奇异切换系统未知输入观测器设计及其滑模控制方法研究

In this project, we study the design methods of reduced-order observer, finite-time observer and finite-time observer-based sliding mode control for a class of singular switched systems containing unknown inputs in both the state and output equations. General speaking, when the output of a control system contains unknown input, the reduced-order observer design will become much more challenging. Therefore, almost all the existing literature regarding to the reduced-order observer design assumes that the output equation does not contain unknown input. In fact, output channels of control systems are usually unavoidably affected by unknown signals such as sensor fault, measurement noise, and so on. In order to break through this limitation, we introduce a new unknown input vector and construct a new measurable output equation, and then put forward a new reduced-order observer design scheme. Secondly, we consider the finite-time observer design for the singular switched system, so as to give accurate estimation of state and unknown input in a finite time, and meanwhile reduce the conservativeness of the traditional asymptotic convergence observer imposed by switching signal. And, based on such the observer, the sliding mode control problem of the singular switched systems is studied. Combining with impulsive control strategy, we design the sliding mode control law to remove the constraint of the switching rule during the sliding mode motion, which leaves rooms for the switching signal design in the stability analysis of the closed-loop system. This project is expected to further improve the observer design and sliding mode control theories of singular switched systems, and may provide new ideas and methods for solving practical engineering problems.

本项目针对一类状态和输出方程均含有未知输入的奇异切换系统研究其降维观测器、有限时间观测器设计及其滑模控制问题。一般来说，若系统输出中包含未知输入，其降维观测器设计会变得异常困难。因此，已有文献大都假设输出方程中不包含未知输入。事实上，控制系统输出中往往不可避免地会受到包括传感器故障、测量噪声等未知输入的影响。为了突破这种限制，拟通过引入新的未知输入并构造新的输出，来提出一种降维观测器设计的新方法。其次，研究奇异切换系统有限时间观测器设计，使得其能够在任意短时间达到对状态和未知输入精确估计的同时，减弱传统渐近收敛观测器对切换信号的限制。在此基础上，研究奇异切换系统滑模控制问题。拟结合脉冲控制设计滑模控制律，以消除系统滑模运动中对切换信号的约束，给闭环系统稳定性分析中切换信号以更大的自由度。本项目有望进一步完善奇异切换系统观测器设计及其滑模控制理论，并为实际工程问题的解决提供新的思路和方法。

本项目对奇异系统未知输入观测器设计和基于观测器的滑模控制及其延伸问题进行了深入研究。研究对象包括奇异切换系统，一般奇异时不变系统，T-S模糊奇异系统以及LPV系统。主要的研究内容有：针对输出方程和状态方程同时含有未知输入的奇异切换系统，通过构造新的辅助输出以消除原输出通道中未知输入的方式，在不增加系统观测器设计保守性的基础上给出了一种降维观测器的设计方法。针对T-S模糊奇异系统，先设计降维观测器，利用其观测出的状态信息实现了滑模控制。利用线性矩阵不等式给出了该系统降维观测器和滑模控制器的存在条件并讨论了观测器和控制器设计的可分离性。针对含有未知输入的连续/离散奇异系统分别给出了有限时间观测器设计方法并讨论了观测器存在的充分必要条件。针对离散LPV系统研究了基于时变增益的有限时间观测器设计方法，利用线性矩阵不等式给出了有限时间观测器存在的充分条件，降低了以往先将LPV系统化为T-S模糊系统而后再设计T-S模糊观测器这种传统方法所带来的保守性。此外，还研究了奇异系统有限时间函数未知输入观测器设计问题。利用矩阵广义逆方法给出了有限时间函数观测器存在的充分必要条件。本项目共发表高水平论文9篇，其中被SCI检索6篇，EI检索3篇，包含控制领域国际著名期刊《IEEE Transactions on Automatic Control》，《IEEE Transactions on Fuzzy Systems》, 《International Journal of Control》以及国内著名期刊《自动化学报》、《控制理论与应用》等。