Application of ADMM to robust model predictive control problems for the turbofan aero-engine with external disturbances

Min Wang; Jiao Teng; Lei Wang; Junmei Wu; Min Wang; Jiao Teng; Lei Wang; Junmei Wu

doi:10.3934/math.2022601

AIMS Mathematics

2022, Volume 7, Issue 6: 10759-10777. doi: 10.3934/math.2022601

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Application of ADMM to robust model predictive control problems for the turbofan aero-engine with external disturbances

1.
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
2.
Key Laboratory of Intelligent Control and Optimization for Industrial Equipment, Ministry of Education, Dalian University of Technology, Dalian 116024, China
3.
Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province, Dalian University of Technology, Dalian 116024, China
4.
School of Science, Shihezi University, Shihezi 832003, China

Received: 11 November 2021 Revised: 07 March 2022 Accepted: 10 March 2022 Published: 31 March 2022
MSC : 37J45, 49J40, 90C25, 90C47, 93C05

In this paper, we investigate a class of optimal control problems for turbofan aero-engines considering external disturbances. The alternating direction method of multipliers (ADMM) is embedded in the framework of robust model predictive control (RMPC), which is not only able to reach a predetermined value of the engine fan speed, but is also developed to maintain the robustness of the engine control system. First, to consider the optimal control strategy for the worst-case scenario, this optimal control problem is formulated as a minimum-maximum convex optimization problem with constraints. Second, through a transformation technique, the problem can be equivalently described by a variational inequality, which is then transformed into a quadratic programming (QP) problem using a proximal point algorithm (PPA). Finally, the ADMM algorithm is used to solve a series of optimization subproblems based on the structural characteristics of the model. Computational examples illustrate the solution efficiency and robustness of the improved algorithm (RMPC-ADMM).
- turbofan aero-engine,
- robust model predictive control,
- alternating direction method of multipliers,
- proximal point algorithm,
- robustness
Citation: Min Wang, Jiao Teng, Lei Wang, Junmei Wu. Application of ADMM to robust model predictive control problems for the turbofan aero-engine with external disturbances[J]. AIMS Mathematics, 2022, 7(6): 10759-10777. doi: 10.3934/math.2022601

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Abstract

In this paper, we investigate a class of optimal control problems for turbofan aero-engines considering external disturbances. The alternating direction method of multipliers (ADMM) is embedded in the framework of robust model predictive control (RMPC), which is not only able to reach a predetermined value of the engine fan speed, but is also developed to maintain the robustness of the engine control system. First, to consider the optimal control strategy for the worst-case scenario, this optimal control problem is formulated as a minimum-maximum convex optimization problem with constraints. Second, through a transformation technique, the problem can be equivalently described by a variational inequality, which is then transformed into a quadratic programming (QP) problem using a proximal point algorithm (PPA). Finally, the ADMM algorithm is used to solve a series of optimization subproblems based on the structural characteristics of the model. Computational examples illustrate the solution efficiency and robustness of the improved algorithm (RMPC-ADMM).

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