An off-line NMPC strategy for continuous-time nonlinear systems using an extended modal series method

Abstract

This paper presents a new off-line nonlinear model predictive control (NMPC) approach for continuous-time affine-input nonlinear systems. In this approach, the NMPC-related nonlinear two-point boundary value problem derived from the Pontryagin’s maximum principle is solved by the extended modal series method. The resulting suboptimal control law explicitly depends on the initial conditions and is updated by replacing the initial conditions with the new state measurements in future sampling instants. Therefore, there is no need to repeat the recursive online optimization process in each sampling instant. Since the applicability of NMPC is generally restricted by computational burden of the online optimization, we propose an NMPC scheme, which not only reduces the online computational burden significantly, but also can be applied to fast dynamic systems with short prediction horizons. An efficient algorithm is presented which approximates the order of the modal series such that feasibility of the optimization problem is guaranteed. Closed-loop stability of the proposed NMPC approach is shown using the off-line terminal region calculations suggested in quasi-infinite horizon NMPC scheme. The applicability and effectiveness of the proposed approach are illustrated by two numerical examples.