We present an algorithm for generating a binary search tree that allows efficient evaluation of piecewise affine (PWA) functions defined on a polyhedral partitioning. This is useful for PWA control approaches, such as explicit model predictive control (MPC), as it allows the controller to be implemented online with small computational effort. The computation time is logarithmic in the number of regions in the PWA function.

Explicit solutions to constrained linear MPC problems can be obtained by solving multi-parametric quadratic programs (mp-QP) where the parameters are the components of the state vector. We study the properties of the polyhedral partition of the state-space induced by the multiparametric piecewise linear solution and propose a new mp-QP solver. Compared to existing algorithms, our approach adopts a different exploration strategy for subdividing the parameter space, avoiding unnecessary partitioning and QP problem solving, with a significant improvement of efficiency.

Explicit solutions to constrained linear MPC problems can be obtained by solving multi-parametric quadratic programs (mp-QP) where the parameters are the components of the state vector. We study the properties of the polyhedral partition of the state-space induced by the multiparametric piecewise linear solution and propose a new mp-QP solver. Compared to existing algorithms, our approach adopts a different exploration strategy for subdividing the parameter space, avoiding unnecessary partitioning and QP problem solving, with a significant improvement of efficiency.

Explicit solutions to constrained linear MPC problems can be obtained by solving multi-parametric quadratic programs (mp-QP) where the parameters are the components of the state vector. We study the properties of the polyhedral partition of the state-space induced by the multiparametric piecewise linear solution and propose a new mp-QP solver. Compared to existing algorithms, our approach adopts a different exploration strategy for subdividing the parameter space, avoiding unnecessary partitioning and QP problem solving, with a significant improvement of efficiency.

Abstract-The general solution to constrained linear and piecewise linear model predictive control (MPC) has recently been explicitly characterized in terms of piecewise linear (PWL) state feedback control. This means that a PWL controller can be precomputed using parametric programming, and the exact explicit MPC implementation amounts to the evaluation of a PWL function in the control unit. It has recently been shown that PWL function evaluation can be accelerated by searching a binary tree data structure, leading to highly efficient, accurate, and verifiable software implementation in low-cost embedded control units. In this work we report hardware synthesis results for this type of PWL control, and show that explicit MPC solutions can be implemented in an application specific integrated circuit (ASIC) with about 20,000 gates, leading to computation times in the microsecond scale. This opens the way for the use of highly advanced control designs such as constrained MPC in small-scale industrial and consumer electronics application areas that are characterized by fast sampling or low cost, including mechatronics, MEMS, automotive control, power electronics, and acoustics. The main limitation of the approach is that the memory requirements increase rapidly with the problem dimensions.