Robust model predictive control with embedded multi-scenario closed-loop prediction

Robust MPC seeks to mitigate the effects of uncertainty which can lead to suboptimal MPC performance. Previous work on robust MPC includes a stochastic multi-scenario approach to simulate multiple plant realizations and create a control scheme to optimize a performance metric based on the plant scenarios. This paper seeks to combine a scenario-based approach with embedded closed-loop prediction under future MPC control action by directly incorporating MPC subproblems into the overall robust MPC formulation. This allows the current MPC to predict closed-loop MPC responses to a range of uncertain future plant realizations. The resulting multilevel programming problem is solved by reformulating the inner MPC optimization subproblems as algebraic constraints corresponding to their first-order optimality conditions, resulting in a single level mathematical program with complementarity constraints (MPCC). The performance of the robust MPC scheme is evaluated against a standard MPC formulation in linear and nonlinear case studies.