Abstract
The paper presents a new approach to model validation and fault diagnosis problems for a class of uncertain systems in which the uncertainty is described by an integral quadratic constraint. The new approach is developed by applying methods from linear quadratic optimal control theory. This leads to a method for model validation and fault diagnosis which is based around a robust Kalman filter type structure.
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PATTON, R., FRANK, P. M., and CLARK, R. N., Fault Diagnosis in Dynamic Systems: Theory and Applications, Prentice-Hall, Englewood Cliffs, New Jersey, 1989.
SMITH, R. S., Model Validation for Uncertain Systems, PhD Thesis, California Institute of Technology, Pasadena, California, 1990.
SMITH, R. S., and DOYLE, J. C., Model Validation: A Connection between Robust Control and Identification, IEEE Transactions on Automatic Control, Vol. 37, pp. 942–952, 1992.
POOLLA, K., KHARGONKAR, P., TIKKU, A., KRAUSE, J., and NAGPAL, K., A Time-Domain Approach to Model Validation, Proceedings of the 1992 American Control Conference, Chicago, Illinois, pp. 313–317, 1992.
ZHOU, T., and KIMURA, H., Input-Output Extrapolation-Minimization Theorem and Its Application to Model Validation and Robust Identification, The Modeling of Uncertainty in Control: Proceedings of the 1992 Santa Barbara Workshop, Edited by R. Smith and M. Dahleh, Springer Verlag, London, England, pp. 127–138, 1993.
YAKUBOVICH, V. A., Minimization of Quadratic Functionals under Quadratic Constraints and Necessity of a Frequency Condition in the Quadratic Criterion for Absolute Stability of Nonlinear Control Systems, Soviet Mathematics Doklady, Vol. 14, pp. 593–597, 1973.
YAKUBOVICH, V. A., Methods of Research of Nonlinear Control Systems, Chapters 2–3, Nauka, Moscow, Russia, 1975 (in Russian).
SAVKIN, A. V., and PETERSEN, I. R., A Connection between H x Control and the Absolute Stabilizability of Uncertain Systems, Systems and Control Letters, Vol. 23, pp. 197–203, 1994.
SAVKIN, A. V., and PETERSEN, I. R., Nonlinear versus Linear Control in the Absolute Stabilizability of Uncertain Linear Systems with Structured Uncertainty, IEEE Transactions on Automatic Control, Vol. 40, pp. 122–127, 1995.
BOYD, S., EL GHAOUI, L., FERON, E., and BALAKRISHNAN, V., Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, Pennsylvania, 1994.
SAVKIN, A. V., and PETERSEN, I. R., An Uncertainty Averaging Approach to Optimal Guaranteed Cost Control of Uncertain Systems with Structured Uncertainty, Automatica, Vol. 31, pp. 1649–1654, 1995.
SAVKIN, A. V., and PETERSEN, I. R., Recursive State Estimation for Uncertain Systems with an Integral Quadratic Constraint, IEEE Transactions on Automatic Control, Vol. 40, pp. 1080–1083, 1995.
BERTSEKAS, D. P., and RHODES, I. B., Recursive State Estimation for a Set-Membership Description of Uncertainty, IEEE Transactions on Automatic Control, Vol. 16, pp. 117–128, 1971.
CLEMENTS, D. J., and ANDERSON, B. D. O., Singular Optimal Control: The Linear-Quadratic Problem, Springer Verlag, Berlin, Germany, 1978.
LEWIS, F. L., Optimal Control, Wiley, New York, New York, 1986.
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Savkin, A.V., Petersen, I.R. New Approach to Model Validation and Fault Diagnosis. Journal of Optimization Theory and Applications 94, 241–250 (1997). https://doi.org/10.1023/A:1022676106903
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DOI: https://doi.org/10.1023/A:1022676106903