Constrained model predictive control for positive systems

This article is devoted to the problem of model predictive control (MPC) design for discrete-time and continuous-time positive systems with state and input constraints. The proposed controllers are so designed that the closed-loop constrained systems are positive and stable, meanwhile, linear infini...

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Bibliographic Details
Published in:IET control theory & applications 2019-07, Vol.13 (10), p.1491-1499
Main Authors: Mehrivash, Hamed, Shafiei, Mohammad Hossein
Format: Article
Language:English
Subjects:
closed loop systems
closed‐loop constrained systems
constrained model predictive control
continuous time systems
continuous‐time case
continuous‐time positive system
continuous‐time positive systems
control system
discrete time systems
discrete‐time case
infinite horizon
input constraints
linear infinite horizon cost functions
linear programming
linear systems
minimisation problems
model predictive control design
MPC
predictive control
Research Article
shorter sampling period results
stability
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Summary:This article is devoted to the problem of model predictive control (MPC) design for discrete-time and continuous-time positive systems with state and input constraints. The proposed controllers are so designed that the closed-loop constrained systems are positive and stable, meanwhile, linear infinite horizon cost functions through their upper bounds are minimised. In the discrete-time case, the performance of the control system compared to existing studies is remarkably improved. Moreover, in the continuous-time case, the proposed MPC is such that can be directly applied to the continuous-time positive system without discretisation. The merit of this method is that the sampling interval has nothing to do with the stability of the system, just a shorter sampling period results in better optimality and performance. In addition, by defining a slack variable and accounting it in the minimisation problems, a fast rate of convergence will be obtained. In order to solve the optimisation problem of MPC, linear programming (LP) is used which needs to be solved at each iteration. All conditions are derived in the form of LP. Finally, to demonstrate the effectiveness of the proposed method, comparisons with the existing studies are presented through practical and numerical examples.
ISSN:1751-8644
1751-8652
1751-8652
DOI:10.1049/iet-cta.2018.5755