【作者】 孙勇；

【导师】 段广仁； 张卯瑞；

【作者基本信息】 哈尔滨工业大学 ， 控制科学与工程， 2012， 博士

【摘要】 近二十年来，临近空间被各大国所特别关注，由于大气稀薄，空气阻力小，是实现全球范围内快速飞行的理想空间，高超声速飞行器既具有入轨的能力，又可以再入大气层快速攻击地面目标，具有大升阻比、机动性强、全球快速到达、威力大等特点，可以进行全球实时侦察、快速部署和远程精确打击能力，对未来的作战方式将产生重要影响。因此，高超声速飞行器相关技术和理论得到了广泛研究，其中，高超声速飞行器快速轨迹优化与高精度制导是保证其完成任务的重要前提，由于运动方程的非线性、环境复杂性和多种约束条件的存在，使得难以求解，本文针对该问题进行相关研究。第一，研究了高超声速飞行器运动和气动建模问题。对于实际项目中的高超声速飞行器，给出了上升段轨迹优化问题的数学描述。在半速度坐标系下，建立了高超声速飞行器再入运动模型。通过分析气动系数数据，综合考虑攻角和速度两个因素，建立了双变量气动系数模型，通过对比，表明该气动模型具有更高的精度。在所建立的气动模型的基础上，分析了高超声速飞行器的升阻比特点，对不同升阻比下的轨迹进行了分析。提出了高超声速飞行器再入轨迹优化与制导问题的数学描述。第二，研究了含有路径约束非线性最优控制问题的计算方法。传统的Gauss伪谱法中终端状态积分约束是非线性的，不利于计算，并且协态变量的计算方法与其他伪谱法不一致。为了提高收敛速度，利用状态微分方程矩阵和Gauss权重系数将非线性的终端状态积分约束等价转化为等价的线性约束形式，减少了非线性约束的个数，基于线性终端状态积分约束，提出了改进的Gauss伪谱法(IGPM)，证明了新的协态映射定理，进一步完善了Gauss伪谱法。新的协态变量计算方法与其他伪谱法具有统一形式。针对初始时刻协态变量不易计算的问题，提出了简单的计算初始时刻协态变量的方法；由于控制变量没有在边界时刻取值，根据极大值原理，考虑动态微分方程约束和路径约束，提出了端点时刻控制变量的计算方法。第三，研究了标准的Bolza型多段非线性最优控制问题的多段轨迹优化方法。对于含有复杂路径约束的非线性最优控制问题，只增加离散点个数，导致微分矩阵维数增大，计算效率下降。因此，引入分段的思想，基于IGPM，提出了多段改进Gauss伪谱法(MIGPM)，证明了多段协态映射定理，可以方便地计算协态变量，并提出了分割点处协态和控制变量的计算方法。为了提高解的精度，提出了基于MIGPM的多段轨迹优化算法，并求解高超声速飞行器再入轨迹纵向航程最大问题，解的精度和收敛速度均优于全局轨迹优化方法。第四，研究了能够高精度处理路径约束和确定间断点能力的动态轨迹优化方法。对于有高精度路径约束要求，并含有不连续控制的问题，全局轨迹优化方法对路径约束的精度不高，并且多段轨迹优化算法难以确定间断点。以综合相对误差向量作为参数更新的判断条件，提出离散点和阶段数量更新方法。重点考虑解和路径约束的满足精度，基于MIGPM提出了动态轨迹优化算法。通过实例验证了该算法的快速收敛性、寻找间断点和处理路径约束的能力。第五，研究了竖直平面和三维空间的高超声速飞行器上升段最省燃料的轨迹优化问题，并研究了再入轨迹纵向航程和横向航程最大的轨迹优化问题。采用基于IGPM的迭代算法一和动态轨迹优化算法分别求解竖直平面上升段最优轨迹和上升段同时转向的最优轨迹，结果表明最省燃料的轨迹均属于先加速后上升的类型。为了提高计算速度和精度，提出了两种全局轨迹优化迭代算法，仿真结果表明，两种迭代算法都能很快地收敛到最优解。应用动态轨迹优化算法和最新的hp自适应伪谱法求解再入纵向航程和横向航程最大轨迹优化问题，结果表明，动态轨迹优化算法的计算效率、收敛半径和处理路径约束的能力都优于hp自适应伪谱法。分析了再入的最优升阻比特性，再入中段最优升阻比基本上等于最大升阻比，为再入轨迹优化问题的初值选取提供了借鉴。第六，研究了高超声速飞行器再入过程在线最优反馈制导问题。为了处理模型中的不确定性和干扰，采用Carathe′odory π轨迹的概念，推导采样时间的取值方法，从而保证在存在计算延迟的条件下，系统的跟踪精度仍然能够满足误差要求。将最优控制与在线最优反馈相结合，利用IGPM快速收敛的特点，提出了在线最优反馈制导算法。将提出的轨迹优化方法与在线最优反馈制导算法相结合，提出了一种满足在线计算要求的高超声速飞行器再入闭环制导系统结构，为提高高超声速飞行器再入过程的自主性、可靠性和最优性提供了解决方案。将在线最优反馈制导算法应用于横向航程最大制导问题、定点定向攻击制导问题和在线自主避障再入制导问题，仿真结果表明该制导方法能够很好地满足指标要求。综上所述，本文提出了高超声速飞行器轨迹优化方法和在线最优反馈制导方法，为高超声速飞行器轨迹在线优化和高精度制导奠定了一定基础。更多还原

【Abstract】 In the past twenty years, near space is focused by some great countries. It is the idealspace to realize the hypersonic flying because of the thin air and the small resistance. Thehypersonic vehicle not only has the ability to entry the space but also can reentry the at-mosphere for attacking the ground targets fast. It has the big lift-to-drag ratio (LDR), wellmaneuverability, fast reaching the global world and great power, etc. It can be used in thefields of the global real-time scout, rapid deployment and remote precision attacking andimpacts the future war greatly. Therefore, much researches on the related technology andtheory of the hypersonic vehicle have won wide studies. It is the essential preconditionfor the mission to realize the trajectory optimization and high-precision guidance. Thisproblem is difcult to solve because of the nonlinear property of the motion equations,complexity of the environment and various nonlinear constraints. The thesis takes someresearches on this problem.1. The motion models and the aerodynamic model of the hypersonic vehicle arediscussed. The mathematical descriptions of the ascent trajectory optimization problem ofthe hypersonic vehicle are given for the engineering problems. The reentry motion modelis presented under the half velocity coordinate system. Considering the attacking angleand velocity variables, the bivariate aerodynamic coefcients model is built by analyzingthe characteristics of the data, The comparison shows that the proposed aerodynamiccoefcients model can well describe the regularity of the aerodynamic coefcients, whichprovides the basic model for the next trajectory optimization. The comparison resultsshow that the bivariate aerodynamic coefcients model has the high accuracy. On thebasis of the aerodynamic model, the characteristic of the LDR and the reentry trajectoryof the hypersonic vehicle with the diferent LDR are analyzed. The reentry trajectoryoptimization and the guidance problems of the hypersonic vehicle are described.2. The algorithm for solving the nonlinear optimal control problem with the pathconstraints is studied. The final state state integral constraints are nonlinear in the tradi-tional Gauss pseudospectral method (GPM). It isn’t in favour of the fast computation. Thecomputation of the costate doesn’t agree with those of the other pseudospectral methods.In order to increase the convergence rate, the nonlinear final state integral constraint istransformed into the linear one equivalently using the state diferential matrix and Gaussweights. Then, the number of the nonlinear constraints decreases. The improved Gauss pseudospectral method (IGPM) is proposed based on the linear final state integral con-straint. The new costate mapping theorem is proved to complete the GPM. The newcostate computation is the same with the other pseudospectral methods The simple com-putation of the initial costate is given to alleviate the complexity of the original method.Since the control doesn’t has the values at the boundaries time, the computations of theboundaries time are proposed based on the maximum principle considering the dynamicdiferential equations and path constraints.3. The multiphase trajectory trajectory optimization method of the standard Bolzamultiphase nonlinear optimal control problem is investigated. The dimension of the d-iferential matrix becomes too big when the number of the discrete points increases forthe nonlinear optimal control problem with the complex path constraints. And the com-putation efciency decreases. Therefore, The multiphase improved Gauss pseudospectralmethod (MIGPM) is proposed based on the IGPM by ideal of the multiple phases. Themultiphase costate mapping theorem is proved to compute the costate easily. The meth-ods of the costates and the controls at the break points are given. In order to increasethe accuracy of the solution, the multiphase trajectory optimization algorithm is proposedbased on MIGPM. It is used to solve the reentry trajectory optimization of the maximaldownrange problem of the hypersonic vehicle. The accuracy and the convergence of thesolution are better than those of the global trajectory optimization method.4. The dynamic trajectory optimization method with the ability of making the pathconstraints high accuracy and finding the discontinuous points is researched. The accura-cy of the path constraints isn’t good using the global trajectory optimization method forthe problem with the requirement of high precision and discontinuous control. The multi-phase trajectory optimization method hardly find the discontinuous points. The updatingmethods of the discrete points and the number of the phases are given by the compositiverelative error vector which is used as the judging conditions. Considering the satisfy-ing accuracy of the solution and the path constraints especially, the dynamic trajectoryoptimization method is proposed based on MIGPM. The examples illustrate that this al-gorithm has the ability of converging fast, finding the discontinuous points and dealingwith the path constraints.5. The minimal fuel ascent trajectory optimization problems of the hypersonic vehi-cle are studied in the vertical plane and the three-dimension space and reentry trajectorymaximal downrange and crossrange problems of the hypersonic vehicle are solved. Theascent optimal trajectory in the vertical plane and the ascent trajectory with the turning operation are solved by the iterative algorithm one based on the IGPM and the dynamictrajectory optimization algorithm. The results show that the minimal fuel trajectories areboth the velocity first and ascent type. In order to increase the convergence and preci-sion, two global trajectory optimization iterative algorithms are put forward. The simula-tion results show that two iterative algorithms can converge to the optimal solution well.The reentry trajectory optimization problems with maximal downrange and crossrangeare solved by the dynamic trajectory optimization algorithm and latest hp adaptive pseu-dospectral method. The dynamic trajectory optimization algorithm behaves better thanthose of the hp adaptive pseudospectral method in the field of the computation efciency,the converging radius and the ability of dealing with the path constraints. The propertyof the reentry optimal LDR is analyzed and the optimal LDR is almost the same with themaximal LDR during the reentry middle phase. It provides the reference for choosing theinitial value of the reentry trajectory optimization problem.6. The reentry on-line optimal feedback guidance problem of the hypersonic vehicleis researched. In order to suppress the model uncertainty and the disturbance, the methodof choosing the sample period is derived using the concept of the Caratheodory trajec-tory. The sampling period can guarantee that the tracking precision satisfies the errorrequirement under the condition of the computation delay. The on-line optimal feedbackguidance algorithm is put forward by the benefit of fast convergence of the pseudospec-tral method and the combination of the optimal control theory and the on-line optimalfeedback. The proposed trajectory optimization method and the on-line optimal feedbackguidance algorithm are combined to construct the framework of the reentry closed loopguidance system of the hypersonic vehicle, which meets the requirement of the on-linecomputation. It provides the solution for the reentry of the hypersonic vehicle with theautonomy, reliability and optimality. The on-line optimal feedback guidance method isapplied to the guidance problems，which are the maximal crossrange problem, the fixedpoints fixed direction attacking problem and the on-line autonomous obstacle-avoidancereentry guidance problem. The results show the proposed guidance framework can satisfythe requirement of the index.In conclusion, this thesis puts forward the trajectory optimization methods and theon-line optimal feedback guidance method for hypersonic vehicle, which lay the founda-tion for the on-line trajectory optimization and high-accuracy guidance.更多还原