论文标题
LQR控制器对扭矩有限的简单摆的吸引力区域的分析估计
Analytic Estimation of Region of Attraction of an LQR Controller for Torque Limited Simple Pendulum
论文作者
论文摘要
线性季度调节剂（LQR）是线性和非线性动力学的控制理论中众所周知的且广泛使用的工具。对于非线性问题，基于LQR的控制器通常仅在局部可行，因此提出了估计吸引区域（ROA）的问题。良好的ROA估计的需求尤其迫切，由于控制措施的失败可能导致不安全且无法恢复的系统状态。基于优化或采样的已知方法虽然工作良好，但临界应用程序可能太慢，很难正式验证。在这项工作中，我们提出了一种新型方法，以基于扭矩有限的简单摆的线性ODE的分析解决方案来估计ROA。在模拟和物理实验中，我们将我们的方法与Lyapunov抽采样基线方法进行了比较，发现我们的方法更快地计算，同时对相似的相空间面积进行了ROA估计。
Linear-quadratic regulators (LQR) are a well known and widely used tool in control theory for both linear and nonlinear dynamics. For nonlinear problems, an LQR-based controller is usually only locally viable, thus, raising the problem of estimating the region of attraction (ROA). The need for good ROA estimations becomes especially pressing for underactuated systems, as a failure of controls might lead to unsafe and unrecoverable system states. Known approaches based on optimization or sampling, while working well, might be too slow in time critical applications and are hard to verify formally. In this work, we propose a novel approach to estimate the ROA based on the analytic solutions to linear ODEs for the torque limited simple pendulum. In simulation and physical experiments, we compared our approach to a Lyapunov-sampling baseline approach and found that our approach was faster to compute, while yielding ROA estimations of similar phase space area.
