Nonlinear/Switching Control Design for Constrained Control Systems with Application to Magnetic Suspension

提案编号0621651PI：HU智能优点：拟议的工作旨在探索在控制能力和资源有限的情况下控制系统的最佳性能。非二次Lyapunov函数将被发展并应用于非线性反馈律的构造，可能具有切换和混合结构。与线性控制器相比，期望非线性控制律能够综合各种约束，更有效地利用有限的资源。在输入输出约束条件下，以稳定域、鲁棒性和干扰抑制等性能指标为优化目标，构造了非线性控制器。为了弥合理论和实践之间的差距，本工作强调了Lyapunov方法的可实现性，并将设计问题转化为数值可处理的线性/双线性矩阵不等式。更广泛的影响：约束在控制系统中无处不在。所有执行器的容量都是有限的，所有物理量都是有界的。磁悬浮系统是具有严格约束的典型例子。从人工心脏泵到磁悬浮列车，它们已经被用于各种工程系统。该项目的成果将造福于社会，为开发高性能、低功耗、经济和紧凑的器件提供方法。计算软件将与已发表的文章一起提供，以促进结果的应用，并刺激非线性控制设计方法的发展。将建造一个嵌入式磁悬浮系统，用于研究和教育目的。女性和少数民族学生将积极参与该项目。与当地产业伙伴建立合作关系，促进研究成果的应用。

Prop No. 0621651PI: HuIntellectual Merits: The proposed work aims to explore the best performances of control systems with limited control capacity and resources. Non-quadratic Lyapunov functions will be developed and applied to the construction of nonlinear feedback laws, possibly with switchingand hybrid structures. It is expected that nonlinear control laws are able to incorporate various constraints and utilize the limited resources more effectively than linear controllers. The nonlinear controllers will be constructed for the optimization of various performances, including stability region, robustness and disturbance rejection, under input and output constraints. To bridge the gap between theory and practice, this work emphasizes the realizablility of the Lyapunov approach and the design problems will be formulated into numerically tractable linear/bilinear matrix inequalities. Broader Impact: Constraints are ubiquitous in control systems. All actuators have limited capacity and all physical quantities are bounded. Magnetic suspension systems are typical examples with severe constraints. They have been utilized in a variety of engineering systems ranging from artificial heart pumps to maglev trains. The outcome of the project will benefit the society with methodologies for the development of high performance, low power, economical and compact devices. Computational software will be made available along with published articles to promote the application of the results and to stimulate the development of nonlinear control design methods. An embedded magnetic suspension system will be constructed for both research and educational purposes. Female and minority students will be actively engaged in the project. Collaboration with local industrial partners will be established to promote the application of research results.