Abort landing in the presence of windshear as a minimax optimal control problem,part 1: Necessary conditions

The landing of a passenger aircraft in the presence of windshear is a threat to aviation safety. The present paper is concerned with the abort landing of an aircraft in such a serious situation. Mathematically, the flight maneuver can be described by a minimax optimal control problem. By transforming this minimax problem into an optimal control problem of standard form, a state constraint has to be taken into account which is of order three. Moreover, two additional constraints, a first-order state constraint and a control variable constraint, are imposed upon the model. Since the only control variable appears linearly, the Hamiltonian is not regular. Thus, well-known existence theorems about the occurrence of boundary arcs and boundary points cannot be applied. Numerically, this optimal control problem is solved by means of the multiple shooting method in connection with an appropriate homotopy strategy. The solution obtained here satisfies all the sharp necessary conditions including those depending on the sign of certain multipliers. The trajectory consists of bang-bang and singular subarcs, as well as boundary subarcs induced by the two state constraints. The occurrence of boundary arcs is known to be impossible for regular Hamiltonians and odd-ordered state constraints if the order exceeds two. Additionally, a boundary point also occurs where the third-order state constraint is active. Such a situation is known to be the only possibility for odd-ordered state constraints to be active if the order exceeds two and if the Hamiltonian is regular. Because of the complexity of the optimal control, this single problem combines many of the features that make this kind of optimal control problems extremely hard to solve. Moreover, the problem contains nonsmooth data arising from the approximations of the aerodynamic forces and the distribution of the wind velocity components. Therefore, the paper can serve as some sort of user's guide to solve inequality constrained real-life optimal control problems by multiple shooting.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.     

D+D 2 Quasiclassical rate constant calculations on parallel computers

Summary The calculation of rate constant values of theH+H ₂ reaction for an extended range of excited vibrational states of the diatomic molecule and temperatures is relevant to the modeling ofH ^– sources. To investigate the effect of isotopic substitutions on the efficiency of vibrational deexcitation processes, we extended the calculations to theD+D ₂ system. These calculations were carried out using a program restructured to run on a shared memory vector and parallel computer. The dependence of the efficiency of vibrational deexcitation processes from both the initial vibrational state and temperature of reactants is reported. Restructuring strategies adopted for implementing the program on both shared and distributed memory computers as well as speedups achieved on both types of machines are also discussed.     

Families of stable manifolds for one-dimensional parabolic equations

We prove that to any invariant subset of the dynamical system generated by a one-dimensional quasilinear parabolic equation there corresponds an invariant family of stable manifolds of finite codimension. Translated fromMatematicheskie Zametki, Vol. 60, No. 1, pp. 11–23, July, 1996.     

Optimal impulsive space trajectories based on linear equations

The problem of minimizing the total characteristic velocity of a spacecraft having linear equations of motion and finitely many instantaneous impulses that result in jump discontinuities in velocity is considered. Fixed time and fixed end conditions are assumed. This formulation is flexible enough to allow some of the impulses to be specifieda priori by the mission planner. Necessary and sufficient conditions for solution of this problem are found without using specialized results from control theory or optimization theory. Solution of the two-point boundary-value problem is reduced to a problem of solving a specific set of equations. If the times of the impulses are specified, these equations are at most quadratic. Although this work is restricted to linear equations, there are situations where it has potential application. Some examples are the computation of the velocity increments of a spacecraft near a real or fictitious satellite or space station in a circular or more general Keplerian orbit. Another example is the computation of maneuvers of a spacecraft near a libration point in the restricted three-body problem.This project was supported by the 1988 NASA/ASEE Faculty Fellowship Program at the California Institute of Technology and the Jet Propulsion Laboratory. The work was performed in the Advanced Projects Group, Section 312, Jet Propulsion Laboratory, Pasadena, California.     

An approximation procedure for solutions to Mayer problems with cost functional not of classC

We consider here control problems in the Mayer form, with a cost functional which is continuous, but not necessarily of classC ¹. The usual necessary conditions for such problems cannot be applied, since they require that the cost functional beC ¹. We describe a convergence procedure, based upon approximations to the cost functional, that will yield an optimal trajectory to such control systems. Criteria are given which justify that this approximation procedure will yield a trajectory and control, satisfying certain prescribed conditions, which minimize the above cost functional within a specified class of such pairs. Examples are presented.     

老山汉墓土遗址盐分调查与分布规律探索

老山汉墓土遗址中可溶-微溶盐导致遗址表面酥碱、起甲、泛白和块状脱落等病害较为严重.利用X射线荧光光谱(XRF)、X射线衍射仪(XRD)、X射线光电子能谱(XPS)以及离子色谱(IC)等方法测定了老山汉墓遗址不同取样位置及距遗址表面不同深度处可溶盐的成分及含量,并分析了盐分对遗址破坏的可能机制.结果表明,该遗址的主要有可溶盐有Na2SO4、Na2SO4·10H2O、Na Cl、Na12Mg7(SO4)13·15H2O,微溶盐有Ca SO4、Ca SO4·2H2O,此外还含有少量的Ca Cl2、KNO3、KCl、Mg Cl2、K2SO4、Mg SO4等盐分.随着取样深度增加,各盐分的种类及含量有所减少,此分布规律可能与可溶盐的赋存环境及水分运移有关.试验结果对于老山汉墓土遗址的保护措施具有一定的参考价值.     

Autonomous movement of silica and glass micro-objects based on a catalytic molecular propulsion system

A general approach for the easy functionalization of bare silica and glass surfaces with a synthetic manganese catalyst is reported. Decomposition of H(2)O(2) by this dinuclear metallic center into H(2)O and O(2) induced autonomous movement of silica microparticles and glass micro-sized fibers. Although several mechanisms have been proposed to rationalise movement of particles driven by H(2)O(2) decomposition to O(2) and water (recoil from O(2) bubbles, ([36,45]) interfacial tension gradient([37-42]), it is apparent in the present system that ballistic movement is due to the growth of O(2) bubbles.     

轴向运动悬臂梁的独立模态振动控制——Ⅰ近似理论分析

利用Euler Bernoulli梁理论并在低速轴向运动假设的基础上 ,对伸展悬臂梁的独立模态振动控制进行了理论近似解的推导 ,为数值仿真计算结果提供了一定意义下的对照参考模型 ,在求解过程中使用了多尺度方法     

基于LS-DYNA的高速破片水中运动特性流固耦合数值模拟

基于大型有限元分析软件ANSYS/LS-DYNA,建立三维长方体高速破片在水介质中运动的有限元动力分析模型,采用ALE方法对破片在水下运动过程进行流固耦合数值模拟,获得了破片的速度衰减曲线。研究了速度衰减规律、破片墩粗变形规律以及冲击波传播过程。得到高速破片的侵彻能力随速度的变化规律:当初速度大于910~1 115m/s时破片头部将产生显著变形,并大大影响其侵彻阻力;当破片速度较小时,水中侵彻距离随破片初速的增大而增大,当破片速度达到某临界值以后,侵彻距离将随初始速度的增大而逐渐减小。