Stochastic Model Predictive Control (SMPC) has been the focus of intense research in the last years. The objective of SMPC is to design control systems corrupted by stochastic noise. Existing solutions include the implementation of Robust MPC schemes, where the worst case scenario is taken into account. As this approach often results in conservative and expensive solutions, a number of researchers have addressed the need for more optimistic and realistic tailored control schemes that can handle stochastic process behaviour. SMPC gives practitioners a tool to take most realization of uncertainty in the controller design, while guaranteeing feasibility and stability. The work presented in this thesis focuses on developing an SMPC algorithm for nonlinear systems with additive stochastic uncertainty. The scheme is carried out in a fast sampled-data approach, which yields an advantageous computational load.

We develop a sampled-data scheme for deterministic systems through sampling control moves. Two sampled-data schemes have been proposed and examined in benchmark simulations including a CSTR system. The first scheme considers a hybrid control system, where a continuous-time flow control occurs during a fine time grid, and a discrete-time jump control looks after jumps in a coarse time grid. The second scheme is a complete sampled-data system through discrete control moves throughout the two time grids. It was shown that the second control scheme succeeded in reducing the cost function along with a huge reduction in CPU time for all the simulations.

Secondly, the latter sampled-data scheme was modified to handle stochastic noise through the inclusion of an expected cost and probabilistic constraints. The resulting control can handle moderate noise signals and produce much better results than conventional nonlinear SMPC schemes. The proposed stochastic sampled-data MPC scheme is designed to tackle nonlinear dynamical systems with moderate noise signals with a large precision and low CPU time.