Development of Synthesis Methods of Robust Nonlinear Control Systems Based on Numerical Optimization

本研究的目的是为鲁棒性分析、非线性系统分析和数值神话提供基础理论，以有效地解决控制问题，旨在回答实际控制问题中对设计工作在不确定性和非线性等条件下并保证控制性能的控制系统的严格要求。研究成果包括增益调度控制器的先进合成方法，基于Rantzer密度函数的稳定性分析推广及其在非线性控制增益合成中的应用，以及鲁棒SDPs的方法，重点是鲁棒SDPs松弛严格性的数值验证

The objective of this research is to provide basic theory for robustness analysis, nonlinear system analysis and numerical mythologies to efficiently solve problems in control, aimed to answer stringent requirements in practical control problems to design control systems that work under such as uncertainties and nonlinearities with guarantee of control performance. The outcomes of this research include advanced synthesis methods of gain-scheduled controllers, generalization of stability analysis by using Rantzer's density functions and its application to synthesis of nonlinear control gains, and methods for robust SDPs focusing on numerical verification of strictness of relaxations of robust SDPs