A Parallel Algorithm for Implicit Model Predictive Control with Barrier Function

An increasing interest of the control community is currently dedicated to reducing the computation time of implicit model predictive controllers, even by looking at algorithms able to get “good” suboptimal solutions and which could be more efficiently implemented in real time. To this aim the potentialities of the weighted barrier function approach has been widely demonstrated in the literature. In this work it is addressed the issue of increasing performances of the barrier method for constrained model predictive control (MPC) through an algorithm that concurrently looks at the outcomes corresponding to different weights of the barrier functions and chooses, at each optimization stage, the “best” optimizing solution. The proposed idea has interesting effects with respect to the performance of the control action, particularly in the situation in which system states and inputs signals are moving close to the constraints. Good results are obtained without increasing the computation time in a significative way thanks to the parallelization. The effectiveness of the approach has been successfully validated in simulations on two different case-studies taken from the recent literature on the application of implicit MPC: the Cessna Citation 500 aircraft and a rotating antenna.