Abstract

This paper addresses the guaranteed cost sampled-data controller synthesis and analysis problems with application to nonlinear chaotic systems. A linear parameter-varying (LPV) model is utilized to represent the nonlinear behaviour of the chaotic system while the gap between the measured and real parameters of the controller and plant are considered as bounded uncertainties. Using the LPV model coupled with the uncertainties, a modified parameter-dependent Lyapunov functional method is utilized and a sampled-data controller is developed that locally asymptotically stabilizes the nonlinear system with guaranteed predefined cost function upper bound. Moreover, employing the cost function upper bound minimization, a suboptimal sampled-data LPV controller is proposed. The central contribution of this work is to present a novel LMI-based formulation with the less conservative results, and thereby, an LMI-based LPV suboptimal sampled-data controller synthesis procedure is developed for nonlinear chaotic systems. The proposed procedure is readily solved by the aid of available off-the-shelf convex optimization techniques. Finally, the proposed sampled-data LPV controller is applied to the well-known chaotic Lorenz and Rossler systems, and the results verify the effectiveness and less conservativeness of the proposed method compared to some state-of-the-art techniques.

中文翻译：

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保证成本的非线性采样数据控制：在一类混沌系统中的应用

摘要

本文讨论了保证成本的采样数据控制器综合和分析问题，并将其应用于非线性混沌系统。利用线性参数变化（LPV）模型来表示混沌系统的非线性行为，而将控制器和设备的实测参数与实际参数之间的差距视为有界不确定性。通过将LPV模型与不确定性结合使用，使用了一种改进的依赖于参数的Lyapunov函数方法，并开发了一种采样数据控制器，该控制器局部渐近地稳定了非线性系统，并保证了预定的成本函数上限。此外，利用代价函数上限最小化，提出了次优采样数据LPV控制器。这项工作的主要贡献是提出了一种基于LMI的新型公式，其结果较为保守，因此，针对非线性混沌系统，开发了基于LMI的LPV次优采样数据控制器合成程序。借助现有的凸优化技术可以轻松解决所提出的过程。最后，将所提出的采样数据LPV控制器应用于著名的混沌Lorenz和Rossler系统，与某些最新技术相比，结果证明了所提出方法的有效性和保守性。借助现有的凸优化技术可以轻松解决所提出的过程。最后，将所提出的采样数据LPV控制器应用于著名的混沌Lorenz和Rossler系统，与某些最新技术相比，结果证明了所提出方法的有效性和保守性。借助现有的凸优化技术可以轻松解决所提出的过程。最后，将所提出的采样数据LPV控制器应用于著名的混沌Lorenz和Rossler系统，与某些最新技术相比，结果证明了所提出方法的有效性和保守性。