输出调节中的新型内模设计及其应用研究

Output regulation is a central feedback control problem. As a necessary component of an effective regulator, the internal model design is crucial for solving the problem. For the problem with unknown or uncertain exosystems, the adaptive internal model approach has been majorly developed in the literature. However, when the plant dynamics are highly complex uncertain nonlinear systems, remarkable technical obstacles may arise in many circumstances due to limits of existing internal model design techniques. Therefore, design of novel nonlinear internal models has been a burning issue for the current development of nonlinear output regulation. In view of this situation, this project aims at developing novel nonlinear internal model design techniques in a constructive fashion, serving the synthesis of nonlinear output regulation problems with unknown exosystems as well as the relevant applications. Firstly, several novel types of nonlinear internal models will be established by shaping certain parameterized nonlinear steady-state generators. Then, the proposed internal models will be applied for solving the output regulation problems. In particular, it enables us to develop systematic design methods to achieve some auxiliary non-adaptive stabilization of the resulting augmented systems. As a major consequence, it leads to a non-adaptive internal model approach. The research of this project can provide novel ideas and systematic methods to resolve nonlinear output regulation with uncertain exosystems. Specifically, it can effectively circumvent the hurdles encountered in the usual adaptive internal model based results due to parameter uncertainties of the exosystems. Hence, it strictly enlarges the application to a much wider range of engineering problems than before.

输出调节是一类核心的综合反馈控制问题，内模设计在其求解过程中起着至关重要的作用，是构成有效调节器的必要组成部分。在外部系统未知或不确定情况下，当前研究主要是利用自适应内模的方法。然而，受此制约，在处理复杂不确定非线性系统时，会面临诸多技术瓶颈。新型非线性内模的构造性设计，已成为一个亟待解决的难题。为此，本项目拟发展新的非线性内模设计思想和方法，并针对性地应用于解决具有未知外部系统的非线性输出调节综合设计及其应用问题。首先，通过提出特定参数化的非线性稳态发生器，获得满足设计约束条件的、构造性的新型非线性内模。其次，运用新型内模，系统地分析和解决相关增广系统的辅助非自适应镇定控制，并最终实现基于非自适应内模方法的输出调节解决方案。本项目研究将为非线性输出调节的求解提供新的思路和系统化的解决方案，有效地突破在外部系统未知情况下应用自适应内模方法所导致的技术瓶颈，拓广该理论的研究及工程应用范围。

本项目聚焦非线性控制系统设计中的内模方法以及相关的内模设计技术问题研究，并应用于几类基础的非线性输出调节问题的可构造性控制器设计问题当中。尤其是针对外部系统未知或存在不确定参数情况下，项目研究能够提供若干可构造性的非线性内模设计方法，进而突破传统自适应内模设计方法带来的复杂性和难以求解的困难。具体地，通过引入参数化的非线性稳态发生器，获得满足设计约束条件的、构造性的非线性内模，进一步对相关的增广系统的辅助非自适应镇定控制进行分析和求解，最终可以实现基于非自适应内模方法的输出调节解决方案。项目研究为非线性输出调节的求解提供了新的系统化的解决方案，有效地突破在外部系统未知情况下应用自适应内模方法所导致技术困难，为拓广该理论研究及工程应用范围提供了新的思路和方法。