随机前馈非线性系统的若干控制问题研究

It is well-known that nonlinearity and randomness are always the essential difficulties of control theory research. The research on control problems of stochastic nonlinear systems is one of the mainstream directions in international control theory research. .The research on feedforward nonlinear systems and control problems has aroused extensive attention in recent years. The research significance of feedforward nonlinear systems lies in: From the theoretical point of view, due to its special upper triangular structures, the traditional design and analysis methods are often inapplicable to such systems. From a view of practical application, many physical models can be described by feedforward equations..Based on the results of deterministic feedforward nonlinear systems and stability theory of stochastic systems, the project is to do further research on the control and stability problems of stochastic feedforward nonlinear systems, these problems are very meaningful both in theory and in practice. The research problems include: Problem 1: Further study the properties of stochastic inverse dynamics, and solve control problems of stochastic feedforward nonlinear systems with stochastic inverse dynamics. Problem 2: Control problems of stochastic feedforward nonlinear systems with input time-delay. Problem 3: Finite-time stability and control problems of stochastic feedforward nonlinear systems. Problem 4: Modeling of stochastic feedforward systems, and the solution to some practical control problems.

众所周知，非线性和随机一直是控制理论研究的本质困难所在，随机非线性系统的控制问题研究是国际控制理论研究的主流方向之一。.近年来，前馈非线性系统及控制问题研究已经引起了广泛关注。前馈非线性系统的研究意义在于：从理论角度看，由于它的特殊的上三角结构，传统的设计和分析方法常常不适用于此类系统。从实际应用角度看，许多物理模型都可由前馈方程描述。.本项目将在确定性前馈非线性系统工作及随机系统稳定性理论的基础上，深入研究随机前馈非线性系统的控制及稳定性问题，这些问题无论从理论还是实际应用都很有研究意义。研究问题包括：问题1：进一步研究随机逆动态的性质，解决具有随机逆动态的随机前馈非线性系统的控制问题。问题2：具有输入时滞的随机前馈非线性系统的控制问题。问题3：随机前馈非线性系统的有限时间稳定及控制问题。问题4：随机前馈系统建模，解决一些实际控制问题。

在国家自然科学基金(No.61673242)的资助下,课题组在随机和非线性系统的控制问题研究方面做了一些工作,较好地完成了预期任务。项目负责人获得教育部自然科学二等奖,担任国际顶级期刊Automatica编委,发表标注国家自然科学基金的国际权威期刊论文38篇,其中IEEE Trans.Automatic Control5篇,Automatica2篇,IEEE Trans.Cybernetics3篇,IEEE Trans.Systems,Man and Cybernetics:Systems3篇,IEEE Trans.Fuzzy Systems1篇,Int.J.Robust and Nonlinear Control5篇,Int.J.Control6篇,J.the Franklin Institute1篇,Int.J.Systems Science7篇,Int.J.Adaptive Control and Signal Processing2篇,SCIENCE CHINA Information Sciences3篇。. 主要研究内容包括：课题组在随机和非线性系统的控制问题研究方面做了一些工作,较好地完成了预期任务。主要研究内容包括:论文[1]-[4],[6]-[7],[16]-[17],[34]-[36]和[38]针对多类随机非线性系统,通过引入新的设计和分析方法到随机系统,克服控制器设计和分析过程中的本质困难,解决了状态/输出反馈控制问题。[8]-[12],[13]-[14],[20]-[22],[27]-[28]针对非线性系统,研究了受约束控制问题。[16],[23],[27]和[31]针对前馈非线性系统,研究了状态/输出反馈控制问题。[18],[28]和[33]针对具有未知的输出函数的非线性系统,研究了状态/输出反馈控制问题。[15],[19],[24],[25],[26],[29]和[30]针对高阶次非线性系统,在非线性函数减弱条件下,研究了不同的控制问题。[5]研究了切换系统的镇定性。[37]研究了自适应控制问题。