Adaptive Control of Time-Varying Systems

在系统控制中，目标是通过使用（自动）控制器使物理系统（设备）以期望的方式运行，例如，在飞机（设备）上使用自动驾驶仪（控制器）来保持速度，高度和方向。控制系统设计的第一步是获得被控对象的数学模型，然后设计一个由数学方程描述的控制器，该控制器通常在软件中实现。在这个过程中，一个常见的绊脚石是工厂模型的不确定性，这可能是由建模错误、由于磨损而改变参数、改变操作条件（如飞机的高度或机器人系统中有效载荷的质量变化）或系统故障（在工业系统中常见）等因素引起的。如果不确定性较大，则不能使用简单的比例-积分-导数（PID）控制器，而必须采用更复杂的方法。一种强大的方法是自适应控制，其中控制器随着时间的推移对对象的了解越来越多，从而使自己适应对象。

In systems control, the objective is to make a physical system (the plant) act in a desired manner through the use of an (automatic) controller, e.g. an autopilot (the controller) is used on an aircraft (the plant) to maintain speed, altitude and direction. The first step in control system design is to obtain a mathematical model of the plant, and then one designs a controller, described by a mathematical equation, which is typically implemented in software. A common stumbling block in this process is uncertainty in the plant model, which can be caused by such things as modelling error, changing parameters due to wear and tear, changing operating conditions (such as the altitude of an aircraft or the changing mass of a payload in a robotic system), or systems faults (common in industrial systems). If the uncertainty is large, then a simple proportional-integral-derivative (PID) controller cannot be used, and a more sophisticated approach muct be adopted. One powerful approach is that of adaptive control, wherein the controller adapts itself to the plant as it learns more and more about it over time. This approach has its roots in the 1950s, and it has grown more and more sophisticated over the years. The increased computational power of computers allows more complicated control algorithms to be implemented in real-time, so it is making inroads in areas like robotics and aerospace. However, there are still unanswered questions in the field, and in my proposed research the goal is to answer several important ones: (i) Is it possible to design adaptive controllers which not only provide good performance asymptotically, but also provide it in the short-run, while the adaptive controller is still learning about the plant? (ii) Is it possible to handle rapidly time-varying parameters as well as the more common case of very slow time-varying parameters? (iii) Is it possible to redesign classical adaptive controllers to make them more powerful: more robust, more noise tolerant, and better at tolerating time-varying parameters? The answers to these questions will enhance the state-of-the-art of adaptive control, and reduce the gap between theory and practise. It will provide control engineers with new algorithms; it will benefit a team of graduate students by engaging in advanced technological training; and it will enhance Canada's position as a leading proponent of advanced automation.