Finite-Time Adaptive Control of Nonlinear Systems and Its Applications

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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.