发表机构
Beijing Institute of Mathematical Sciences and Applications; School of Mathematics and Shing-Tung Yau Center, Southeast University; Shanghai Institute for Mathematics and Interdisciplinary Sciences; Research Institute of Intelligent Complex Systems, Fudan University（北京数学与应用数学研究所; 东南大学数学学院及陈省身数学中心; 上海数学与交叉学科研究院; 复旦大学智能复杂系统研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对SDRE控制中在线求解CAREs的计算瓶颈，提出投影通道$H_\infty$公式与离散卡尔曼滤波调度，采用SDA或Newton--Kleinman算法求解，在F-16和四旋翼仿真中验证了高效性与鲁棒性。
AI 中文摘要
状态依赖Riccati方程（SDRE）控制需要在线重复求解连续时间代数Riccati方程（CAREs）。一种投影通道$H_\infty$公式保留了欠驱动、部分观测系统的物理执行器和传感器维度。我们推导了一个可计算的充分衰减界，用于正半定镇定Riccati解，并构造了一种更新，以强制满足其谱半径耦合条件。离散卡尔曼递推提供调度状态估计。控制器综合中出现的两个CAREs通过保结构倍增算法（SDA）或配备倍增Lyapunov求解器的热启动Newton--Kleinman迭代求解。数值研究使用一个具有完整气动力、力矩和配平的十二状态F-16模型，以及四旋翼螺旋跟踪。在瞬时指令更新下，所有三个CARE后端给出基本相同的闭环响应。在跟踪仿真中，测量计算时间决定何时施加新的控制输入，计算期间保持先前的输入。SDA和Newton在所有六次配对飞机跟踪运行中减少了空速和俯仰误差。在计算资源有限的更快四旋翼任务中，SDA和Newton完成所有配对运行，而使用MATLAB \texttt{icare}的运行提前终止。
英文摘要
State-dependent Riccati equation (SDRE) control requires repeated online solution of continuous-time algebraic Riccati equations (CAREs). A projected-channel $H_\infty$ formulation preserves the physical actuator and sensor dimensions of under-actuated, partially observed systems. We derive a computable sufficient attenuation bound for positive-semidefinite stabilizing Riccati solutions and construct an update that enforces their spectral-radius coupling condition. A discrete Kalman recursion supplies the scheduling state estimates. The two CAREs arising in controller synthesis are solved by a structure-preserving doubling algorithm (SDA) or a warm-started Newton--Kleinman iteration equipped with a doubling Lyapunov solver. Numerical studies use a twelve-state F-16 model with complete aerodynamic forces, moments, and trim, together with quadrotor spiral tracking. With instantaneous command updates, all three CARE backends give essentially the same closed-loop response. In the tracking simulations, measured computation times determine when new control inputs are applied, and the previous inputs are held during computation. SDA and Newton reduce airspeed and pitch errors in all six paired aircraft tracking runs. In the faster quadrotor task with limited computational resources, SDA and Newton complete all paired runs, while runs using MATLAB \texttt{icare} terminate early.
Comments27 pages, 6 figures
