Finite-Time Adaptive Control of Nonlinear Systems and Its Applications

非线性系统的有限时间自适应控制及其应用

• 批准号: RGPIN-2017-05367
• 负责人: Liu, Xiaoping
• 金额: $ 1.6万
• 依托单位: Lakehead University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=678687
• 关键词: Finite; Time; Adaptive; Control; Nonlinear

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.

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，并且在最近几十年中引起了越来越多的关注。 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，而另一些参数则无法获得。即使对于可测参数，由于时变特性、温度敏感特性、负载依赖性等原因，有时也不容易得到精确值，因此，设计控制器以实现控制目标，设计自适应律以估计可能不精确或未知的参数，具有重要的理论和实际意义.这被称为自适应控制。自70年代以来，自适应控制一直受到控制工程领域专家的极大关注。*** 控制理论比它在真实的世界中的应用要先进得多。控制理论与其在工程领域的应用之间存在着很大的差距，特别是非线性控制理论。为了缩小这个差距，本研究计画将探讨非线性有限时间适应控制在移动的机器人上的应用。为了使移动的机器人能够在期望的位置执行某些任务，首先要做的就是设计一条合理的路径，使其能够在不与路径上的其他物体发生碰撞的情况下移动到期望的位置，这就是路径规划。然后设计反馈控制器，使移动的机器人能够在有限时间内跟踪设计的路径。因此，需要有限时间控制才能使移动的机器人在有限的时间内遵循给定的路径。* 本课题的主要目的是解决非线性常微分方程/微分代数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的机器人的控制。