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 \(\left( k_{1} \right) \) 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.

在本文中，研究了由广义洛伦兹模型组成的四维磁流体动力学模型的动力学行为。使用李雅普诺夫指数和分岔图进行非线性动力学分析，重点关注与分岔参数\(\left( k_{1} \right) \)相关的混沌和超混沌行为，该参数将流体位移方程与感应磁场耦合场地。状态相关的 Riccati 方程 (SDRE) 和最优线性反馈控制 (OLFC) 技术被认为是设计状态反馈控制系统，将系统稳定到先前定义的轨道。控制系统的性能进行了比较，表明 OLFC 表现出更好的结果。