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: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=711623
• 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.

拟议的研究计划将研究由普通微分方程和差分 - 代数方程式描述的一类非线性系统的有限时间自适应控制问题，以及其在控制移动机器人控制的应用。特别是，考虑的问题包括有限的时间稳定，有限的时间跟踪，有限的时间扰动衰减，有限的自适应控制和有限的时间容忍度控制。大多数用于反馈控制的可用技术导致闭环系统，解决方案在无限沉降时间内会收敛到所需的位置。但是，从实际的角度来看，安顿的时间越短，越好。实际上，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，即使有限的时间控制问题比传统的控制问题更难解决，但实际上它们更重要，并且在近几十年来吸引了越来越多的关注。 几乎所有物理系统都包含一定数量的参数。这些参数中的一些可以测量，而其他参数则无法访问。即使对于可测量的参数，有时由于各种原因（例如时变属性，对温度敏感的特征，负载依赖性等）获得确切值并不容易。因此，设计两个控制器以实现控制目标和适应性定律以估计可能不确定甚至可能未知的参数，这既是理论上的重要性，又是实际的重要性，被称为自适应控制。自1970年代以来，自适应控制一直引起了控制工程领域专家的极大关注。 控制理论远比其在现实世界中的应用要高得多。控制理论及其在工程领域的应用之间存在很大差距，尤其是对于非线性控制理论。为了减少这一差距，该研究计划将调查非线性有限时间自适应控制对移动机器人的应用。为了使移动机器人在所需的位置执行某些任务，要做的第一件事是设计合理的路径，以便它能够移动到所需的位置，而不会与路径上的其他对象相撞，这称为路径规划。之后，应设计反馈控制器，以便移动机器人能够在有限的时间内遵循设计路径。因此，移动机器人在有限的时间段内遵循给定路径需要有限的时间控制。 该项目的主要目的是解决非线性ODE/DAE系统的有限时间自适应控制问题，并将有限的时间自适应控制理论应用于移动机器人的控制。