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A Hamiltonian Decomposition-based Splitting Method for Interior Point Solvers in Model Predictive Control

Model Predictive Control (MPC) is an advanced control technique that is widely used in industry. At the core of the MPC algorithm lies an optimization problem that is solved by a numerical method at every time step. Increased demand for more self-contained modular processes has seen MPC embedded in small-scale platforms, such as Programmable Logic Controllers (PLCs). This has prompted a need for custom-made and highly efficient numerical optimization algorithms. In this paper, we propose a novel approach for factorizing the Newton system of the interior point method. This factorization is based on the eigenvalue decomposition of the Hamiltonian system associated with the MPC optimization problem. Once the augmented system is in the Hamiltonian form, the matrix can be decomposed into the sum of a constant matrix and a variable one. We show that most of the factorization of the constant matrix can be computed offline, whereas the remaining part can be computed using a splitting method. Numerical experiments demonstrate that the proposed approach is feasible and efficient compared to other state-of-the-art methods.