Finite-Time Adaptive Control of Nonlinear Systems and Its Applications

提出的研究计划将研究一类由常微分方程和微分代数方程描述的非线性系统的有限时间自适应控制问题及其在移动机器人控制中的应用。具体考虑的问题包括有限时间镇定、有限时间跟踪、有限时间干扰衰减、有限时间自适应控制和有限时间容错控制。大多数可用的反馈控制技术导致闭环系统的解在无限的沉降时间内收敛到期望的位置。但从实用角度看，沉降时间越短越好。事实上，大多数现实系统都要求在有限的时间内满足设计需求。因此，尽管有限时间控制问题比传统控制问题更难解决，但在实际应用中却更加重要，近几十年来越来越受到人们的关注。几乎所有的物理系统都包含一定数量的参数。其中一些参数可以测量，而另一些则无法获得。即使对于可测量的参数，有时由于各种原因（如时变特性、温度敏感特性、负载依赖性等），获得精确值也不是一件容易的事情。因此，既要设计控制器来实现控制目标，又要设计自适应律来估计不精确已知甚至未知的参数，这就是自适应控制，具有重要的理论意义和实际意义。自20世纪70年代以来，自适应控制一直受到控制工程领域专家的高度关注。控制理论比它在现实世界中的应用要先进得多。控制理论及其在工程领域的应用还有很大的差距，尤其是非线性控制理论。为了缩小这一差距，本研究计划将研究非线性有限时间自适应控制在移动机器人中的应用。为了使移动机器人在期望的位置执行特定的任务，首先要设计一条合理的路径，使其能够移动到期望的位置，而不会与路径上的其他物体发生碰撞，这就是路径规划。然后设计一个反馈控制器，使移动机器人能够在有限时间内沿着设计的路径运动。因此，移动机器人需要在有限的时间内沿着给定的路径进行有限时间控制。本课题的主要目标是解决非线性ODE/DAE系统的有限时间自适应控制问题，并将有限时间自适应控制理论应用于移动机器人的控制。

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. Almost all physical systems contain a certain number of parameters. Some of these parameters can be measured and others are not accessible. Even for measurable parameters, sometimes it is not an easy task to obtain the exact values for a variety of reasons, such as time-varying properties, temperature-sensitive features, load dependency, and so on. Therefore, it is of both theoretical and practical importance to design both controllers to achieve control objectives and adaptive laws to estimate parameters that may not be precisely known or may even be unknown, which is referred to as adaptive control. Adaptive control has been drawing great attention from experts in the field of control engineering since the 1970s. Control theory is far more advanced than its applications in the real world. There is a large gap between control theory and its applications in the engineering field, especially for nonlinear control theory. In order to reduce this gap, this research program will investigate the applications of nonlinear finite-time adaptive control to mobile robots. In order for a mobile robot to perform certain tasks at a desired location, the first thing to do is to design a reasonable path so that it will be able to move to the desired location without colliding with other objects on the path, which is called path-planning. After that, a feedback controller should be designed so that the mobile robot is able to follow the designed path in a finite time. Therefore, finite-time control is required for a mobile robot to follow a given path within a limited time period. The main objective of this project is to solve some problems of finite-time adaptive control for nonlinear ODE/DAE systems and to apply the finite-time adaptive control theory to control of mobile robots.