This paper presents a method for solving linear stochastic model predictive control (SMPC) subject to joint chance constraints. The chance constraints are decoupled using Boole's inequality and by introducing a set of unknowns representing allowable violation for each constraint (the risk). A tailored interior point method is proposed to explore the special structure of the resulting SMPC problem. The proposed method is compared with existing two-stage algorithms with the first stage allocating the risks and the second stage optimizing the feedback control gain. The approach is applied to building control problems that minimizes energy usage while keeping thermal comfort by making use of uncertain predictions of thermal loads and ambient temperature. Extensive numerical tests show the effectiveness of the proposed approach.
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