A new switched off-line NMPC approach for nonlinear systems with a switching performance index using an extended modal series method

AssumptionRemarkDefinitionCorollaryTheoremAlgorithmExampleProof This paper presents a new switched nonlinear model predictive control (NMPC) approach for continuous-time affine-input nonlinear systems with a number of different cost functions where switching occurs between them in order to improve the performance. In this approach, the NMPC-related nonlinear two-point boundary value problem derived from Pontryagin's maximum principle is solved by the extended modal series method. The resulting suboptimal control law as to each of the cost functions is feasible and has an explicit form. In order to guarantee closed-loop stability, certain assumptions are considered in the NMPC literature and in the switched systems literature, such as finding an invariant terminal region and a feasible solution for the NMPC and considering a certain average dwell time for switching signals. In this paper, we consider switching among different cost functions using the average dwell-time approach. Since, in our proposed method, the NMPC problem solution obtained by the extended modal series method is feasible and since the invariance condition for the terminal region is satisfied, the common assumptions for the stability of the switched NMPC can be established. Furthermore, we show that this method guarantees the stability of the entire closed-loop system in the presence of unknown persistent disturbances. The applicability and effectiveness of the proposed approach are illustrated by two numerical examples.