerical results are obtained for several combinations of windshear intensities and initial altitudes. The main conclusions are given below with reference to strong-to-severe windshears.In Scheme (S1), the touchdown requirements can be satisfied for relatively low initial altitudes, while they cannot be satisfied for relatively high initial altitudes; the major inconvenient is excess of velocity at touchdown. In Scheme (S2), the touchdown requirements cannot be satisfied, regardless of the initial altitude; the major inconvenient is defect of horizontal distance at touchdown.In Scheme (S3), the touchdown requirements can be satisfied, and the optimal trajectories exhibit the following characteristics: (i) the angle of attack has an initial decrease, which is followed by a gradual, sustained increase; the largest value of the angle of attack is attained near the end of the shear; in the aftershear region, the angle of attack decreases gradually; (ii) initially, the power setting increases rapidly until maximum power setting is reached; then, maximum power setting is maintained in the shear region; in the aftershear region, the power setting decreases gradually; (iii) the relative velocity decreases in the shear region and increases in the aftershear region; the point of minimum velocity occurs at the end of the shear; and (iv) depending on the windshear intensity and the initial altitude, the deviations of the flight trajectory from the nominal trajectory can be considerable in the shear region; however, these deviations become small in the aftershear region, and the optimal flight trajectory recovers the nominal trajectory.A comparison is shown between the optimal trajectories of Scheme (S3) and the trajectories arising from alternative guidance schemes, such as fixed controls (fixed angle of attack, coupled with fixed power setting) and autoland (angle of attack controlled via path inclination signals, coupled with power setting controlled via velocity signals). The superiority of the optimal trajectories of Scheme (S3) is shown in terms of the ability to meet the path inclination, velocity, and distance requirements at touchdown. Therefore, it is felt that guidance schemes based on the properties of the optimal trajectories of Scheme (S3) should prove to be superior to alternative guidance schemes, such as the fixed control guidance scheme and the autoland guidance scheme.Portions of this paper were presented at the AIAA 26th Aerospace Sciences Meeting, Reno, Nevada, January 11–14, 1988 (Paper No. AIAA-88-0580).This research was supported by NASA-Langley Research Center, Grant No. NAG-1-516, by Boeing Commercial Airplane Company (BCAC), and by Air Line Pilots Association (ALPA).The authors are indebted to Dr. R. L. Bowles, NASA-Langley Research Center, and to Dr. G. R. Hennig, Boeing Commercial Airplane Company, for helpful discussions.     

The topology of the sectional streamlines

The unsteady, three-dimensional full Navier-Stokes equations are solved using a Beam-Warming implicit algorithm in this paper. Computations of the flow over a 76° sweep delta wing at 36.5° angle of attack is presented. The sectional streamlines are depicted and the evolution of the instantaneous crossflow topology of the leading-edge vortex is analyzed. It is found that, along the axis, the topology of the primary vortex alters several times starting from stable focus near the apex to unstable focus, and lasts back to stable focus near wake edge; The stable limit cycle and unstable limit cycle are shown in this evolution. These various altering topologies stem from the stretching and compression of the vortex core.     

广义Bayes诊断法

系统地阐述了Bayes的诊断思想,推广了多输入单输出诊断方法,对多输入多输出的诊断作出一次尝试,克服以往诊断的局限性,给出一种广泛应用的诊断方法,并通过仿真示例,表现出其可行性及有效性.     

Quasi-steady flight to quasi-steady flight transition in a windshear: Trajectory optimization and guidance

This paper is concerned with the near-optimum guidance of an aircraft from quasi-steady flight to quasi-steady flight in a windshear. The take-off problem is considered with reference to flight in a vertical plane. In addition to the horizontal shear, the presence of a downdraft is considered. It is assumed that the power setting is held at the maximum value and that the aircraft is controlled through the angle of attack. Inequality constraints are imposed on both the angle of attack and its time derivative.First, trajectory optimization is considered. The optimal transition problem is formulated as a Chebyshev problem of optimal control: the performance index being minimized is the peak value of the modulus of the difference between the absolute path inclination and a reference value, assumed constant. Two types of optimal trajectories are studied: type 1 is concerned with gamma recovery (recovery of the initial value of the relative path inclination); and type 2 is concerned with quasisteady flight recovery (recovery of the initial values of the relative velocity, the relative path inclination, and the relative angle of attack). The numerical results show that the type 1 trajectory and the type 2 trajectory are nearly the same in the shear portion, while they diverge to a considerable degree in the aftershear portion of the optimal trajectory.Next, trajectory guidance is considered. A guidance scheme is developed so as to achieve near-optimum quasi-steady flight recovery in a windshear. The guidance scheme for quasi-steady flight recovery includes three parts in sequence. The first part refers to the shear portion of the trajectory and is based on the result that this portion of the trajectory depends only mildly on the boundary conditions; therefore, any of the guidance schemes already developed for type 1 trajectories can be employed (for instance, variable gamma guidance). The second part (constant gamma guidance) refers to the initial aftershear portion of the trajectory and is designed to achieve almost velocity recovery. The third part (constant rate of climb guidance) refers to the final aftershear portion of the trajectory and is designed to achieve almost complete restoration of the initial quasi-steady state.While the shear guidance and the initial aftershear guidance employ constant gain coefficients, the final aftershear guidance employs a variable gain coefficient. This is done in order to obtain accuracy and prompt response, while avoiding oscillations and overshoots. The numerical results show that the guidance scheme for quasi-steady flight recovery yields a transition from quasi-steady flight to quasi-steady flight which is close to that of the optimal trajectory, ensures the restoration of the initial quasi-steady state, and has good stability properties.This paper is based on Refs. 1 and 2.This research was supported by NASA-Langley Research Center, Grant No. NAG-1-516, and by Boeing Commercial Aircraft Company. The authors are indebted to Dr. R. L. Bowles, NASA-Langley Research Center, for helpful discussions.     

Abort landing in the presence of windshear as a minimax optimal control problem,part 2: Multiple shooting and homotopy

In Part 1 of the paper (Ref. 2), we have shown that the necessary conditions for the optimal control problem of the abort landing of a passenger aircraft in the presence of windshear result in a multipoint boundary-value problem. This boundary-value problem is especially well suited for numerical treatment by the multiple shooting method. Since this method is basically a Newton iteration, initial guesses of all variables are needed and assumptions about the switching structure have to be made. These are big obstacles, but both can be overcome by a so-called homotopy strategy where the problem is imbedded into a one-parameter family of subproblems in such a way that (at least) the first problem is simple to solve. The solution data to the first problem may serve as an initial guess for the next problem, thus resulting in a whole chain of problems. This process is to be continued until the objective problem is reached.Techniques are presented here on how to handle the various changes of the switching structure during the homotopy run. The windshear problem, of great interest for safety in aviation, also serves as an excellent benchmark problem: Nearly all features that can arise in optimal control appear when solving this problem. For example, the candidate for an optimal trajectory of the minimax optimal control problem shows subarcs with both bang-bang and singular control functions, boundary arcs and touch points of two state constraints, one being of first order and the other being of third order, etc. Therefore, the results of this paper may also serve as some sort of user's guide for the solution of complicated real-life optimal control problems by multiple shooting.The candidate found for an optimal trajectory is discussed and compared with an approximate solution already known (Refs. 3–4). Besides the known necessary conditions, additional sharp necessary conditions based on sign conditions of certain multipliers are also checked. This is not possible when using direct methods.An extended abstract of this paper was presented at the 8th IFAC Workshop on Control Applications of Nonlinear Programming and Optimization, Paris, France, 1989 (see Ref. 1).This paper is dedicated to Professor Hans J. Stetter on the occasion of his 60th birthday.     

Approximate formulas for heat flows towards an ideally catalytic surface near a plane of symmetry

The three-dimensional flow of a chemically unstable viscous gas near a plane of symmetry of blunt bodies streamlined at the angle of attack, is considered. The investigation is carried out using a model of a thin, viscous shock layer. To a first approximation of the method of successive approximations for a uniform gas simple formulas are obtained for the distribution of the heat flux over the surface, referred to its value at the stagnation point. It is shown that for a chemically unstable gas the distribution of the heat flux along an ideally catalytic surface depends only slightly on the conditions prevailing within the incident flow, is determined mainly by the geometrical characteristics of the body, and is described quite satisfactorily by the formulas obtained. The accuracy of these formulas is determined by comparison with numerical computations carried out for bodies of various shapes, moving at different angles of attack along a planing trajectory of re-entry into the Earth's atmosphere, and during re-entry into the atmosphere at a constant velocity.     

Nonlinear dynamical systems of trajectory design for 3D horizontal well and their optimal controls

The trajectory design of horizontal well is a optimal control problem of nonlinear multistage dynamical system. It is often sought using trial-and-error methods, but these methods depend on experience of designers and workers. In this paper, we create new optimal control model of nonlinear dynamical system for the trajectory design of horizontal well. Several properties are discussed. Uniform design method is used to choose the initial points in the feasible region. We demonstrate how to decompose the feasible region into finite subregions in which improved Hook–Jeeves algorithm is employed to search optimal solution. Finally, the feasible optimization algorithm is constructed to find the optimal solution of the system. Several results show the validity of our algorithm. This is preferable, since our method is independent of the experience.     

The turnpike property in finite-dimensional nonlinear optimal control

Turnpike properties have been established long time ago in finite-dimensional optimal control problems arising in econometry. They refer to the fact that, under quite general assumptions, the optimal solutions of a given optimal control problem settled in large time consist approximately of three pieces, the first and the last of which being transient short-time arcs, and the middle piece being a long-time arc staying exponentially close to the optimal steady-state solution of an associated static optimal control problem. We provide in this paper a general version of a turnpike theorem, valuable for nonlinear dynamics without any specific assumption, and for very general terminal conditions. Not only the optimal trajectory is shown to remain exponentially close to a steady-state, but also the corresponding adjoint vector of the Pontryagin maximum principle. The exponential closedness is quantified with the use of appropriate normal forms of Riccati equations. We show then how the property on the adjoint vector can be adequately used in order to initialize successfully a numerical direct method, or a shooting method. In particular, we provide an appropriate variant of the usual shooting method in which we initialize the adjoint vector, not at the initial time, but at the middle of the trajectory.