A Robust Model Predictive Control Algorithm with a Reactive Safety Mode

A reactive safety mode is built into a robust model predictive control algorithm for uncertain nonlinear systems. The algorithm is designed to obey all state and control constraints and blend two operational modes: (I) standard mode guarantees re-solvability and asymptotic convergence to the origin in a robust receding-horizon manner; (II) safety mode, if activated, guarantees containment within an invariant set about a safety reference for all time. The research is motivated by vehicle control-algorithm design (e.g., spacecraft and hovercraft) in which operation mode changes must be considered. Incorporating the reactive safety mode provides robustness to unexpected state-constraint changes; e.g., other vehicles crossing/stopping in the feasible path, or unexpected ground proximity in landing scenarios. The safety-mode control is provided by an offline designed control policy that can be activated at any arbitrary time during standard mode. The standard-mode control consists of separate feedforward and feedback components; feedforward comes from online solution of a FHC (Finite-Horizon optimal Control problem), while feedback is designed offline to generate an invariant tube about the feedforward trajectory. The tube provides robustness (to uncertainties and disturbances in the dynamics) and guarantees FHC re-solvability. The algorithm design is demonstrated for a class of systems with uncertain nonlinear terms that have norm-bounded Jacobians.