Chapter 4Design of Fractional-Order Controllers for Nonlinear Chaotic Systems and Some Applications
4.1 Fractional-Order Control for a Novel Chaotic System Without Equilibrium
4.1.1 Problem Statement
In this section, a novel chaotic system will be proposed by only considering the straight-line position 
and the pitch angle 
of the two-wheeled self-balancing robot of Googol Technology. A mathematical model related to the two-wheeled self-balancing robot of Googol Technology was established by Son and Anh [208]. The linear mathematical model for 
and 
of the two-wheeled self-balancing robot of Googol Technology is described in the form of
where 
denotes the pitch torque.
To transform the linear mathematical model into a chaotic system, we consider 
as a nonlinear term , which will be ...
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