Performance testing of an approximate model predictive control algorithm

Abstract

An approximate version of model predictive control proposed previously by the author is simulated using MATLAB. The experiments show how the algorithm's performance depends on its precision. Finally, the study gives insight into the effective implementation of the algorithm.

Feedback approximation in model predictive control

“…When the system state x is in a set where the sets overlap, controls provided by the piecewise-affine functions are compared and the one closest to the optimal one is chosen. The comparison is done using the dynamical programming principle as described in [6].…”

“…The feedback may even be discontinuous. However, it has been demonstrated in [6] that the optimal value of the cost function employed in the MPC algorithm is a continuous Lipschitz function of the initial system state. It allows one to approximate it with a piecewise-affine function and reduce the dimensionality of the optimization problem by means of the dynamical programming approach.…”

“…In the present paper the ideas of [6] are taken one step further. Based on the Lipschitz property of the optimal cost value, it is proven that even if the MPC feedback is discontinuous, approximating it with a piecewise affine and piecewise continuous function leads to a feedback which is close to MPC in the sense that the cost value is close to optimal.…”