论文标题
统计上一致的逆最佳控制，用于离散时间不定时间线性季度系统
Statistically consistent inverse optimal control for discrete-time indefinite linear-quadratic systems
论文作者
论文摘要
逆最佳控制（IOC）问题是一个结构化的系统识别问题，旨在基于观察到的最佳轨迹识别基础目标函数。这为建模专家的行为提供了一种数据驱动的方式。在本文中，我们考虑了离散时间有限的线性季度问题的情况：物镜中的二次成本项不一定是半明确的阳性；计划范围是一个随机变量；我们既有过程噪声又有观察噪声；动力学可以具有漂移术语；以及我们可以在目标中具有线性成本期限的地方。在这种情况下，我们首先制定了何时可以解决远期最佳控制问题的必要条件。接下来，我们证明相应的IOC问题是可识别的。利用存在最佳问题问题的条件，然后我们为正向问题的目标函数中的参数制定估计器，作为凸优化问题的全球最佳解决方案，并证明估计器是统计的一致性。最后，在两个数值示例中证明了该算法的性能。
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.
