时滞输入大规模前馈非线性系统的控制设计

项目名称： 时滞输入大规模前馈非线性系统的控制设计

项目编号： No.61503214

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 自动化技术、计算机技术

项目作者： 刘庆荣

作者单位： 山东财经大学

项目金额： 20万元

中文摘要： 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。

中文关键词： 时滞输入；大规模系统；前馈系统；Lyapunov泛函；分散控制

英文摘要： 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.

英文关键词： Delayed inputs;large-scale systems;feedforward systems;Lyapunov functional;decentralized control