A Terminal State Feasibility Governor for Real-Time Nonlinear Model Predictive Control Over Arbitrary Horizons

Abstract

This article introduces a novel feasibility governor (FG), which enlarges the region of attraction (ROA) of a nonlinear model predictive control (NMPC) setpoint regulation law with an arbitrarily short prediction horizon. The efficient online FG is developed for nonlinear systems subject to pointwise-in-time state and input constraints and relies on a discrete-time solution of a trajectory-based explicit reference governor (ERG) with Lyapunov-based terminal energy constraint. It ensures the FG-NMPC scheme's recursive feasibility to any target and asymptotic stability to constant targets by adaptively integrating the derivative of an auxiliary reference applied to the closed-loop NMPC. Compared to recently published FG schemes, this scheme scales better to higher-dimensional nonlinear systems with a priori unknown constraints, as it does not require expensive offline computations to construct the feasible set or the maximal output admissible set (MOAS) associated with the NMPC's terminal control law. The scheme is implemented as a C++ algorithm and validated through simulations on a quadrotor that aggressively but safely flies through a priori unknown environments cluttered with obstacles. It is shown to satisfy all constraints for any piecewise-continuous reference, achieve asymptotic stability and zero-offset tracking to constant constraint-admissible targets, and require low computational effort. Supplementary video material can be found at https://youtu.be/2LSYNwuYpzI.