时滞输入大规模前馈非线性系统的控制设计

Large-scale systems can be found in many applications such as power systems, multi-robot systems, and so on. A large-scale system is often considered as a set of interconnected subsystems. Time delays, due to the information transmission between subsystems, also naturally exist in large-scale systems. On the other hand, feedforward nonlinear systems represent a large class of nonlinear systems. In this project, the problem of the control design will be solved for large-scale feedforward nonlinear systems with delayed inputs. The nonlinear terms involved here will admit either a constant incremental rate or a function incremental rate depending on the measurable states and inputs, and the decentralized control will be applied in the former case while the decentralized hierarchical control in the latter. Firstly, by using the Newton-Leibnitz formula, large-scale feedforward nonlinear systems with delayed inputs will be converted into large-scale feedforward nonlinear systems with delayed states. Secondly, by using the state transformation of nonlinear systems, the problem of designing controller will be further converted into that of designing either a constant parameter, or a dynamic parameter which is dynamically regulated by an upper-level system. Thirdly, by appraising the nonlinear terms of the given systems, either the constant parameter or the upper-level system can be delicately constructed. At last, with the help of Lyapunov stability theorem, it is provided the stability analysis for the closed-loop system consisting of the designed controller and the given large-scale systems. Compared with many existing control designs for large-scale feedforward nonlinear systems, the innovations of this project can be summarized as follows. (i) We do not use the forwarding or saturation control, which are commonly applied in studying feedforward nonlinear systems, and thus avoid the too complicated recursive procedure and get a structurally simple controller. (ii) The delay type involved here can be either discrete or distributed, and thus the systems considered here will include a wide variety of time-delay systems. (iii) The decentralized hierarchical control will be introduced here to stabilize large-scale feedforward systems with strong nonlinearities.

大规模系统常见于电力系统和多机器人系统等实际问题中。大规模系统是由多个子系统级联而成，而子系统之间的信息传递使得时滞现象难以避免。本项目将研究时滞输入大规模前馈非线性系统的控制设计。针对非线性项受限于常值增长率和函数增长率情形，分别给出镇定系统的分散控制器和分散递阶控制器。首先，用Newton-Leibnitz公式，把时滞输入大规模前馈系统转化为时滞状态大规模前馈系统。其次，用状态变换把控制器设计问题转化为常值参数、或受另一高层系统调节的动态参数的构造问题。然后，估计非线性项，设计常值参数或调节动态参数的高层系统。最后，用Lyapunov稳定性理论分析闭环系统稳定性。创新点如下：①未用研究前馈系统常见的前推与饱和控制法，避开了繁琐的迭代程序，所得控制器形式简单；②涉及的时滞可以是离散型或分布型时滞，研究结果适用于多类型时滞系统；③分散递阶控制被用于镇定带“强”非线性特征的大规模前馈系统。

本项目运用静态或者动态增益控制设计方法，将控制器设计问题转化为常值参数或者动态方程的构造问题。主要研究内容体现在三个方面。第一，研究了非线性系统的稳定性分析问题，这是对系统进行控制设计的基础。第二，研究了单个非线性系统的控制设计问题，这是从事大规模系统控制设计的基础。第三，研究了大规模系统控制设计和切换系统的切换控制问题。.经过三年的深入研究，在本项目资助下，共发表了8篇学术论文，其中在《Nonlinear Analysis: Hybrid Systems》、《IET Control Theory & Applications》、《Neurocomputing》、《Advances in Mathematical Physics》和《Advances in Difference Equations》发表期刊论文5篇。.基于静态增益控制设计方法，研究了带离散时滞和分布时滞的前馈非线性系统，设计了一个状态反馈控制器，解决了渐近镇定控制设计问题。基于动态增益控制设计方法，研究了输出约束非线性系统，分别设计了输出约束非线性的状态反馈控制器和大规模输出约束非线性时滞系统的输出反馈控制器。基于多个离散共正性Lyapunov-Krasovskii泛函，研究了正切换时滞系统的稳定性问题，得到了连续时间正切换时滞系统的全局一致渐近稳定性的充分条件。.项目的主要科学意义在于为时滞输入大规模前馈非线性系统建立了一个基于静态或者动态增益控制设计方法的理论研究框架，通过引入常值参数或者动态方程等概念，丰富了大规模前馈非线性系统的控制设计方法。