A control Lyapunov function approach for the computation of the infinite-horizon stochastic reach-avoid problem

This work is devoted to the solution of the stochastic reach-avoid problem over controlled discrete-time Markov processes (cdt-MP) with general state and action spaces. Whereas the finite time horizon case allows for the use of discretization techniques that compute the quantities of interest with any given precision under mild conditions on the model, the infinite-horizon counterpart demands a more elaborate analysis. This contribution introduces control Lyapunov functions over cdt-MP and shows how these functions help solving the reach-avoid problem over the infinite time horizon. As an example, we show how to apply these technique to the ruin problem arising in the risk theory of insurance companies.