Synthesis of simple explicit MPC optimizers by function approximation

Explicit Model Predictive Control (MPC) is an attractive control strategy, especially when one aims at a fast, computationally less demanding implementation of MPC. However the major obstacle that prevents a successful application of explicit MPC controllers lies in the increased memory occupancy. This is a major limitation of the approach when aiming at implementing MPC in control hardware that has restricted amount of memory storage. Therefore in this paper we propose to obtain a much more simpler representation of explicit MPC solutions that occupy less memory. We propose to achieve this goal by constructing a simpler, albeit suboptimal, representation of the explicit MPC optimizer. This task is accomplished by first synthesizing a simpler explicit optimizer as a piecewise affine function that maps state measurements onto the predicted sequence of control inputs. Subsequently, parameters of such a function are refined as to achieve better performance. We show that such a function approximation problem is always feasible. Efficacy of the proposed procedure is demonstrated on several examples.