Stochastic constrained control: trading performance for state constraint feasibility

In this paper, we address finite-horizon control for a stochastic linear system subject to constraints on the control and state variables. A control design methodology is proposed where the appropriate trade-off between the minimization of the control cost (performance) and the satisfaction of the state constraints (safety) can be decided by introducing appropriate chance-constrained problems depending on some parameter to be tuned. From an algorithmic viewpoint, a computationally tractable randomized approach to find approximate solutions which are guaranteed to be feasible for the original chance-constrained problem is proposed. A numerical example concludes the paper.