Interval Observer based Min-max MPC scheme for LPV Systems with bounded uncertainties

An interval observer (IO) based output feedback robust min-max model predictive control (MPC) framework is first proposed for linear parameter-varying (LPV) systems with bounded model uncertainties, disturbances and noises. It is not easy to estimate accurate states of uncertain systems and the performance of the observer based output feedback control cannot be guaranteed. Instead, interval observer is more suitable for estimating the unmeasurable states of the LPV systems with bounded uncertainties. In this paper, interval observer is established for output feedback robust MPC by properties of positive system and Schur stability criteria. An interval predictor (IP) is constructed from interval observer to predict the future dynamics of MPC algorithm. The Schur stability of the IP is further proved. Interval observer based min-max robust MPC scheme is designed and the controller gain is obtained by solving linear matrix inequalities (LMIs) in optimization problem. Meanwhile, the stability of real system is proved. Finally, a numerical example is presented to verify and demonstrate the effectiveness of the proposed interval observer based robust min-max MPC scheme.