Approximate Stochastic Optimal Control for Linear Time Invariant Systems with Heavy-tailed Disturbances

Autor:	Priore, Shawn, Petersen, Christopher, Oishi, Meeko
Rok vydání:	2022
Předmět:	Electrical Engineering and Systems Science - Systems and Control Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	We propose an open loop control scheme for linear time invariant systems perturbed by multivariate $t$ disturbances through the use of quantile reformulations. The multivariate $t$ disturbance is motivated by heavy tailed phenomena that arise in multi-vehicle planning planning problems through unmodeled perturbation forces, linearization effects, or faulty actuators. Our approach relies on convex quantile reformulations of the polytopic target sets and norm based collision avoidance constraints to enable fast computation. We embed quantile approximations of the Student's $t$ distribution and the beta prime distribution in a difference-of-convex function framework to compute provably safe but likely suboptimal controllers. We demonstrate our method with three satellite rendezvous examples and provide a comparison with particle control. Comment: Initial submission to AIAA Journal of Guidance, Control, and Dynamics
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2210.09479 Zobrazit plný text záznamu View this record from Arxiv