Stability of model predictive control using Markov Chain Monte Carlo optimisation

We apply stochastic Lyapunov theory to perform stability analysis of MPC controllers for nonlinear deterministic systems where the underlying optimisation algorithm is based on Markov Chain Monte Carlo (MCMC) or other stochastic methods. We provide a set of assumptions and conditions required for employing the approximate value function obtained as a stochastic Lyapunov function, thereby providing almost sure closed loop stability. We demonstrate convergence of the system state to a target set on an example, in which simulated annealing with finite time stopping is used to control a nonlinear system with non-convex constraints.