Computation of stochastic reachable and viable sets enables assurances of safety and feasibility through the synthesis of optimal control policies. These control policies are typically generated under the assumption of accurate characterization of additive noise processes. We consider the case in which independent noise processes are not fully characterized. Specifically, we consider linear time-invariant dynamics with additive noise, with known mean and bounded (but unknown) variance. We propose a method to compute a conservative underapproximation to the stochastic viable set for problems with convex viable and target sets. We underapproximate probability values through linear transformation based on bounds on the unknown variance. We demonstrate this method (via dynamic programming) on a simple example.
['Joseph Gleason', 'Abraham P. Vinod', 'Meeko M. K. Oishi', 'R. Scott Erwin']
Viable set approximation for linear-Gaussian systems with unknown, bounded variance