Recursive Least Squares Identification With Variable-Direction Forgetting via Oblique Projection Decomposition

In this paper,a new recursive least squares(RLS)identification algorithm with variable-direction forgetting(VDF)is proposed for multi-output systems.The objective is to enhance parameter estimation performance under non-persistent excitation.The proposed algorithm performs oblique projection decomposition of the information matrix,such that forgetting is applied only to directions where new information is received.Theoretical proofs show that even without persistent excitation,the information matrix remains lower and upper bounded,and the estimation error variance converges to be within a finite bound.Moreover,detailed analysis is made to compare with a recently reported VDF algorithm that exploits eigenvalue decomposition(VDF-ED).It is revealed that under non-persistent excitation,part of the forgotten subspace in the VDF-ED algorithm could discount old information without receiving new data,which could produce a more ill-conditioned information matrix than our proposed algorithm.Numerical simulation results demonstrate the efficacy and advantage of our proposed algorithm over this recent VDF-ED algorithm.

Special issue on system identification and estimation

It is our great pleasure and honor to organize this special issue“System Identification and Estimation”.System identification has been a surprisingly lively and resilient area of research in the control community for many years.It grew out of statisticians’interest in time series analysis beginning in the 1940s and became a“regular control topic”in the 1960s,as indicated by thefirst IFAC Symposium on System Identification held in Prague,Czech Republic,in 1967.Sixty years later,it is still an important area of research in thefield of control.It is relevant to ask why the interest in system identification has remained so intense.One answer might be that more and more applications in engineering require mathematical models and the combined use of system identification and physical modeling is the basic way to obtain reliable models.This special issue is focusing on the latest development,trends,and novel methods for system identification and estimation and these contributions will give interesting and inspiring insights into the current status of the area.