Ma Lanlan, Kong Qian
International Center of Quantum Artificial Intelligence for Science and Technology (QuArtist), Department of Physics, Shanghai University, Shanghai 200444, China.
Entropy (Basel). 2023 Apr 26;25(5):719. doi: 10.3390/e25050719.
We combined an inverse engineering technique based on Lagrange mechanics and optimal control theory to design an optimal trajectory that can transport a cartpole in a fast and stable way. For classical control, we used the relative displacement between the ball and the trolley as the controller to study the anharmonic effect of the cartpole. Under this constraint, we used the time minimization principle in optimal control theory to find the optimal trajectory, and the solution of time minimization is the bang-bang form, which ensures that the pendulum is in a vertical upward position at the initial and the final moments and oscillates in a small angle range.
我们结合了基于拉格朗日力学和最优控制理论的逆向工程技术，以设计出一种能快速稳定地运输摆杆车的最优轨迹。对于经典控制，我们使用球与小车之间的相对位移作为控制器来研究摆杆车的非谐效应。在此约束下，我们运用最优控制理论中的时间最小化原理来寻找最优轨迹，而时间最小化的解为开关控制形式，这确保了摆锤在初始和最终时刻处于垂直向上位置，并在小角度范围内摆动。
