论文标题
协方差转向具有最佳风险分配
Covariance Steering with Optimal Risk Allocation
论文作者
论文摘要
本文扩展了线性随机系统的最佳协方差转向问题，但受到机会限制，以考虑最佳风险分配。先前的工作假设了统一的风险分配，以将最佳控制问题作为半准计划（SDP）施加最佳控制问题，可以使用标准的SDP求解器有效地解决该问题。我们采用迭代风险分配（IRA）形式主义，该形式使用两阶段的方法来解决协方差转向的最佳风险分配问题。 IRA的上层阶段优化了风险，这被证明是一个凸问题，而下阶段则通过新约束来优化控制器。这是迭代完成的，以便找到达到最低总成本的最佳风险分配。所提出的框架导致解决方案倾向于最大化终端协方差，同时仍然满足机会限制，从而导致与以前的方法相比，导致保守的解决方案较少。我们还介绍了两种新型的凸松弛方法，以将二次机会约束作为二阶锥体约束。我们最终演示了解决航天器会合问题的方法，并比较结果。
This paper extends the optimal covariance steering problem for linear stochastic systems subject to chance constraints to account for optimal risk allocation. Previous works have assumed a uniform risk allocation to cast the optimal control problem as a semi-definite program (SDP), which can be solved efficiently using standard SDP solvers. We adopt an Iterative Risk Allocation (IRA) formalism, which uses a two-stage approach to solve the optimal risk allocation problem for covariance steering. The upper-stage of IRA optimizes the risk, which is proved to be a convex problem, while the lower-stage optimizes the controller with the new constraints. This is done iteratively so as to find the optimal risk allocation that achieves the lowest total cost. The proposed framework results in solutions that tend to maximize the terminal covariance, while still satisfying the chance constraints, thus leading to less conservative solutions than previous methodologies. We also introduce two novel convex relaxation methods to approximate quadratic chance constraints as second-order cone constraints. We finally demonstrate the approach to a spacecraft rendezvous problem and compare the results.
