Volume 31, Issue 18 pp. 9358-9371
RESEARCH ARTICLE

Control of input-affine nonlinear systems via linear programming

Farshad Merrikh-Bayat

Corresponding Author

Farshad Merrikh-Bayat

Department of Electrical and Computer Engineering, University of Zanjan, Zanjan, Iran

Correspondence Farshad Merrikh-Bayat, Department of Electrical and Computer Engineering, University of Zanjan, Zanjan, Iran.

Email: [email protected]

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Mehdi Afshar

Mehdi Afshar

Department of Mathematics and Statistics, Zanjan Branch, Islamic Azad University, Zanjan, Iran

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First published: 07 September 2021

Abstract

An effective and user-friendly method to control a large portion of input-affine nonlinear systems is proposed. This method works based on transforming the nonlinear control problem to a linear programming (LP) in unknown controls, the state variables of plant, and possibly the constraints imposed on the controls and state variables. The solution of this LP provides the control to be applied to the plant. The main advantages of the proposed method are: simplicity of applying to multi-input multi-output systems, taking into account the actuator saturation and constraints on states, and robustness to uncertainties in the model. Two numerical examples are presented to verify the effectiveness of the proposed method. These are output voltage regulation of a two-input two-output dc–dc boost converter with actuator saturation and position control of a magnetic levitation system with a constraint on the speed of ball.

CONFLICT OF INTEREST

The authors declare no potential conflict of interests.

DATA AVAILABILITY STATEMENT.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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