# Optimal Control of Two-Wheeled Self-Balancing Robot with Interval Uncertainties Using Chebyshev Inclusion Method

• Navid Razmjooy Department of Electrical Engineering, University of Tafresh, Tafresh, Iran. http://orcid.org/0000-0002-0102-1482
• Mehdi Ramezani Department of Mathematics, University of Tafresh, Tafresh, Iran.
Keywords: Optimal control, interval analysis, LQR, Chebyshev inclusion method, Monte Carlo, Two-Wheeled Self-Balancing Robot.

### Abstract

Since two-wheeled and self-balancing robot has a complicated and non-linear structure, its model has some uncertainties. These uncertainties cause that the system has an incorrect solution if while using the classic methods for controlling of it. In this paper, a new method based on interval analysis is proposed for modeling the optimal control of the two-wheeled and self-balancing robot with interval uncertain parameters which requires only lower and upper bounds of uncertain parameters, with no needing to know about probability distributions. Because the system has uncertainties in it, controllability is first analyzed based on interval arithmetic. Afterwards, LQR based method based on Pontryagin principle is utilized to solve the problem. Finally, by solving the interval Ricatti equations, the confidence interval for feedback controller has been achieved.  Final results are compared with Monte Carlo method and the results demonstrate the effectiveness of the proposed method.

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Published
2018-01-01
How to Cite
Razmjooy, N., & Ramezani, M. (2018). Optimal Control of Two-Wheeled Self-Balancing Robot with Interval Uncertainties Using Chebyshev Inclusion Method. Majlesi Journal of Electrical Engineering, 12(1), 13-21. Retrieved from http://mjee.iaumajlesi.ac.ir/index/index.php/ee/article/view/2500
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Articles