  Motivated by the recent interest in risk-aware control, we study a
continuous-time control synthesis problem to bound the risk that a stochastic
linear system violates a given specification. We use risk signal temporal logic
as a specification formalism in which distributionally robust risk predicates
are considered and equipped with the usual Boolean and temporal operators. Our
control approach relies on reformulating these risk predicates as deterministic
predicates over mean and covariance states of the system. We then obtain a
timed sequence of sets of mean and covariance states from the timed automata
representation of the specification. To avoid an explosion in the number of
automata states, we propose heuristics to find candidate sequences effectively.
To execute and check dynamic feasibility of these sequences, we present a
sampled-data control technique based on time discretization and constraint
tightening that allows to perform timed transitions while satisfying the
continuous-time constraints.
