Identification of Nonlinear Systems

自动控制系统在现代世界中无处不在。它们的范围很广，从调节硬盘读写头位置的位置控制器，到控制飞机运动的自动驾驶仪，再到调节大城市交通流量的先进交通控制系统。由于控制器是根据被控制系统的数学模型设计的，因此系统的性能将受到其设计中使用的模型的准确性的限制。因此，拥有目标系统的精确数学模型是设计高性能控制系统的必要前提。******虽然相对简单的系统模型可以基于第一原理推导出来，但是随着系统的规模和/或复杂性的增加，这种方法很快变得难以处理。另一方面，系统识别是一个数据驱动的过程，它通过测量动态系统的输入和输出来创建动态系统的数学模型。该研究计划将开发系统识别技术，该技术可以从在正常运行条件下和某种形式的控制系统运行时收集的数据中创建非线性系统的精确数学模型。******如果系统的输入与影响系统的任何干扰或测量中可能包含的任何噪声无关，则系统识别过程将大大简化。不幸的是，许多系统只能在“闭环”配置中运行，其中测量系统输出，将其与期望的轨迹进行比较，然后使用该误差来调整输入信号。这种类型的反馈控制可能是必要的安全，性能或经济原因。在本研究计划中开发的非线性系统识别算法将被设计用于在闭环条件下收集的数据，因为这将允许它们在不需要单独的，通常不可能执行的开环实验的情况下应用。相反，我们将专注于从正常的操作数据构建模型，因为这将最小化生成模型的经济影响。

Automatic control systems are ubiquitous in the modern world. They can range in scale from the position controller that regulates the position of the read/write head in a hard disk, to the autopilots that control the movement of aircraft, to the advanced traffic control systems that regulate the flow of traffic in major cities. Since the controller is designed based on a mathematical model of the system that will be controlled, the system's performance will be limited by the accuracy of the model used in its design. Thus, having an accurate mathematical model of the target system is a necessary pre-requisite to the design of a high-performance control system.******While models of comparatively simple systems can be derived based on first principles, this approach quickly becomes intractable as the system's scale and/or complexity increases. System identification, on the other hand, is a data-driven process that creates mathematical models of dynamic systems from measurements of their inputs and outputs. This research programme will develop system identification techniques that can create accurate mathematical models of nonlinear systems from data that have been gathered under normal operating conditions and when some form of control system is operating. ******The system identification process is greatly simplified if the input to the system is independent of any disturbances that affect the system, or of any noise that may be contained in the measurements. Unfortunately, many systems can only be operated in a "closed-loop" configuration, where the system output is measured, compared to a desired trajectory, and this error is then used to adjust the input signal. This type of feedback control may be necessary for safety, performance or economic reasons. The nonlinear system identification algorithms developed in this research programme will be designed to operate on data that have been gathered under closed-loop conditions, as this will allow them to be applied without the need for a separate, often impossible to perform, open-loop experiment. Instead, we will concentrate on constructing models from normal operating data, as this will minimize the economic impact of generating the model.