In this work, dynamical analysis and synchronization control for a four-dimensional Lorenz system are presented. Numerical simulations have shown that for certain parameters, the system has chaotic or recurrent behavior. The chaotic behavior is analyzed by means of phase portraits, bifurcation diagram, fast Fourier transform, and Lyapunov exponents calculation. The synchronization control strategy involves the application of two control signals: a nonlinear feedforward control to maintain the synchronization and a state feedback control to synchronize with the system. Two control strategies are presented for the feedback control project, one considering the State-Dependent Riccati Equation (SDRE) accounting for a nonlinear state matrix and a second one accounting for the Optimal Linear Feedback Control (OLFC), whose state matrix is linear. In addition, the control robustness is investigated through analyzing parametric errors.

在这项工作中，提出了四维洛伦兹系统的动力学分析和同步控制。数值模拟表明，对于某些参数，系统具有混沌或重复行为。通过相图、分岔图、快速傅立叶变换和李雅普诺夫指数计算来分析混沌行为。同步控制策略涉及两个控制信号的应用：保持同步的非线性前馈控制和与系统同步的状态反馈控制。为反馈控制项目提出了两种控制策略，一种考虑状态相关的 Riccati 方程 (SDRE)，考虑非线性状态矩阵，另一种考虑最佳线性反馈控制 (OLFC)，其状态矩阵是线性的。