Sampled-data estimation and control of nonlinear plants

该提案涉及多速率非线性控制系统设计和非线性设备的状态估计，特别关注通信容量有限的系统。更具体地说，我们将考虑以下问题：非线性观察者设计和相关的过滤问题：观察者理论是系统论中的经典问题，在各个领域都有应用。近年来，我们开发了非线性 Lipschitz 系统滤波器设计的综合理论。我们将重点关注这一领域工作的扩展，并研究以下问题：（i）网络上非线性 Lipschitz 系统的非线性观测器和滤波器，以及（ii）单侧 Lipschitz 系统的观测器。第一个问题将我们的理论扩展到通过容量有限的通信通道接收信息的系统，这是系统文献中非常感兴趣的问题。第二个是对一类新系统的重要扩展，它概括了 Lipschitz 系统并呈现出重要的优点。多速率采样数据控制设计：过去几年出现了非线性采样数据控制系统理论。我们通过提出使用多速率采样数据控制器对这一理论做出了贡献，并表明多速率系统比单速率系统具有优势。我们的大部分工作都集中在多速率系统的稳定性上。在本提案中，我们将重点关注多速率采样数据控制设计和相关的网络问题。更具体地说，我们将重点关注（i）将稳定性结果扩展到网络情况，以及（ii）基于（a）（基于李亚普诺夫）构造方法和（b）H-无穷综合来制定非线性多速率设计的一般理论。

This proposal is concerned with multirate nonlinear control systems design and state estimation of nonlinear plants with special attention to systems subject to limited communication capacity. More specifically, we will consider the following problems:Nonlinear Observer Design and associated filtering problems: Observer theory is a classical problem in system theory that finds application in various areas. In recent years we have developed a comprehensive theory of filter design for nonlinear Lipschitz systems. We will focus on extensions of our work in this area and study the following problems: (i) Nonlinear observers and filters for nonlinear Lipschitz systems over networks, and (ii) observers for one-sided Lipschitz systems. The first problem extends our theory to systems where information is received through a communication channel with limited capacity, a problem of great interest in the systems literature. The second is an important extension to a new class of systems that generalizes Lipschitz systems and presents important advantages.Multirate Sampled-Data Control Design: The past few years have seen the emergence of the theory of nonlinear sampled-data control systems. We have contributed to this theory by proposing the use of multirate sampled-data controller and showed that multirate systems have advantages over their single-rate counterparts. Most of our work has focussed on stability of multirate systems. In this proposal, we will focus on multirate sampled-data control design and associated network problems. More specifically, we will focus on (i) the extension of stability results to the network case, and (ii) the formulation of a general theory of nonlinear multirate design based on (a) (Lyapunov-based) constructive methods, and (b) H-infinity synthesis.