Construction of a unified approach from modeling to control-system design of nonlinear systems

本研究的最终目的是建立一个具有理论背景的非线性系统从建模、辨识到控制系统设计的统一方法，所得结果如下：非线性系统的建模：研究了将一个非线性系统建模为多个工作点的一组线性化系统的建模方法的可行性。识别方法：作为基于上述建模方法的识别方法，提出了线性模型集识别（LM-sets ID）方法，该方法是工作点移位下非线性装置的识别方法。将此方法应用于非线性装置，我们可以从输入-输出数据中将装置识别为有限数量的线性模型集（lm集）的集合，每个线性模型集都包含装置在每个工作点的精确线性化模型。控制系统的设计与分析：在上述LM-sets ID方法的基础上，导出了非线性对象的增益调度控制系统的设计方法。理论分析保证了调度控制系统状态的收敛性。通过数值仿真验证了上述方法的有效性。

The final purpose of this research is to construct a unified approach from modeling and identification to control-system design of nonlinear systems with theoretical background, and the followings are the obtained results.1. Modeling of nonlinear systems : The feasibility of the modeling method was investigated, by which a nonlinear system is modeled as a set of linearized systems at plural operating points.2. Identification method: As an identification method based on the above modeling method, the linear-model-sets identification (LM-sets ID) method was proposed, which was the identification method for nonlinear plants under shifts of operating points. Applying this method to a nonlinear plant, we can identify the plant from input-output data as a collection of a finite number of linear-model-sets (LM-sets), each of which includes the exact linearized model of the plant at each operating point.3. Control-system design and analysis : Design method of gain scheduled control systems was derived for nonlinear plants based on the above LM-sets ID method. A theoretical analysis was achieved which ensures the convergence of the state of the scheduled control system.4. A numerical simulation was given to prove the effectiveness of the above methods.