强不确定系统“全系数之和等于1”的实现方法

摘要： 研究强不确定系统“全系数之和等于1”的实现方法，强不确定系统指的是系统的静态增益及其界不完全确知且范围较大.“全系数之和等于1”是吴宏鑫院士20世纪80年代发现的，该原理表明，对于未知连续系统，其离散化系统的系数的和在一定条件下是1.该原理的发现对于解决闭环辨识和自适应控制的瓶颈问题具有关键作用.“全系数之和等于1”是在一定条件下成立的.为了实现系统的“全系数之和等于1”，需要对系统进行一定的变换，以满足所需条件.其中，采用静态增益的标称值的倒数进行输入变换的方法在实际中得到了广泛应用.但是，当系统的不确定性较大时，该变换将带来较大偏差.针对该问题开展了深入研究，明确给出了系统静态增益的不确定性与标称值的比值的关系对于实现“全系数之和等于1”的影响.当不确定性与标称值的比值较小时，可以近似实现“全系数之和等于1”；当比值较大时，进一步给出了通过选取合适的采样周期，近似实现“全系数之和等于1”的方法.本文的研究对于特征模型理论在实际中的应用提供了一定的基础.

Realization Methods of “Sum of All Coefficients Being One”for Strongly Uncertain Systems

Abstract： In this paper, the realization methods of “sum of all coefficients being one (SACO)” for the strongly uncertain system are researched, where the strongly uncertain system means that its static gain and its bound are unknown and the range of the static gain is large. The principle SACO was found by Prof. Hongxin Wu in 1980’, which shows that the sum of the coefficients for the discretized systems of unknown continuous systems is one under certain conditions, playing an important role on the solution to the key problems in close loop identification and adaptive control. A transformation is needed for systems to realize the conditions because the SACO holds under certain conditions, where using the reciprocal of the nominal value of the static gain as the input transformation has been widespread utilized due to easy implementation. However, when the uncertainties are larger, the transformation will bring larger errors. This problem is deeply investigated in this paper. We specifically show that the effects on the realization of SACO of the ratio between the uncertainties and the nominal value of the static gain. When the ratio is lower, the SACO can be realized approximately; otherwise, when the ratio is higher, we need to furthermore choose appropriate sampling duration to approximately realize the SACO. The conclusions obtained in this paper lay certain foundation on the practical applications of the characteristic model theory.