Robustly stable adaptive horizon nonlinear model predictive control

Abstract

We present a new method for adaptively updating nonlinear model predictive control (NMPC) horizon lengths online via nonlinear programming (NLP) sensitivity calculations. This approach depends on approximation of the infinite horizon problem via selection of terminal conditions, and therefore calculation of non-conservative terminal conditions is key. For this, we also present a new method for calculating terminal regions and costs based on the quasi-infinite horizon framework that extends to large-scale nonlinear systems. This is accomplished via bounds found through simulations under linear quadratic regulator (LQR) control. We show that the resulting controller is Input-to-State practically Stable (ISpS) with a stability constant that depends on the level of nonlinearity in the terminal region. Finally, we demonstrate this approach on a quad-tank system and a large-scale distillation application. Simulation results reveal that the proposed approach is able to achieve significant reduction in average computation time without much loss in the performance with reference to fixed horizon NMPC.