Efficient online update of model predictive control in embedded systems using first-order methods

Model Predictive Control (MPC) is typically characterized for being computationally demanding, as it requires solving optimization problems online; a particularly relevant point when considering its implementation in embedded systems. To reduce the computational burden of the optimization algorithm, most solvers perform as many offline operations as possible, typically performing the computation and factorization of its expensive matrices offline and then storing them in the embedded system. This improves the efficiency of the solver, with the disadvantage that online changes on some of the ingredients of the MPC formulation require performing these expensive computations online. This article presents an efficient algorithm for the factorization of the key matrix used in several first-order optimization methods applied to linear MPC formulations, allowing its prediction model and cost function matrices to be updated online at the expense of a small computational cost. We show results comparing the proposed approach with other solvers from the literature applied to a linear time-varying system.