基于最小值原理的逆最优控制问题可解性分析
Solvability of the Inverse Optimal Control problem based on the minimum principle
AI总结：
本文分析基于最小值原理的逆最优控制可解性，给出轨迹充分条件化判据，发现开环系统对硬约束方法影响更强，并经仿真验证。
摘要：
本文分析了基于两种现有最小值原理方法的逆最优控制（IOC）问题的可解性。本文旨在回答以下问题：对于原始最优控制问题，哪些类型的轨迹（取决于闭环系统的初始条件和系统动力学）能够使得软约束和硬约束方法[1]，[2]恢复出奖励函数的真实权重。文中给出了解析条件，用以验证一条轨迹是否充分条件化，即是否包含足够的信息以恢复最优控制问题的真实权重。研究发现，与软约束方法相比，原始问题的开环系统对硬约束方法的逆最优控制问题可解性有更强的影响。这些解析结果通过仿真得到了验证。
英文摘要：
In this paper, the solvability of the Inverse Optimal Control (IOC) problem based on two existing minimum principal methods, is analysed. The aim of this work is to answer the question regarding what kinds of trajectories, that is depending on the initial conditions of the closed-loop system and system dynamics, of the original optimal control problem, will result in the recovery of the true weights of the reward function for both the soft and the hard-constrained methods [1], [2]. Analytical conditions are provided which allow to verify if a trajectory is sufficiently conditioned, that is, holds sufficient information to recover the true weights of an optimal control problem. It was found that the open-loop system of the original optimal problem has a stronger influence on the solvability of the Inverse Optimal Control problem for the hard-constrained method as compared to the soft-constrained method. These analytical results were validated via simulation.
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