Structure exploitation of practical MPC formulations for speeding up first-order methods

This paper presents structure exploitation techniques that lead to faster convergence of first-order methods for practical Model Predictive Control (MPC) formulations. We exploit the special structure of output box constraints as well as input bound and rate constraints. The output constraints are included in the MPC objective as exact penalty functions, in order to avoid feasibility issues due to e.g. plant-model mismatch. Observations from a new derivation of exact penalty functions enable us to formulate exact penalty functions that do not require additional auxiliary variables if first-order solution methods are used. We use the dual fast gradient method to illustrate the effectiveness of our approach. An average speedup of x8 and a worst case speed-up of x6 were obtained, compared with the fastest state-of-the-art first-order method for a subsea separation process. Moreover, hardware-in-the-loop simulations using an ANSI C implementation on a PLC reveal that our first-order solver outperforms the fastest second-order solver deployed for the subsea separation process.