Accelerating online MPC with partial explicit information and linear storage complexity in the number of constraints

Model predictive control (MPC) is an acclaimed method for the control of constrained systems. Since a constrained optimization problem has to be solved in every time step, the online computational effort of MPC is high. Explicit MPC provides an analytical solution to the same optimization problem, but explicit MPC is only useful for small systems, since the storage requirements for the explicit control law grow exponentially in the number of constraints of the optimization problem. We show that online MPC can be accelerated with information on the structure of the control law, where this structural information is calculated offline with techniques from explicit MPC. Our two main contributions are as follows: We demonstrate that online MPC can be sped up significantly if only q state space regions, the regions of activity, are stored, where q is the number of constraints. Note that this linear growth in q is obviously very different from the exponential growth in q of the number of polytopes that need to be stored in explicit MPC. Secondly, we claim that the proposed method is a variant of a family of methods, which comprises online MPC and explicit MPC as two limiting cases.