Explicit interpolation-based nonlinear model predictive control with a convex approximation of the feasible set

In this paper, an approach to explicit interpolation-based MPC of constrained nonlinear systems is proposed, which is based on the ideas in [9], [10] for explicit constrained control of linear systems by applying interpolation techniques. The developed approach can be considered as an extension of the method in [9], [10] in the following directions: (i) nonlinear discrete-time systems are considered, which are regulated to the origin by solving an NMPC problem, (ii) a method for construction of a convex approximation of the feasible set for the formulated NMPC problem is suggested, (iii) the vertex control (the control values at the vertices of the approximate feasible set) is determined by solving the NMPC problem, instead of maximizing the control action, (iv) an algorithm for explicit interpolation-based NMPC is developed, where the explicit approximate solution is defined on a simplicial partition of the convex approximate feasible set. The proposed approach is illustrated on a numerical example.