Analysis and Synthesis of Nonlinear System Based on Multi-model Method

为了克服大多数控制系统设计方法所假定的线性与大多数被控对象普遍存在的非线性之间的矛盾，我们提出了多模型系统的新概念。多模型系统的可镇定性是本文研究的主要内容，首先，我们将多模型系统看作是系统连续体中离散点的集合，这些离散点被描述为围绕标称对象模型的扰动集。这使我们能够利用各种技术的鲁棒稳定。提出了一种基于代数Riccati方程正解的多模型系统镇定器的构造方法。多模型系统的可镇定性可表示为代数Riccati方程解的正性。该条件的直观意义是明确的，并从极点配置的角度考虑了多模型系统的可镇定性。结果表明，稳定化问题归结为求解一组多线性不等式。对于二阶多模型系统，将此多线性不等式化为线性不等式，得到了二阶多模型系统可镇定的充要条件.由于多模型系统的控制与鲁棒镇定密切相关，而鲁棒镇定问题又可以通过H控制策略来解决，因此发展H控制理论具有重要意义.在这个项目中，我们已经建立了一个统一的方法来H控制问题的基础上的新概念的共轭。

In order to overcome the inconsistency between the linearity assumed in most design methods of control systems and the nonlinearity which is common in most plants to be controlled, we propose the new notion of multi-model systems. the stabilizability of multi-model systems is the main concern of this research.First, we regard the multi-model system as a collection of the discrete points in the continuum of systems described as a perturbation set around the nominal plant model. This enables us to utilize various techniques of robust stabilization. We have proposed a method of constructing a stabilizer of a multi-model system based on the positive solution of an algebraic Riccati equation. The stabilizability of multi-model systems can be represented as the positivity of the solution of the algebraic Riccati equation. The intuitive meaning of this condition is clear.The stabilizability of multi-model systems has also been considered from the viewpoint of pole assignment. It has been shown that the stabilization is reduced to solving a set of multi-linear inequalities. For multi-model systems of the second order, this multi-linear inequalities are reduced to linear ones, and we obtain a necessary and sufficient condition of the stabilizability of the second-order multi-model system.Since it turned out that the control of multi-model systems is closely related to robust stabilization, and robust stabilization is solved by H control strategy, it is important to develop H control theory. In this project, we have established a unified approach to H control problem based on the new notion of conjugation.