Navid Razmjooy - Department of Electrical and Control Engineering, Tafresh University, Tafresh, Iran
Roujin Mousavifard - Department of Mechanical Engineering, Amirkabir University of Technology
Mohammad Abolghasemzadeh - Department of Mechanical Engineering, Amirkabir University of Technology
Youness Alizadeh - Department of Mechanical Engineering, Amirkabir University of Technology

Since the main structure of a self-balancing robot is nonlinear and complicated, it has always some uncertainties in it. Using ordinary optimal control approaches for solving these kinds of problems make an incorrect solution for that. In this research, a newtechnique is proposed to solve the optimal control of a self-balancing robot in the presence of interval uncertainties. The proposed method is constructed with an interval extension of the second kind Chebyshev polynomials. Because of the system uncertainties, the controllability of the system is first analyzed. Afterward, an interval based version of the linear quadratic regulator (LQR) is introduced to solve the interval Ricatti equations and to obtain proper confidence interval. Final results are compared with Monte Carlo method and the results demonstrate the effectiveness of the proposed method.

self-balancing robot, LQR, interval analysis, second kind Chebyshev polynomials, Monte Carlo