Chance Constrained Stochastic Optimal Control for Linear Systems with a Time Varying Random Control Matrix

This work proposes an open-loop methodology to solve chance constrained stochastic optimal control problems for linear systems with a stochastic control matrix. We consider a joint chance constraint for polytopic time-varying target sets under moment and unimodality assumptions. We reformulate the chance constraint into individual biconvex constraints using the one-sided Vysochanskij-Petunin inequality. We demonstrate our methodology on two spacecraft rendezvous problems. We compare the proposed method with the scenario approach and moment-based methods based on Cantelli's inequality.Comment: Final Submission to CCTA 202

Chance Constrained Stochastic Optimal Control for Linear Systems with Time Varying Random Plant Parameters

We propose an open loop control scheme for linear systems with time-varying random elements in the plant's state matrix. This paper focuses on joint chance constraints for potentially time-varying target sets. Under assumption of finite and known expectation and variance, we use the one-sided Vysochanskij-Petunin inequality to reformulate joint chance constraints into a tractable form. We demonstrate our methodology on a two-bus power system with stochastic load and wind power generation. We compare our method with situation approach. We show that the proposed method had superior solve times and favorable optimally considerations.Comment: Final submission for ACC 202