权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Robust Design of Nonlinear Control Systems

非线性控制系统的鲁棒设计

基本信息

批准号：
06452248
负责人：
SHIMA Masasuke
金额：
$ 4.86万
依托单位：
HOKKAIDO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (B)
财政年份：
1994
资助国家：
日本
起止时间：
1994 至 1995
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06452248/
关键词：
Nonlinear H^* control Robust control L_2-gain Robust stability Nonlinear control Digital-redesign problem Robust relative degree

项目摘要

In this year, we have obtained the following results.1.The nonlinear non-standard H^* control problem is studied. In this research, two cases are concerned with : (a) the case in which the direct-through term from the input to the output does not have full-rank, and (b) the case in which the direct-through term from the disturbance to the measurement output does not have full-rank. In these cases, the square compliment cannot be carried out with the usual method, and thus the Hamilton-Jacobi-Issacs partial differential inequality is not well-defined. To resolve this difficulty, the term includes undecided function is added to the dissipative inequality, which makes the direct-through term have full-rank. The function is determined as the added term is equal to zero, and substitutes the undecided function in the Hamilton-Jacobi-Issacs partial differential inequality. Therefore the sufficient conditions for the cases (a) and (b) are obtained.2.The stability condition of the linear systems which includes uncertain parameters nonlinearly is studied. The mapping theorem is extended to the case that the assumption of the monotonicity with respect to the uncertain parameters holds, while the original mapping theorem assumes the multi-linearity. By means of the extended mapping theorem the sufficient condition of stability is derived. Also the sufficient condition of monotonicity is obtained.3.In the MIMO nonlinear system of which the vector relative degree cannot be defined, the robust vector relative degree is defined. The control law is derived using the robust vector relative degree, and it achieves BIBS stability of the control system.4.To run the above control laws on computers, a new nonlinear digital-redesign method is developed, which ensures the precision of third order with respect to the sampling interval.

本文主要研究了非线性非标准H^* 控制问题。在本研究中，两种情况下：（a）从输入到输出的直通项不具有满秩的情况，和（B）从干扰到测量输出的直通项不具有满秩的情况。在这些情况下，平方补不能用通常的方法进行，因此Hamilton-Jacobi-Issacs偏微分不等式不是很好定义的。为解决这一困难，在耗散不等式中加入了包含待定函数的项，使直通项具有满秩。该函数被确定为附加项等于零，并取代Hamilton-Jacobi-Issacs偏微分不等式中的待定函数。2.研究了含有非线性不确定参数的线性系统的稳定性条件。将映射定理推广到关于不确定参数的单调性假设成立的情况，而原来的映射定理假设了多线性。利用推广的映射定理，得到了系统稳定的充分条件。对于向量相对度无法定义的MIMO非线性系统，定义了鲁棒向量相对度。利用鲁棒向量相对度推导出控制律，实现了控制系统的BIBS稳定性。4.为了在计算机上运行上述控制律，提出了一种新的非线性数字再设计方法，该方法保证了采样间隔的三阶精度。