Algorithms for Online Implementations of Explicit MPC Solutions

Abstract One of the key problems in Model Predictive Control (MPC) is the inherent on-line computational complexity, which restricts its application to slow dynamic systems. To address this issue, multi-parametric programming technique is introduced in MPC (explicit MPC), where the optimization effort is moved off-line. The optimal solution is given in an explicitly piecewise affine function defined over a polyhedral subdivision of the set of feasible states. Instead of solving an optimization problem, the on-line work is simplified to identify the region the current state belongs to and simply evaluate the piecewise affine function. Hence, identifying of the member of the solution partition that contains a given point (referred to as a point location problem) impacts on the time to implement the explicit controller in real-time, which is one component of the complexity of explicit MPC. In this paper, two simple algorithms for point location problems are proposed to efficiently implement of explicit MPC solutions, which aim at reducing the number of polyhedral sets that are candidates to contain the state at the next time instant.