Fast Explicit Nonlinear Model Predictive Control Via Multiresolution Function Approximation with Guaranteed Stability Nonlinear Control Systems

In this paper an algorithm for nonlinear explicit model predictive control is introduced based on multiresolution function approximation that returns a low complexity approximate receding horizon control law built on a hierarchy of second order interpolets. Feasibility and stability guarantees for the approximate control law are given using reachability analysis, where interval methods are used to construct a capture basin (feasible region). A constructive algorithm is provided that combines adaptive function approximation with interval methods to build a receding horizon control law that is suboptimal, yet with a region of guaranteed feasibility and stability. The resulting control law is built on a grid hierarchy that is fast to evaluate in real-time systems.