Finite-Time Adaptive Control of Nonlinear Systems and Its Applications

本研究计画将探讨一类由常微分方程与微分代数方程所描述之非线性系统之有限时间自适应控制问题及其在移动的机器人控制上的应用。特别是，考虑的问题包括有限时间稳定，有限时间跟踪，有限时间干扰衰减，有限时间自适应控制，有限时间容错控制。大多数可用的反馈控制技术导致闭环系统的解决方案收敛到所需的位置在一个无限的建立时间。但是，从实际的角度来看，建立时间越短越好。事实上，大多数真实的系统都要求在有限的时间内满足设计要求。因此，尽管有限时间控制问题比传统的控制问题更难解决，但它们在实际中更重要，近几十年来受到越来越多的关注。

The proposed research program will investigate the finite-time adaptive control problem for a class of nonlinear systems described by both ordinary differential equations and differential-algebraic equations and its applications to control of mobile robots. In particular, the problems in consideration include finite-time stabilization, finite-time tracking, finite-time disturbance attenuation, finite-time adaptive control, and finite-time fault-tolerant control. Most of the available techniques for feedback control lead to closed-loop systems with solutions converging to the desired location within an infinite settling time. However, from a practical point of view, the shorter the settling time, the better. As a matter of fact, most of real systems require that the design requirements should be satisfied in a finite time. Therefore, even though finite-time control problems are much harder to be solved than traditional control problems, they are more important practically and have attracted more and more attention in recent decades.