RESEARCH INITIATION AWARD: Nonlinear Control Tools and Applications

[9309523] Teel非线性控制领域不断出现令人兴奋的突破，但这些发展往往很难进入实际实施的领域。本研究计划的目的是阐述非线性控制的理论力量，同时为非线性控制工具在工程应用中的使用提供更坚实的基础。前者将通过对固有非线性控制系统和控制解的进一步研究来完成。后者将通过同时重视开发鲁棒和高效的算法来实现。这项研究将包括对时变反馈、饱和、滞后、死区和次线性反馈的进一步研究。以前关于饱和函数的工作已经证明，对于全局稳定输入受幅度约束的临界不稳定线性系统，以及稳定具有挑战性的非线性系统，都是非常富有成效的。在非完整系统稳定的时变反馈研究方面也取得了重要进展。这一次，重点将放在鲁棒性和实用性，通过关注输出反馈解决方案，并允许不确定性和未建模的动态。性能也将得到重视，在此阶段采用计算机模拟来评估设计算法。＊＊＊

9309523 Teel The field of nonlinear control continues to see exciting breakthroughs yet such developments often have a difficult time finding their way into the realm of practical implementation. The objective of this research program is to elaborate on the theoretical power of nonlinear control while at the same time providing a more solid foundation for the use of nonlinear control tools in engineering applications. The former will be accomplished by furthering results on inherently nonlinear control systems and control solutions. The latter will be achieved by concurrently putting a premium on developing algorithms that are robust and efficient. This research will include further investigation employing time- varying feedback, saturation, hysteresis, dead-zones and sublinear feedback. Previous work with saturation functions has already proved very fruitful for globally stabilizing critically unstable linear systems with inputs subject to magnitude constraints, as well as for stabilizing challenging nonlinear systems. Important progress has also been made in the development of time-varying feedback for the stabilization of nonholonomic systems. This time the emphasis will be placed in robustness and practicality by focusing on output feedback solutions and by allowing for uncertainty and unmodeled dynamics. A premium will also be placed on performance, employing computer simulation at this stage to evaluate the design algorithms. ***