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.

所提出的研究计划将研究由常微分方程和微分代数方程描述的一类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。具体而言，所考虑的问题包括有限时间稳定、有限时间跟踪、有限时间扰动衰减、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都会导致闭环系统，其解决方案在无限的稳定时间内收敛到所需的位置。但从实际应用的角度来看，稳定时间越短越好。事实上，大多数实际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控制问题更难解决，但它们在实践中更为重要，并且在近几十年来引起了越来越多的关注。***几乎所有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访问。即使对于可测量的参数，有时由于各种原因，例如时变特性、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。因此，设计实现控制目标的控制器和自适应律来估计可能不精确已知甚至未知的参数（称为自适应控制）具有重要的理论和实践意义。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。 *** 控制理论远比其在现实世界中的应用先进。控制理论与其在工程领域的应用之间存在很大差距，特别是非线性控制理论。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。移动机器人为了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，使其能够移动到期望的位置而不与路径上的其他物体发生碰撞，这就是路径规划。之后，应该设计反馈控制器，使得移动机器人能够在有限的时间内遵循设计的路径。因此，移动机器人需要有限时间控制来在有限的时间内遵循给定的路径。*** 本项目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的一些问题，并将有限时间自适应控制理论应用于移动机器人的控制。