Solving optimal control problems under interval uncertainty using robust model predictive control

Document Type : Research Paper

Authors

1 Mathematics Faculty, University of Sistan and Baluchestan, Zahedan, Iran

2 Faculty of Industry and Mining (Khash), University of Sistan and Baluchestan, Zahedan, Iran

3 Faculty of Electrical and Computer Engineering, University of Sistan and Baluchestan, Zahedan, Iran

4 Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Abstract

In this paper, as a novel control strategy that is implemented online, we use the model predictive control. In natural phenomena, some parameters may have uncertainty in which their exact amount is unknown, but we know that they are in a certain range. In this case, the predictive control formulation can be changed so that the control system becomes resistant to these parameters. In this article, two methods for solving optimal control problems with uncertainty will be proposed using model predictive control. In first one, we introduce the robust control, in which discretize the continuous time dynamic model and apply the predictive control algorithm of the resilient model to a typical system. In the second one, when the range of parameter has a certain uncertainty, it is appropriate that the solutions are in the form of interval values. So, we introduce the interval model predictive control and solve two sub-models for optimal control problems. According to the simulation results, it can be conclude that even though the dynamic of the system has severe uncertainty and the behavior of the system changes randomly between stable and unstable mode, but the predictive controller of the interval optimal control problems is well able to converge the state variables.

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Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 22, Issue 6
November and December 2025
Pages 147-165

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