We present a stochastic model predictive control (MPC) method for linear discrete-time systems subject to possibly unbounded and correlated additive stochastic disturbance sequences. Chance constraints are treated in analogy to robust MPC using the concept of probabilistic reachable sets for constraint tightening. We introduce an initialization of each MPC iteration which is always recursively feasible and guarantees chance constraint satisfaction for the closed-loop system, which is typically challenging for systems under unbounded disturbances. Under an i.i.d. zero-mean assumption, we provide an average asymptotic performance bound. A building control example illustrates the approach in an application with time-varying, correlated disturbances.

我们提出了一种线性离散时间系统的随机模型预测控制（MPC）方法，该方法受可能无界和相关的加性随机干扰序列的影响。机会约束类似于稳健的MPC，使用概率可到达集合的概念来约束约束。我们介绍了每次MPC迭代的初始化，该初始化始终是递归可行的，并且可以确保闭环系统的机会约束满足，这对于无界干扰下的系统通常具有挑战性。在iid零均值假设下，我们提供了平均渐近性能界限。建筑物控制示例说明了具有时变，相关干扰的应用中的方法。