Complexity reduction of explicit model predictive control via separation

The problem of reducing complexity of explicit MPC feedback laws for linear systems is considered. We propose to simplify controllers defined by continuous Piecewise Affine (PWA) functions by employing separating functions. If a state resides in a region where the optimal control action attains a saturated value, the optimal control move is determined from the sign of the separator. Thus, instead of storing all regions, only the unconstrained regions and the separator are needed. We propose several approaches to construct separators with different efficacy and properties.