Computing the cost of multiplexed MPC

MPC outperforms other control strategies through its ability to deal with constraints. This requires on-line optimization, hence computational complexity can become an issue when applying MPC to complex systems with fast response times or to embedded applications where computational resources are limited. Multiplexed MPC (MMPC) has been proposed as a strategy to reduce computational complexity and stability results for MMPC have also been established. It has been suggested that the MMPC strategy of distributing the control moves over a complete update cycle, in contrast to conventional MIMO MPC which updates all the control variables simultaneously in one update cycle, may result in improved performance, despite finding sub-optimal solutions to the original problem. In this paper, we show that MMPC can be interpreted as a piecewise linear periodic state feedback law in the augmented state space. This provides a framework for systematic analysis and investigation of the properties of MMPC. In particular, the formula for computing the quadratic cost of MMPC is derived and illustrated through a numerical example.