Guerman, Anna; Seabra, Ana; Smirnov, Georgi Optimization of parameters of asymptotically stable systems. (English) Zbl 1214.93097 Math. Probl. Eng. 2011, Article ID 526167, 19 p. (2011). Summary: This work deals with numerical methods of parameter optimization for asymptotically stable systems. We formulate a special mathematical programming problem that allows us to determine optimal parameters of a stabilizer. This problem involves solutions to a differential equation. We show how to chose the mesh in order to obtain discrete problem guaranteeing the necessary accuracy. The developed methodology is illustrated by an example concerning optimization of parameters for a satellite stabilization system. Cited in 1 Document MSC: 93D21 Adaptive or robust stabilization 93D20 Asymptotic stability in control theory 49M25 Discrete approximations in optimal control 49N90 Applications of optimal control and differential games Keywords:numerical methods of parameter optimization; asymptotically stable system; discrete problem; satellite stabilization system PDFBibTeX XMLCite \textit{A. Guerman} et al., Math. Probl. Eng. 2011, Article ID 526167, 19 p. (2011; Zbl 1214.93097) Full Text: DOI EuDML References: [1] R. N. Ismailov, “The peack effect in stationary linear systems with scalar inputs and outputs,” Automation and Remote Control, vol. 48, no. 8, part 1, pp. 1018-1024, 1987. · Zbl 0711.93040 [2] H. J. Sussmann and P. V. Kokotović, “The peaking phenomenon and the global stabilization of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 36, no. 4, pp. 424-440, 1991. · Zbl 0749.93070 · doi:10.1109/9.75101 [3] Ya. Z. Cypkin and P. V. Bromberg, “On the degree of stability of linear systems,” USSR Academy of Sciences, Branch of Technical Sciences, vol. 1945, no. 12, pp. 1163-1168, 1945. · Zbl 0060.05705 [4] F. H. Clarke, Optimization and Nonsmooth Analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, New York, NY, USA, 1983. · Zbl 0582.49001 [5] G. Smirnov and F. Miranda, “Filippov-Gronwall inequality for discontinuous differential inclusions,” International Journal of Mathematics and Statistics, vol. 5, no. A09, pp. 110-120, 2009. [6] V. A. Sarychev, “Investigation of the dynamics of a gravitational stabilization system,” in XIIIth International Astronautical Congress, pp. 658-690, Varna, Bulgaria, 1964. [7] R. L. Borrelli and I. P. Leliakov, “An optimization technique for the transient response of passively stable satellites,” Journal of Optimization Theory and Applications, vol. 10, pp. 344-361, 1972. · Zbl 0233.70018 · doi:10.1007/BF00935399 [8] V. A. Sarychev and V. V. Sazonov, “Optimal parameters of passive systems for satellite orientation,” Cosmic Research, vol. 14, no. 2, pp. 183-193, 1976. [9] R. Fletcher, Practical Methods of Optimization, John Wiley & Sons, Chichester, UK, 2nd edition, 1987. · Zbl 0905.65002 [10] A. M. Liapunov, Stability of Motion, Academic Press, New York, NY, USA, 1966. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.