A Robustly Stabilizing Model Predictive Control Algorithm

33 A model predictive control (MPC) algorithm that differs from prior MPC algorithms has been developed for controlling an uncertain nonlinear system. This algorithm guarantees the resolvability of an associated finite-horizon optimal-control problem in a recedinghorizon implementation. Given a feasible solution to the finite-horizon optimal control problem at an initial time, resolvability implies the ability to solve the optimal control problem at subsequent times. Originally developed for the control of spacecraft in the proximity of small celestial bodies, the algorithm can also be applied to other systems (such as industrial and automotive systems) for which robust feedback control may be required. The algorithm consists of a feedforward and a feedback component. The feedforward part is computed by the on-line solution of the finite-horizon optimal control problem with the nominal system dynamics, with a relaxation of the initial state constraint at each computation. The feedback component makes this relaxation possible, which in turn guarantees resolvability and asymptotic stability once an initial feasible solution is obtained at the start of a maneuver. The feedback part involves off-line design of a feedback control policy based on the uncertainty bounds in the dynamical model of the system. Consequently, this algorithm is robust to system uncertainties that are explicitly accounted for in the design of the feedback portion of the control input. This explicit characterization of the robustness to the uncertainties (which can easily be extended to external disturbances) is particularly desirable in a realtime autonomous control application. Furthermore, the ability to solve for an open-loop trajectory during a maneuver enables model updates (possibly based on real-time information) into the control problem to reduce model uncertainty and improve optimality for the open-loop trajectory. The algorithm has been shown to be robustly stabilizing under state and control constraints with a region of attraction composed of initial states for which solution of the finite-horizon optimal control problem is feasible. This work was done by A. Behçet Açkmeçe and John M. Carson III of Caltech for NASA’s Jet Propulsion Laboratory. Further information is contained in a TSP (see page 1). The software used in this innovation is available for commercial licensing. Please contact Karina Edmonds of the California Institute of Technology at (626) 395-2322. Refer to NPO-42754. A Robustly Stabilizing Model Predictive Control Algorithm The algorithm can be applied to industrial and automotive systems. NASA’s Jet Propulsion Laboratory, Pasadena, California Information Sciences