Model predictive control with guarantees for discrete linear stochastic systems subject to additive disturbances with chance constraints

We propose a stochastic model predictive control scheme for linear discrete-time and time-invariant systems with chance constraints and additive normal distributed disturbance with known covariance. The proposed approach allows to balance between performance optimization and robustness by adjusting the probability p of the chance constraints. The Controllability Gramian and the Riccati inequality are used to determine a set that contains all disturbances with a probability p. The proposed approach guarantees asymptotic stability of the nominal system, probabilistic convergence of the real system as well as constraint satisfaction and recursive feasibility in terms of probability. A proof of concept example considers the control of a wind turbine, where the wind acts as a normal distributed disturbance.