Abstract
For bilinear control systems with quadratic cost, the so-called bilinear-quadratic problems, a feedback controller for the finite-time case is designed. An iteration procedure in close proximity to the Riccati approach is presented, and the proof of convergence is outlined. The potential of the new method is discussed, and the design procedure is illustrated for two examples.
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References
Mohler, R. R., andRink, R. E.,Multivariable Bilinear System Control, Proceedings of the IFAC Symposium on Multivariable Control Systems, Düsseldorf, Germany, 1968.
Mohler, R. R.,Bilinear Control Processes, Academic Press, New York, New York, 1973.
Hofer, E. P.,Optimal Control of Bilinear Systems with Applications to an Electric Circuit, Proceedings of the 4th Asilomar Conference on Circuits and Systems, Asilomar, California, 1970; Western Periodicals Company, North Hollywood, California, 1971.
Bruni, C., DiPillo, G., andKoch, G.,Bilinear Systems: An Appealing Class of Nearly Linear Systems in Theory and Applications, IEEE Transactions on Automatic Control, Vol. AC-19, No. 4, pp. 334–348, 1974.
Cebuhar, W. A., andCostanza, V.,Approximation Procedures for the Optimal Control of Bilinear and Nonlinear Systems, Journal of Optimization Theory and Applications, Vol. 43, No. 4, pp. 615–627, 1984.
Ryan, E. P.,Optimal Feedback Control of Bilinear Systems, Journal of Optimization Theory and Applications, Vol. 44, No. 2, pp. 333–362, 1984.
Tzafestas, S. G., Anagnostou, K. E., andPimenides, T. G.,Stabilizing Optimal Control of Bilinear Systems with a Generalized Cost, Optimal Control Applications and Methods, Vol. 5, No. 2, pp. 111–117, 1984.
Cebuhar, W. A., andCostanza, V.,Nonlinear Control of CSTR's, Chemical Engineering Science, Vol. 39, No. 12, pp. 1715–1722, 1984.
Hofer, E. P.,Nonlinear and Bilinear Models for Chemical Reactor Control, Proceedings of the 5th International Conference on Mathematical Modelling, Berkeley, California, 1985; Pergamon Press, Oxford, England, 1986.
Athans, M., andFalb, P.,Optimal Control, McGraw-Hill, New York, New York, 1966.
Walter, W.,Gewöhnliche Differentialgleichungen, Springer, Berlin, Germany, 1972.
Collatz, L., andNicolovius, R., Rand-und-Eigenwertprobleme bei Gewöhnlichen und Partiellen Differentialgleichungen und Integralgleichungen, Mathematische Hilfsmittel des Ingenieurs, Vol. 2, Edited by R. Sauer and I. Szabó, Springer, Berlin, Germany, 1969.
Collatz, L.,Differentialgleichungen, Teubner, Stuttgart, Germany, 1981.
Boltyanskii, V. G.,Sufficient Conditions for Optimality and the Justification of the Dynamic Programming Method, SIAM Journal on Control, Vol. 4, No. 2, pp. 326–361, 1966.
Hofer, E. P.,Bilinear Process Control with Applications in Chemical Reactor Control, Proceedings of the 2nd Japanese-German Seminar on Nonlinear Problems in Dynamical Systems, Edited by E. Shimemura and K. Hirai, Kawaguchiko, Japan, 1985.
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Communicated by G. Leitmann
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Hofer, E.P., Tibken, B. An iterative method for the finite-time bilinear-quadratic control problem. J Optim Theory Appl 57, 411–427 (1988). https://doi.org/10.1007/BF02346161
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DOI: https://doi.org/10.1007/BF02346161