非线性ODE-PDE串接系统的输入-状态镇定与逆最优控制

随着科学实践和理论研究的深入，执行器动态由偏微分方程（PDE）描述，受控对象由常微分方程（ODE）描述的串接系统正在成为控制理论与工程研究的热点之一。本项目应用无穷维Backstepping变换和Lyapunov方法，系统深入地研究非线性ODE与交通PDE、 非线性一阶双曲PDE、波PDE串接系统的输入-状态镇定（ISS）与逆最优控制。研究内容包括：ISS与逆最优控制的正则性条件；控制律设计及鲁棒性分析；串接系统的跟踪控制；及利用石油钻井系统等实际模型的控制仿真。研究的目标为：得到ISS与逆最优控制的正则性条件，然后给出控制律设计和鲁棒性分析。进而，得到与这些控制律设计相对应的逆最优泛函，并将结果推广到非线性ODE-PDE串接系统的跟踪设计中，结合实际模型验证所获得成果的正确性和有效性。从而丰富和发展非线性ODE-PDE串接系统设计的控制理论。

With the development of scientific practice and theoretical research, the cascade system of actuator dynamics described by partial differential equation (PDE) and controlled object described by ordinary differential equation (ODE) becomes one of the research hotspots of control theory and control engineering. Based on infinite-dimensional backstepping transformations and Lyapunov method, input-to-state stabilization (ISS) and inverse optimal control for the cascade systems of nonlinear ODE and transport PDE; nonlinear first order hyperbolic PDE; wave PDE are systematically and profoundly investigated in this project. The research contains: the regularity conditions of ISS and inverse optimal control; control laws design and robustness analyses; tracking controls of the cascade systems; control simulations of petroleum drilling system and so on practical models. The research objects are: to get the regularity conditions of ISS and inverse optimal control; to achieve control laws and robustness analyses; to obtain the inverse optimal functionals corresponding to the control laws; to extend the results to the tracking of nonlinear ODE-PDE cascade systems; to verify the correctness and effectiveness of the obtained results by the practical models. The research of this project will enrich and develop control theory of nonlinear ODE-PDE cascade systems.