Fast explicit MPC with multiway trees

Abstract We show that explicit model predictive control (EMPC) laws, or more generally continuous piecewise affine control (PWA) laws on polyhedra, can be represented by multiway trees with two important features: (i) Their height can be reduced arbitrarily by increasing their order m (i.e. the number of binary tree nodes hidden in each multiway node). (ii) A multiway node can be evaluated as fast as a binary node with a simple but massively concurrent (or “parallel”) procedure for m ≫ 1. As a result the control law evaluation can be evaluated considerably faster than with a binary tree. Furthermore, we show that a multiway tree representation of an EMPC control law can be derived from the corresponding binary tree representation with a simple algorithm. Finally, we demonstrate that programmable logic devices are ideally suited for an implementation. First tests show that EMPC control laws with several thousand hyperplanes can be evaluated in a few clock cycles on compact, low-cost, low-power programmable logic devices.