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提出一种对非线性动力系统周期解进行预测追踪的新型算法．它利用系统周期解的稳态及瞬态信息、反解雅可比矩阵，实现对系统周期解的预测追踪．同时，利用反解得出的雅可比矩阵，还可以得出系统周期解的Ｆｌｏｑｕｅｔ乘子，判别其非线性稳定性．与现有的此类算法相比，新算法在实施时，所需要的信息均可通过对系统周期解的未扰及受扰运动的观测获得，因而具有广泛的适应性．文中以非线性轴承转子系统为例，实现了周期解的预测追踪及非线性稳定性判别，说明了新算法的有效性．
A new algorithm for predictive tracking of periodic solutions of nonlinear dynamical systems is proposed. It uses the steady-state and transient information of the system periodic solution, anti-Jacobian matrix to achieve the predictive tracking of the system periodic solution. At the same time, by using the Jacobian matrix obtained by the anti-solution, the Floquet multiplier of the periodic solution of the system can be obtained and the nonlinear stability can be judged. Compared with the existing algorithms, all the information needed by the new algorithm can be obtained by observing the undisturbed and disturbed motions of the periodic solutions of the system, so it has a wide range of adaptability. Taking the nonlinear bearing rotor system as an example, the predictive tracking of the periodic solution and the identification of nonlinear stability are realized, and the effectiveness of the new algorithm is illustrated.