Abstract
In this article, we present an algorithm leading to an optimal controller gain for the automatic regulation of a linear system (closed-loop policy) and to an optimal auxiliary input. This is used for the purpose of either system identification, resulting in the maximum sensitivity measure and thus increased accuracy (Refs. 1–25), or system sensitivity reduction, resulting in the minimum sensitivity measure and thus reliable operation (Refs. 26–46). These results, which are robust in terms of parameter variations, are developed without constraints on the input functions.
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Aoki, M., andStaley, R.,On Input Signal Synthesis in Parameter Identification, Automatica, Vol. 6, pp. 431–440, 1970.
Bonivento, C.,Structural Insensitivity versus Identifiability, IEEE Transactions on Automatic Control, Vol. 18, pp. 190–192, 1973.
Eslami, M.,Optimal Input Policy for System Identification versus System Sensitivity Reduction with Plant Operator, University of Wisconsin-Madison, Electrical and Computer Engineering, Technical Report ECE-79-2, 1979.
Gagliardi, R. M.,Input Selection for Parameter Identification in Discrete Systems, IEEE Transactions on Automatic Control, Vol. 12, pp. 597–599, 1967.
Georganas, N. D.,Optimal Inputs and Sensitivities for Nonlinear Process Parameter Estimation Using Imbedding Techniques, IEEE Transactions on Automatic Control, Vol. 21, pp. 415–417, 1976.
Geromel, J. C., andDa Cruz, J. J.,On the Robustness of Optimal Regulators for Nonlinear Discrete-Time Systems, IEEE Transactions on Automatic Control, Vol. 32, pp. 703–712, 1987.
Jury, E. I., andTsypkin, Ya. Z.,On the Theory of Discrete Systems, Automatica, Vol. 7, pp. 89–107, 1971.
Kalaba, R. E., andSpingarn, K.,Optimal Inputs and Sensitivities for Parameter Estimation, Journal of Optimization Theory and Applications, Vol. 11, pp. 56–67, 1973.
Kalaba, R. E., andSpingarn, K.,Optimal Input System Identification for Nonlinear Dynamic Systems, Journal of Optimization Theory and Applications, Vol. 21, pp. 91–102, 1977.
Levadi, V. S.,Design of Input Signals for Parameter Estimation, IEEE Transactions on Automatic Control, Vol. 11, pp. 205–211, 1966.
Lim, K. Y., andEslami, M.,Adaptive Controller Designs for Robot Manipulator Systems Using Lyapunov Direct Method, IEEE Transactions on Automatic Control, Vol. 30, pp. 1229–1233, 1985.
Lim, K. Y., andEslami, M.,Adaptive Controller Design for Robot Manipulator Systems Yielding Reduced Cartesian Error, IEEE Transactions on Automatic Control, Vol. 32, pp. 184–187, 1987.
Lim, K. Y., andEslami, M.,Robust Adaptive Controller Designs for Robot Manipulator Systems, IEEE Journal of Robotics and Automation, Vol. 3, pp. 54–66, 1987.
Lopez-Toledo, A. A., andAthans, M.,Optimal Policies for Identification of Stochastic Linear Systems, IEEE Transactions on Automatic Control, Vol. 20, pp. 754–765, 1975.
Mehra, R. K.,Synthesis of Optimal Inputs for Multiinput/Multioutput Systems with Process Noise, Parts 1 and 2, Harvard University, Division of Engineering and Applied Physics, Technical Report TR 649, 1974.
Mehra, R. K.,Optimal Inputs for Linear System Identification, IEEE Transactions on Automatic Control, Vol. 19, pp. 192–200, 1974.
Mehra, R. K.,Optimal Input Signals for Parameter Estimation in Dynamic Systems—Survey and New Results, IEEE Transactions on Automatic Control, Vol. 19, pp. 753–768, 1974.
Mehra, R. K., andLainiotis, D. G., Editors,System Identification: Advances and Case Studies, Academic Press, New York, New York, 1976.
Nahi, N. E., andNapjus, G.,Design of Optimal Probing Signals for Vector Parameter Estimation, Proceedings of the IEEE Conference on Decision and Control, Miami, Florida, pp. 162–168, 1971.
Nahi, N. E., andWallis, D.,Optimal Inputs for Parameter Estimation in Dynamic Systems with White Observation Noise, Proceedings of the Joint Automatic Control Conference, Boulder, Colorado, pp. 506–512, 1969.
Rektorys, K., Editor,Survey of Applicable Mathematics, MIT Press, Cambridge, Massachusetts, 1969.
Sage, A. P., andWhite, C. C., III,Optimum Systems Control, 2nd Edition, Prentice-Hall, Englewood Cliffs, New Jersey, 1977.
Sawaragi, Y., andOgino, K.,Sensitivity Approach to Optimal Input Synthesis for Parameter Identification of Bilinear System, Proceedings of the 5th IFAC Congress, Paris, France, Vol. 3, pp. 31.2.1–31.2.6, 1972.
Schweppe, F. C.,On the Accuracy and Resolution of Radar Signals, IEEE Transactions on Aerospace and Electronic Systems, Vol. 1, pp. 235–245, 1965.
Zarrop, M. B., andGoodwin, G. C.,Comments on Optimal Inputs for System Identification, IEEE Transactions on Automatic Control, Vol. 20, pp. 299–300, 1975.
Bradt, A. J.,Sensitivity Functions in the Design of Optimal Controllers, IEEE Transactions on Automatic Control, Vol. 13, pp. 110–111, 1968.
Byrne, P. C., andBurke, M.,Optimization with Trajectory Sensitivity Considerations, IEEE Transactions on Automatic Control, Vol. 21, pp. 282–283, 1976.
Ciric, V. V., andLeeds, J. V.,Further Results on Sensitivity Consideration of Multiple-Input Controller Design for Dynamic Optimization, International Journal of Control, Vol. 15, pp. 849–863, 1972.
Eslami, M.,On Sensitivity Minimization Algorithms with Quadratic Performances, Proceedings of the 21st IEEE Conference on Decision and Control, Orlando, Florida, pp. 637–641, 1982.
Eslami, M.,An Introduction to the Theory of Sensitivity in Dynamic Systems, Springer-Verlag, New York, New York (in press).
Eslami, M., and Marleau, R. S.,On Sensitivity Minimization with an Adaptive Controller, Proceedings of the Joint Automatic Control Conference, Philadelphia, Pennsylvania, pp. 219–228, 1978.
Fleming, P. J., andNewmann, M. M.,Trajectory Sensitivity Reduction in the Optimal Linear Regulator, Recent Mathematical Developments in Control, Edited by D. J. Bell, Academic Press, New York, New York, pp. 137–151, 1971.
Fleming, P. J., andNewmann, M. M.,Comments and Corrections to Optimization with Trajectory Sensitivity Considerations, IEEE Transactions on Automatic Control, Vol. 22, p. 151, 1977.
Fleming, P. J., andNewmann, M. M.,Design Algorithms for a Sensitivity Constrained Suboptimal Regulator, International Journal of Control, Vol. 25, pp. 965–978, 1977.
Harvey, C. A., andPope, R. E.,Study of Synthesis Techniques for Insensitive Aircraft Control Systems, Honeywell Systems Research Center, Minneapolis, Minnesota, Technical Report, 1976.
Kamiya, Y.,Construction of a Low Parameter and Disturbance Sensitivity System by a Model-Following Method, International Journal of Control, Vol. 23, pp. 515–524, 1976.
Kreindler, E.,On Minimization of Trajectory Sensitivity, International Journal of Control, Vol. 8, pp. 89–96, 1968.
Kreindler, E.,Formulation of the Minimum Trajectory Sensitivity Problem, IEEE Transactions on Automatic Control, Vol. 14, pp. 206–207, 1969.
Leondes, C. T., andPezet, P.,Sensitivity Requirements for Suboptimal Controllers, IEEE Transactions on Automatic Control, Vol. 20, pp. 426–428, 1975.
Missaghie, M. M., andFairman, F. W.,Sensitivity Reducing Observers for Optimal Feedback Control, IEEE Transactions on Automatic Control, Vol. 22, pp. 952–957, 1977.
Missaghie, M. M., andFairman, F. W.,Desensitizing Observers for LQG Feedback Control, International Journal of Systems Science, Vol. 12, pp. 161–175, 1979.
Newell, R. B., andFisher, D. B.,Experimental Evaluation of Optimal, Multivariable Regulatory Controllers with Model-Following Capabilities, Automatica, Vol. 8, pp. 247–262, 1972.
Newmann, M. N.,On Attempts to Reduce the Sensitivity of the Optimal Linear Regulator to a Parameter Change, International Journal of Control, Vol. 11, pp. 1079–1084, 1970.
Sannuti, P., andCruz, J. B., Jr.,A Note on Trajectory Sensitivity of Optimal Control Systems, IEEE Transactions on Automatic Control, Vol. 13, pp. 111–113, 1968.
Wilson, D. J., andLeitmann, G.,Minimax Control of Systems with Uncertain State Measurements, Applied Mathematics and Optimization, Vol. 2, pp. 315–336, 1976.
Winsor, C. A., andRoy, R. J.,The Application of Specific Optimal Control to the Design of Desensitized Model-Following Control Systems, IEEE Transactions on Automatic Control, Vol. 15, pp. 326–333, 1970.
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Communicated by J. B. Cruz, Jr.
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Eslami, M. Optimal input for identification versus sensitivity reduction of systems with large parameter variations. J Optim Theory Appl 77, 591–612 (1993). https://doi.org/10.1007/BF00940452
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DOI: https://doi.org/10.1007/BF00940452