The Inverse Optimal Control (IOC) problem is a structured system identification problem that aims to identify the underlying objective function based on observed optimal trajectories. This provides a data-driven way to model experts’ behavior. In this paper, we consider the case of discrete-time finite-horizon linear–quadratic problems where: the quadratic cost term in the objective is not necessarily positive semi-definite; the planning horizon is a random variable; we have both process noise and observation noise; the dynamics can have a drift term; and where we can have a linear cost term in the objective. In this setting, we first formulate the necessary and sufficient conditions for when the forward optimal control problem is solvable. Next, we show that the corresponding IOC problem is identifiable. Using the conditions for existence of an optimum of the forward problem, we then formulate an estimator for the parameters in the objective function of the forward problem as the globally optimal solution to a convex optimization problem, and prove that the estimator is statistical consistent. Finally, the performance of the algorithm is demonstrated on two numerical examples.

中文翻译：

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离散时间不定线性二次系统的统计一致逆最优控制


逆最优控制（IOC）问题是一个结构化系统识别问题，旨在根据观察到的最优轨迹来识别潜在的目标函数。这提供了一种数据驱动的方式来模拟专家的行为。在本文中，我们考虑离散时间有限范围线性二次问题的情况，其中： 目标中的二次成本项不一定是正半定的；规划范围是一个随机变量；我们既有过程噪声，也有观察噪声；动力学可以有一个漂移项；以及我们可以在目标中使用线性成本项。在这种情况下，我们首先制定前向最优控制问题可解的充分必要条件。接下来，我们证明相应的 IOC 问题是可识别的。利用前向问题最优存在的条件，我们将前向问题目标函数中的参数制定为凸优化问题的全局最优解的估计量，并证明该估计量是统计一致的。最后，通过两个数值例子证明了该算法的性能。