Efficient prediction strategies for disturbance compensation in stochastic MPC

The optimisation of predicted control policies in model predictive control (MPC) enables the use of information on uncertainty that, though not available at current time, will be so at a future point on the prediction horizon. Optimisation over feedback laws is however prohibitively computationally expensive. The so-called affine-in-the-disturbance strategies provide a compromise and this article considers the use of disturbance compensation in the context of stochastic MPC. Unlike the earlier approaches, compensation here is applied over the entire prediction horizon (extending to infinity) thereby leading to a significant constraint relaxation which makes more control authority available for the optimisation of performance. In addition, our compensation has a striped lower triangular dependence on the uncertainty on account of which the relevant gains can be obtained sequentially, thereby reducing computational complexity. Further reduction in computation is achieved by performing this computation offline. Simulation results show that this reduction can be gained at a negligible cost in terms of closed-loop performance.