https://doi.org/10.1140/epjs/s11734-021-00236-4
Regular Article
Analysis and chaos control of a four-dimensional magnetohydrodynamic model with hyperchaotic solutions
1
Federal Technological University of Paraná, Ponta Grossa, PR, Brazil
2
School of Engineering, São Paulo State University, Bauru, SP, Brazil
3
Faculty of Mechanical Engineering, Lublin University of Technology, Lublin, Poland
4
Institute of Science and Technology, São Paulo State University, Sorocaba, SP, Brazil
Received:
10
March
2021
Accepted:
7
July
2021
Published online:
28
July
2021
In this paper, the dynamical behavior of a four-dimensional magnetohydrodynamic model, consisting of a generalized Lorenz model, is investigated. A nonlinear dynamical analysis is performed using Lyapunov exponents and bifurcation diagrams, focusing on the chaotic and hyperchaotic behaviors associated with the bifurcation parameter 
that couples the equations of fluid displacement to the induced magnetic field. The State-dependent Riccati Equation (SDRE) and the Optimal Linear Feedback Control (OLFC) techniques are considered to design the state feedback control system that stabilizes the system to a previously defined orbit. The performance of the control systems are compared showing that the OLFC presents better results.
Key words: Nonlinear dynamics / SDRE control / OLFC control
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2021
