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This work proposes an open-loop methodology to solve chance constrainedstochastic optimal control problems for linear systems with a stochasticcontrol matrix. We consider a joint chance constraint for polytopictime-varying target sets under moment and unimodality assumptions. Wereformulate the chance constraint into individual biconvex constraints usingthe one-sided Vysochanskij-Petunin inequality. We demonstrate our methodologyon two spacecraft rendezvous problems. We compare the proposed method with thescenario approach and moment-based methods based on Cantelli's inequality.

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