A tractable approximation for stochastic MPC and application to mechanical pulping processes

Abstract

This paper develops a tractable approximation for stochastic model predictive control (SMPC). Under the proposed approach, we solve multiple deterministic MPC (DMPC) problems over individual scenarios of the uncertain variables to obtain a set of control policies and select from this candidate set a control input that yields the best approximation of the SMPC solution (i.e., yields the smallest statistical measure of the objective function (e.g., expected value) and of the constraints). This approach is a scenario decomposition scheme that overcomes tractability issues of SMPC (which solves problems that incorporate multiple scenarios all-at-once). Moreover, the approach enables flexible handling of complex statistical measures (e.g., medians, quantiles, and chance constraints) and enables prioritization of objectives and constraints (this is difficult to do with off-the-shelf optimization solvers). An application to a nonlinear mechanical pulping process demonstrates that the approach provides high quality solutions. We hypothesize that this is because the optimal SMPC policy lives in a space that is spanned by the control policies for the individual scenarios. Moreover, we note that a traditional DMPC policy corresponds to the policy of an individual scenario (the mean scenario is typically chosen). Consequently, the proposed approach can do no worse than DMPC and can be interpreted as an approach that seeks to find a DMPC policy that best approximates the SMPC policy.