A Computationally Efficient Robust Tube-Based MPC for Tracking of Linear Systems
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RESEARCH PAPER
A Computationally Efficient Robust Tube-Based MPC for Tracking of Linear Systems Y. Abbasi1 • H. R. Momeni1
•
A. Ramezani1
Received: 12 December 2019 / Accepted: 9 August 2020 Shiraz University 2020
Abstract This paper addresses a computationally efficient robust tube-based model predictive control (RTBMPC) strategy of linear systems in the presence of bounded disturbance. In the RTBMPC strategy, a nominal system is introduced by ignoring the disturbances of uncertain system, and then the uncertain system will be controlled in a robust manner through its nominal system as well as an additional feedback term which rejects a bounded additive disturbance. In this paper, the tracking problem is converted into the regulation problem by introducing an extra system called regulation nominal system that its constraints are translated from tracking into regulation. It leads to a reduction in complexity of the objective function and simplification of driving the stability theory. On the other hand, RTBMPC strategy solves optimization problem for nominal system which ignores the disturbances. Since in the absence of disturbances, the state measured at the following sample will be the same as the one predicted by model, a variable prediction horizon is suggested to reduce the computational burden. In addition, new constraints are introduced to prove the recursive feasibility, local and asymptotic stability. The constrained sampled double integrator is presented to illustrate the effectiveness of the proposed RTBMPC. Keywords Robust tube-based MPC Disturbance invariant set Region of attraction Linear systems
1 Introduction Model predictive control (MPC) is a powerful optimal control strategy for its ability to deal with constraints on states and inputs and also to take into account a certain performance criterion within the control design. It is an advanced method to control a broad range of process (Sardashti et al. 2019). The MPC is utilized to calculate the optimal control input sequence by minimizing an objective function subject to constraints (Borrelli et al. 2011). One of the main concerns about MPC is its robustness to model uncertainty and noise. The robustness of MPC means that the stability is maintained and the performance specifications are met for a specified range of model variations and a class of noise signals. Several methods are proposed to
& H. R. Momeni [email protected] http://www.modares.ac.ir/*momeni_h 1
Automation Laboratory, Electrical Engineering Department, Tarbiat Modares University, P.O. Box 14115-194, Tehran, Iran
achieve robustness (Scokaert and Rawlings 1995). One of the control strategies to deal with uncertainty is min–max MPC which proposed by Campo and Morari (1987). Lazar et al. (2008) and Kerrigan and Maciejowski (2004) utilize min–max MPC to minimize control efforts and maximize disturbance sequences by solving an open-loop control problem. Liu et al. (2018) propose a min–max MPC framework for constrained d
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