Basic research on subspace identification method for practical use

对于多输入多输出系统的状态空间模型辨识，可以先从输入输出数据中估计脉冲响应，然后构造Hankel矩阵，再通过Ho-Kalman实现算法或基于奇异值分解的Kung实现算法得到状态空间模型。但是，从输入输出数据中很难得到高精度的MIMO系统冲激响应估计。基于子空间的状态空间系统辨识方法直接从输入输出数据中得到状态空间模型的系统矩阵（A，B，C，D），而不需要脉冲响应或差分方程等中间表达式。本研究针对子空间辨识方法的实际应用展开了以下几方面的研究：用途：1）将各种连续时间系统辨识方法的软件包进行了封装，并利用该软件包对各种辨识方法进行了比较。2)发展一种鲁棒控制的建模方法。3)提出了基于偏差补偿原理的一致性估计方法。4)提出了一种子空间辨识的递推算法。5)子空间辨识法在连续系统与非线性系统之推广。

For state space model identification of MIMO systems, the methods may be used for estimating impulse response from input-output data, then constructing Hankel matrix and deriving the state space model by Ho-Kalman's realization algorithm or Kung's realization algorithm based on singular value decomposition. But it is difficult to get highly accurate impulse response estimates of MIMO system from input-output data. Also, there is a problem that appropriate structure indices have to be decided for estimating the coefficient matrix of difference equation from input-output data and deriving the state space model.Subspace-based state space system identification methods directly realize system matrices (A,B,C,D) of state space model from input-output data without intermediate expression, such as impulse responses or difference equations. The methods are essentially suitable for MIMO systems and therefore have attracted much attention as strong identification methods instead of traditional identification methods based on linear regression equations.In this research, the following studies on subspace identification methods are carried out for practical use: 1) Packaging the software of various continuous-time system identification methods, and comparing various identification methods by this software package. 2) Developing a modeling method for robust control. 3) Proposing consistent estimation methods based on bias-compensation principal. 4) Presenting a recursive calculation algorithm of subspace identification. 5) Extension of subspace identification method to continuous-time systems and nonlinear systems.