Computation of piecewise affine terminal cost functions for model predictive control

This paper proposes a method for the construction of piecewise affine terminal cost functions for model predictive control (MPC). The terminal cost function is constructed on a predefined partition by solving a linear program for a given piecewise affine system, a stabilizing piecewise affine controller, an invariant set and a piecewise convex stage cost function. The constructed terminal cost function satisfies the sufficient conditions for asymptotic stability if it is used in an MPC scheme. In general, the constructed terminal cost function will be nonconvex. However, optional additional constraints in the linear program ensure that the cost function is convex, reducing the computational effort involved with solving the MPC optimization problem. Multiple examples illustrate the approach