Recent results on the analytic center approach for bounded error parameter estimation
- 99 Downloads
In this paper, we present an overview of some recent work  on the so-called analytic center approach for bounded error parameter estimation. First, we discuss the optimality properties of well-known algorithms such as the Chebychev center, the projection and the min-max estimates. Subsequently, we propose the analytic center as an alternative algorithm for recursive estimation. We show that the analytic center minimizes the output error and, on the contrary of other estimates like Chebychev, allows for an easy-to-compute sequential algorithm. We argue that the maximum number of Newton iterations required to evaluate a sequence of analytic centers is linear in the number of observed data points and it is comparable to the complexity of off-line algorithms for estimating a single analytic center. Finally, we briefly discuss a number of open problems which are currently under investigation.
KeywordsLinear Matrix Inequality Analytic Center Interior Point Method Newton Iteration Output Error
Unable to display preview. Download preview PDF.
- (1995). “Special Issue on Bounded Error Estimation (Part II),” International Journal of Adaptive Control and Signal Processing, Vol. 9.Google Scholar
- (1992). “Special Issue on System Identification for Robust Control Design,” IEEE Transactions on Automatic Control, Vol. 37.Google Scholar
- (1995). “Special Issue on Trends in System Identification,” Automatica, Vol. 31.Google Scholar
- Afkhamie, K. H., Z.-Q. Luo and K. M. Wong (1997). “Interior Point Column Generation Algorithms for Adaptive Fltering,” Technical Report Mc Master University, Ontario, Canada.Google Scholar
- Bai, E.-W., Y. Ye and R. Tempo (1997). “Bounded Error Parameter Estimation: A Sequential Analytic Center Approach,’ Proceedings of the IEEE Conference on Decision and Control, San Diego; also submitted to IEEE Transactions on Automatic Control.Google Scholar
- Bai, E.-W., M. Fu, R. Tempo and Y. Ye (1997). “Analytic Center Approach to Parameter Estimation: Convergence Analysis,” Technical Report University of Newcastle, Newcastle, Australia.Google Scholar
- Bai, E.-W., R. Tempo and Y. Ye (1997). “Open Problems in Sequential Parametric Estimation,” Technical Report CENS-CNR, Politecnico di Torino, Torino, Italy.Google Scholar
- Ljung, L. (1995). “System Identification: Theory for the Users,” Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
- Sonnevend, G. (1987). “A new method for solving a set of linear inequalities and its applications,” Dynamic Modelling and Control of National Economics, Pergamon, Oxford-New York, pp. 465–471.Google Scholar
- Ye, Y. (1997). Interior-Point Algorithm: Theory and Analysis, Wiley, New York.Google Scholar