Semi-Proximal ADMM for Model Predictive Control Problem with Application to a UAV System

A lasso model predictive control (MPC) problem solved by the alternative direction method of multipliers (ADMM) is investigated in this work. More specifically, a semi-proximal ADMM algorithm with Gauss-Seidel iterations is proposed to solve the lasso MPC problem with singular weighting matrices. It is well-known that the interior-point algorithm is an effective and efficient algorithm, which is commonly used to obtain the real-time solution to the MPC optimization problem. However, when the weighting matrices of the lasso MPC problem are singular, it is extremely challenging to solve the optimization problem by using the classical interior-point algorithm. In fact, in some special cases, the interior-point algorithm is entirely infeasible for solving the aforementioned problems. In the work here, our developments reveal that the proposed optimization methodology (a semi-proximal ADMM algorithm with Gauss-Seidel iterations) is much more advantageous compared to the interior-point algorithm in some specific cases, especially in the case where singular weighting matrices exist in the cost function. An MPC based tracking problem of an unmanned aerial vehicle (UAV) system is implemented to compare the performance of the proposed algorithm to the performance of the existing solver. The simulation result shows that with the proposed algorithm, higher accuracy and computational efficiency can be realized.