Feedback approximation in model predictive control

Model predictive control of a nonlinear dynamical system with linearizable and Lipschitz right-hand side is studied. It is proven that the exact model predictive control feedback allows approximation with a piecewise-affine, possibly discontinuous, function defined by its precalculated values on a finite grid. Approximation is understood not in the sense that control values are close but rather in the sense of closeness of the cost values. Additionally, if such approximation is close enough, stability of the approximate MPC is proven.