Ask not what ADMM can do for you, ask what you can do for ADMM — Virtual subsystems in MPC

In a range of applications, model predictive control (MPC) is implemented on embedded devices, motivating the use of conceptually and computationally simple optimization techniques. The alternating direction method of multipliers (ADMM) is a promising candidate for such situations since it relies on simple algebraic operations and shows large potential for problem-specific adaptation. In this paper, we exploit structure in the controlled system by introducing virtual subsystems, which make it possible to customize ADMM and to utilize this structure. When applied to an appropriate system, the resulting algorithm shows (i) reduced computational cost, (ii) the opportunity for parallelization, (iii) better scalability, and (iv) overall improved convergence performance.