非线性切换系统的输出反馈控制研究

As a typical class of hybrid systems, switched systems are of great significance in both theory development and engineering applications. By adding a power integrator technique, homogenous domination approach, dynamic gain technique and Lyapunov stability theory, this project aims to study a variety of control problems for switched nonlinear systems. According to Lyapunov stability theory, the output feedback control problem will be investigated for switched nonlinear systems under different switching powers and unknown control directions. A series of new coordinate transformations are introduced in order to increase the freedom degree of the design parameters. Nussbaum-type functions are used to deal with the unknown control directions. Output feedback controllers and the corresponding switching law are designed by adding a power integrator method such that the states of the closed-loop system converge to the equilibrium point. Then, based on the dynamic gain technique, a homogeneous observer is constructed. Adaptive output feedback controllers are designed to achieve stabilization and tracking performance for switched nonlinear systems with unknown output function, unknown growth rate and input saturation. On the basis of aforementioned works, the problem of quantized feedback tracking control of switched nonlinear systems will be further studied by combining the average dwell time approach with the sector bound method. In summary, the research results of this project will further enrich the theory of switched nonlinear systems.

切换系统作为一类典型的混杂系统，有着重要的理论研究价值和广泛的工程应用背景。本项目将利用增加幂积分法、齐次占优方法、动态增益技术和Lyapunov稳定性理论，研究非线性切换系统若干控制问题。根据Lyapunov稳定性理论，研究不同幂次切换和未知控制方向情形下非线性切换系统的输出反馈控制问题。通过引入新的坐标变换以增加设计参数的自由度，运用Nussbaum型函数处理未知控制方向；利用增加幂积分法设计输出反馈控制器和相应的切换律，使得闭环系统的状态渐近收敛到平衡点。基于动态增益技术构造齐次观测器，借助自适应控制技术设计未知输出函数和增长率未知以及输入饱和等情形下的自适应输出反馈控制器，实现非线性切换系统的镇定和跟踪。在此基础上，结合平均驻留时间方法和扇形界方法，研究非线性切换系统的量化反馈跟踪控制问题。本项目研究成果将进一步丰富非线性切换系统控制理论。

切换系统作为一类典型的混杂系统，有着重要的理论研究意义和实际应用价值。本项目研究内容如下：（1）根据Lyapunov稳定性理论，研究了不同幂次切换和未知控制方向情形下非线性切换系统的输出反馈控制问题。利用增加幂积分法设计输出反馈控制器和相应的切换律，使得闭环系统的状态渐近收敛到平衡点。（2）借助自适应控制技术设计未知输出函数和增长率未知以及输入饱和等情形下的自适应输出反馈控制器，实现了非线性切换系统的镇定和跟踪。（3）结合平均驻留时间方法和扇形界方法，研究了非线性切换系统的量化反馈跟踪控制问题。综上所述，本项目研究成果丰富和完善了非线性切换系统控制理论，并为实际工程应用提供了理论依据。在本项目的资助下，在国内外学术期刊和会议上发表论文48篇，其中SCI收录40篇；获国家发明专利授权4件；培养博士生毕业2名，硕士生毕业3名。