论文标题
Sylvester，Lyapunov和代数Riccati方程的自动分化
Automatic differentiation of Sylvester, Lyapunov, and algebraic Riccati equations
论文作者
论文摘要
Sylvester，Lyapunov和代数Riccati方程是控制理论家的面包和黄油。它们用于计算无限 - 马利亚人，解决连续或离散时间的最佳控制问题以及设计观察者。尽管流行的数值计算框架（例如Scipy）为这些方程式提供了有效的求解器，但这些求解器仍然在大多数自动分化库中大部分都缺少。在这里，我们将解决方案的前向和反向模式衍生物推导到所有三种方程式上，并在反控制问题上展示其应用程序。
Sylvester, Lyapunov, and algebraic Riccati equations are the bread and butter of control theorists. They are used to compute infinite-horizon Gramians, solve optimal control problems in continuous or discrete time, and design observers. While popular numerical computing frameworks (e.g., scipy) provide efficient solvers for these equations, these solvers are still largely missing from most automatic differentiation libraries. Here, we derive the forward and reverse-mode derivatives of the solutions to all three types of equations, and showcase their application on an inverse control problem.
