On design of MPC with soft constraint based on multistep control set for stochastic multiplicative system

This paper develops a stochastic model predictive control method with soft constraint based on robust multistep control set with two major improvements: the region of probabilistic invariant set is enlarged compared with previous work and stochastic stability under current control method is guaranteed. Referring to multistep control set, we extend the concept of probabilistic invariant set from a single ellipsoid set to probabilistic control set, i.e. linear combination of multiple ellipsoid sets with time-varying feedback gains. Soft constraint method based on enlarged probabilistic control set is adopted to steer system states into the probabilistic control set as much as possible while taking performance index into account. This method also has low computation burden. Numerical example verifies these properties.