Two alternate approaches for characterization of the terminal region for continuous time quasi-infinite horizon NMPC

In this work, two alternate approaches are developed for characterization of the terminal region within the nominal stability framework developed by Chen and Allgower [3]. The proposed approaches directly make use of the weighting matrices in the NMPC cost function as a basis for choosing the tuning parameters required to characterize the terminal set. In the first approach, a quadratic regulator (LQR) is designed in the terminal region. It is shown that the solution of the associated algebraic Riccati equation can be directly used for the characterization of the terminal set. The second approach works with any arbitrary stabilizing linear state feedback controller designed in the terminal set and this feature provides additional flexibility to characterize the terminal set. The efficacy of the proposed approaches is demonstrated using the benchmark quadruple tank system example from the literature. The simulation studies reveal that the sizes of the terminal sets obtained using the proposed approaches are significantly higher than the size of the terminal region obtained using the approach given by Chen and Allgower [3].