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Feedback linearization of the Lorenz system: stabilization and tracking control

机译：反馈Lorenz系统的线性化：稳定和跟踪控制

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This paper presents a control study of the Lorenz system by using, feedback linearization. The effects of the state transformation on the dynamics of the Lorenz system are studied first. Then, composite controllers are developed for both stabilization and tracking of the system. The controls are designed to overcome the barrier in controllability imposed by the state transformation. The transition through the manifold defined by such a singularity is achieved by inducing the chaotic response within a boundary layer that contains the singularity. Outside this region, a conventional feedback nonlinear control is applied. In this fashion, the authority of the control is enlarged to the whole state space and the need for high control efforts is substantially mitigated. Tracking problems that involve single and cooperative objectives are studied by using the differential flatness property of the system. A good understanding of the system dynamics proves to be invaluable in the design of better controls. In all numerical examples, the proposed approach led to excellent control performances.
机译：本文介绍了通过使用反馈线性化对Lorenz系统的控制研究。第一次研究了状态转换对洛伦茨系统动态的影响。然后，开发了复合控制器，用于稳定和跟踪系统。该控制旨在克服状态变换施加的可控性的屏障。通过诱导包含奇点的边界层内的混沌响应来实现通过这种奇点限定的歧管的过渡。在该区域之外，应用了传统的反馈非线性控制。以这种方式，控制权的权威被扩大到整个状态空间，并且基本上减轻了对高控制力工作的需求。通过使用系统的差分平坦性研究，研究了涉及单一和合作目标的问题。良好地理解系统动态的理解在更好的控制方面证明是非常宝贵的。在所有数值例子中，所提出的方法导致了优异的控制性能。

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