2023/03/23 by Shawn Priore, Priore, Shawn, Meeko Oishi +1
Computer Science · Decision Sciences · Mathematics · Social Sciences · #Bayesian Modeling and Causal Inference #Computer science #Constraint (computer-aided design) #Covariance #FOS: Electrical engineering #FOS: Mathematics #Gaussian #Insurance, Mortality, Demography, Risk Management #Mathematical optimization #Mathematics #Optimal control #Optimization and Control (math.OC) #Probabilistic logic #Risk and Portfolio Optimization #Sample (material) #Statistics #Stochastic control #Systems and Control (eess.SY) #Variance (accounting) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2303.13036
openalex publication_date 2023/03/23 · openalex created_date 2023/03/25 · openalex updated_date 2026/07/28
We propose an open loop methodology based on sample statistics to solve chance constrained stochastic optimal control problems with probabilistic safety guarantees for linear systems where the additive Gaussian noise has unknown mean and covariance. We consider a joint chance constraint for time-varying polytopic target sets under assumptions that the disturbance has been sufficiently sampled. We derive two theorems that allow us to bound the probability of the state being more than some number of sample standard deviations away from the sample mean. We use these theorems to reformulate the chance constraint into a series of convex and linear constraints. Here, solutions guarantee chance constraint satisfaction. We demonstrate our method on a satellite rendezvous maneuver and provide comparisons with the scenario approach.