On prediction strategies in stochastic MPC

The optimization of predicted control policies in Model Predictive Control (MPC) enables the use of information on future disturbance inputs which, although unknown at current time, will be known at a future point on the prediction horizon. However, optimization over feedback laws can be prohibitively computationally expensive. The so-called affine-in-the-disturbance strategies provide a compromise, and this paper considers the use of disturbance compensation in the context of stochastic MPC. Unlike earlier approaches, compensation is applied over the entire horizon, thereby leading to a significant constraint relaxation which makes more control authority available for the optimization 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 afforded by computing these feedback gains offline. Simulations show this can be achieved at a modest cost in terms of performance.