Design of adaptive model predictive control for a class of uncertain non-linear dynamic systems: stability, convergence, and robustness analysis

Aside from relying on the robustness of the model predictive control (MPC) against model uncertainties, tracking performance degradation in the transient time is an inevitable challenge which is the main motivation of the adaptive MPC (AMPC). To that aim, in this study, a fast online identification scheme is suggested to identify a suitable linear state-space model used in the control algorithm. Then, the authors prove the convergence of the identification error sequence using Lyapunov candidate function in the time domain and also, in the frequency domain (graph topology) point of view. Also, due to the dependency of the convergence error on the initial selection of the identification model, the authors introduce a stability and convergence ball as a function of generalised stability margin and the v-gap criteria. Then, the stability and feasibility of the proposed AMPC is guaranteed when using the identified linear model at each sampling time. Moreover, the identification error convergence applies a constraint on the MPC in which, with a suitable selection of the update rate, MPC cost function is been relaxed from the constraint. In the simulations, the authors consider two examples of highly non-linear dynamic systems. In both cases the proposed control strategy gives satisfactory conclusions.