论文标题
使用动态编程解决整个任务范围的最佳控制
Solving Mission-Wide Chance-Constrained Optimal Control Using Dynamic Programming
论文作者
论文摘要
本文旨在提供动态编程（DP）方法来解决整个任务范围内的最佳控制问题（MWCC-OCP）。整个任务的机会约束确保了整个状态轨迹在约束/安全区域内的概率高于规定的级别，并且与在单个时间步骤中施加的阶段机会限制不同。控制目标是找到一个最佳的策略顺序，该顺序既可以满足（i）对整个任务限制的满意以及（ii）最小化成本函数的满意度。通过通过拉格朗日方法将阶段的机会约束问题转换为不受限制的对应物，可以部署标准DP。但是，对于MWCC-OCP而言，此方法无法应用，因为由于后者之间的时间相关，因此无法使用阶段的机会约束来轻松地制定整个任务的机会约束（单个状态通过系统动力学结合）。首先，为了填补这一空白，我们详细介绍了经典DP解决方案存在此类问题所需的条件；其次，我们通过引入其他功能状态变量，通过状态增强为MWCC-OCP提出了DP解决方案。
This paper aims to provide a Dynamic Programming (DP) approach to solve the Mission-Wide Chance-Constrained Optimal Control Problems (MWCC-OCP). The mission-wide chance constraint guarantees that the probability that the entire state trajectory lies within a constraint/safe region is higher than a prescribed level, and is different from the stage-wise chance constraints imposed at individual time steps. The control objective is to find an optimal policy sequence that achieves both (i) satisfaction of a mission-wide chance constraint, and (ii) minimization of a cost function. By transforming the stage-wise chance-constrained problem into an unconstrained counterpart via Lagrangian method, standard DP can then be deployed. Yet, for MWCC-OCP, this methods fails to apply, because the mission-wide chance constraint cannot be easily formulated using stage-wise chance constraints due to the time-correlation between the latter (individual states are coupled through the system dynamics). To fill this gap, firstly, we detail the conditions required for a classical DP solution to exist for this type of problem; secondly, we propose a DP solution to the MWCC-OCP through state augmentation by introducing an additional functional state variable.
