Robust output feedback predictive controller with adaptive invariant tubes and observer gains
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Robust output feedback predictive controller with adaptive invariant tubes and observer gains Withawin Vilaivannaporn1 · Suthida Boonsith1 · Warangkana Pornputtapitak1 · Pornchai Bumroongsri1 Received: 25 April 2020 / Revised: 31 July 2020 / Accepted: 13 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This work aims to develop a robust output feedback predictive controller that can guarantee the recursive feasibility and the system stability as the invariant tubes and the observer gains can be updated at each sampling time. The recursive feasibility is guaranteed by using the invariant tubes with non-increasing size so the satisfactions of more tightened constraints ensure the satisfactions of less tightened constraints as time proceeds. The system stability is guaranteed by bounding the control error and the estimation error using the invariant tubes that can be updated at each sampling time. The online computational complexity can be reduced as the invariant tubes and the observer gains can be updated at each sampling time. This can be done by computing offline the invariant tubes for the estimation error, the invariant tubes for the control error and the observer gains. The smallest invariant tube containing the estimation error is determined at each sampling time and the corresponding observer gain is chosen as the real-time observer gain. The proposed algorithm can reduce the online computational complexity as compared with the case when the invariant tubes and the observer gains are computed online while the same level of control performance is obtained. In addition, the proposed algorithm can improve the control performance as compared with the case when the invariant tubes and the observer gains are constant. Keywords Predictive controller · Output feedback · Invariant tubes · Observer gains · Robust stability
1 Introduction The disturbances and measurement noises usually exist in the control system so it is important to develop a robust control algorithm for the industrial processes. Model predictive control (MPC) based on tubes has gained considerable attentions due to its ability to handle disturbances [1]. The main idea of this approach is to restrict the effects of disturbances in the invariant tubes. Chisci et al. [2] shows that the robustness against bounded disturbances can be guaranteed by using suitable constraint restrictions for the optimal controller. Langson et al. [3] develops an optimal control problem with a control law that maintains the trajectories inside a tube. In Mayne et al. [4], robust exponential stability is established by employing the initial state as a decision variable. Limon et al. [5] develops a tube MPC scheme that can * Pornchai Bumroongsri [email protected] 1
Department of Chemical Engineering, Faculty of Engineering, Mahidol University, Nakhon Pathom 73170, Thailand
steer the state to the admissible target set. The main assumption of tube MPC is that all state variables are measurable. Some researchers have developed MP
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