基于间接Radau伪谱法的滑翔段轨迹跟踪制导律

针对高超声速飞行器滑翔段制导问题,提出一种利用间接Radau伪谱法求解最优反馈控制律的全状态标称轨迹跟踪制导律。将标称轨迹跟踪问题转化为线性时变系统状态调节器问题,基于Pontryagin极大值原理进一步将状态调节器问题转化为线性两点边值问题;利用间接Radau伪谱法求解所得的线性两点边值问题,获得最优反馈控制律,并在此基础上设计了易于在线执行的闭环轨迹跟踪制导律。数值仿真结果表明,该制导律对飞行器初始状态量的较大范围偏差和飞行环境参数的有限扰动不敏感,具有良好的鲁棒性,并且能够满足实时性的需求。

Indirect Radau pseudospectral method for the receding horizon control problem

To solve the receding horizon control （RHC） problem in an online manner, a novel numerical method called the indirect Radau pseudospectral method （IRPM） is proposed in this paper. Based on calculus of variations and the first-order necessary optimality condition, the RHC problem for linear time-varying （LTV） system is transformed into the two-point boundary value problem （TPBVP）. The Radau pseudospectral approximation is employed to discretize the TPBVP into well-posed linear algebraic equations. The resulting linear algebraic equations are solved via a matrix partitioning approach afterwards to obtain the optimal feedback control law. For the nonlinear system, the linearization method or the quasi linearization method is employed to approximate the RHC problem with successive linear approximations. Subsequently, each linear problem is solved via the similar method which is used to solve the RHC problem for LTV system. Simulation results of three examples show that the IRPM is of high accuracy and of high compu- tation efficiency to solve the RHC problem and the stability of closed-loop systems is guaranteed.

最优协调电压控制间接拉道排列算法

根据准稳态假设建立含连续–离散时间微分–代数方程约束的最优协调电压控制模型。该模型综合考虑长期电压稳定性和控制成本因素,协调不同地理位置和不同种类的控制手段。根据Pontryagin极大值原理建立该协调电压控制问题的1阶最优性条件,该条件是一个典型的两点边值问题。在此基础上采用拉道(Radau)排列法求解这个两点边值问题。该算法具有计算精度高、数值稳定性好等特点。此外,为考虑有载调压变压器变比、可投切电容器组和待切除负荷的离散特性,还在控制模型中引入了二次罚函数的处理方法。以新英格兰39节点系统为基础构造算例,算例结果表明了该方法的有效性。

基于邻域最优控制律的再入轨迹在线修正

针对再入轨迹制导中存在初始扰动的问题,提出一种基于间接Radau伪谱法的邻域最优控制律。首先,通过分段Radau伪谱法获得最优参考轨迹,利用极小值原理将轨迹跟踪问题转化为线性两点边值问题,然后通过间接Radau伪谱法在LGR离散点上求解控制量的修正值。这种方法不需积分及迭代运算,也不用求解Riccati方程,只需简单的矩阵运算。仿真结果表明,邻域最优控制律对飞行器初始状态量的较大范围偏差具有良好的鲁棒性,并且能够满足实时性的需求。