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This study covers the model predictive control of linear discrete-time systems subject to stochastic additive disturbances and state chance constraints. The stochastic optimal control problem is reformulated in a dynamic programming fashion to obtain a closed-loop performance and is solved using the interior-point method combined with a Riccati-based approach. The proposed method eliminates active sets in conventional explicit model predictive control and does not suffer from the curse of dimensionality because it finds the value function and feedback policy only for a given initial state using the interior-point method. Moreover, the proposed method is proven to converge globally to the optimal solution Q-superlinearly. The numerical experiment shows that the proposed method achieves a less conservative performance with a low computational complexity compared to existing methods.

A recursive Riccati interior-point method for chance-constrained stochastic model predictive control