广义哈密顿控制系统的光滑状态反馈和动力状态反馈

Smooth State Feedback and Dynamic State Feedback of Generalized Hamiltonian Control Systems

研究了受控耗散Hamilton系统的全局渐近稳定性问题。其研究方法是基于非仿射的耗散系统理论以及有界状态反馈的平衡和技巧。利用此方法,列出了一种受控耗散Hamilton系统的光滑状态反馈和两种动力状态反馈,并给出它们的具体表达式,获得光滑状态稳定的一个充分条件和动力状态反馈稳定的两个充分条件。这些状态反馈有易于控制、灵活等特点,而且光滑状态反馈还可以任意小。该文提出的光滑状态反馈和动力状态反馈可以明确地构造出来,在系统的镇定及相关控制问题中起重要作用。最后列举了一个动力状态反馈稳定的应用例子来说明此结果的可行性。

In this paper, we investigate the problem of global asymptotic stability of controlled dissipative Hamiltonian systems. Our methods are based on the development of non -affine passive systematic theory, the idea of feedback equivalence and the technique of bounded state feedback. With the approaches proposed in this paper, we show a sort of smooth state feedback and two dynamic state feedbacks as well as their explicit formulae. We, furthermore, obtain one sufficient condition for smooth state feedback stability and two sufficient conditions for dynamic state feedback stability. The characteristics of these state feedbacks are feasible and easy to control The smooth state feedback can be arbitrarily small. The smooth state feedback and dynamic state feedback can be constructed explicitly and play an important role in the investigation of the stability of systematic control. At last, as an application, an example of dynamic state feedback stability is employed to illustrate the feasible of our results.