The sensitivity functionals in the Bolts problem for multivariate dynamic systems described by integral equations with delay time | Vestnik Tomskogo gosudarstvennogo universiteta. Upravlenie, vychislitelnaja tehnika i informatika – Tomsk State University Journal of Control and Computer Science. 2019. № 46. DOI: 10.17223/19988605/46/10

The sensitivity functionals in the Bolts problem for multivariate dynamic systems described by integral equations with delay time

The variational method of calculation of sensitivity functionals (connecting first variation of quality functionals with variations of variable parameters) and sensitivity coefficients (components of vector gradient from the quality functional to constant parameters) for multivariate non-linear dynamic systems described by continuous vectorial Volterra's integral equations of the second-kind with delay time is developed. The presence of a discontinuity in an initial value of coordinates and dependence the initial and final instants and magnitude of delay time from parameters are taken into account also. The base of calculation is the decision of corresponding integral conjugate equations for Lagrange's multipliers in the opposite direction of time.

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Keywords

variational method, sensitivity functional, sensitivity coefficient, integral equation, conjugate equation, delay time, вариационный метод, функционал чувствительности, интегральное уравнение с запаздывающим аргументом, функционал качества работы системы, задача Больца, сопряженное уравнение

Authors

Name	Organization	E-mail
Rouban Anatoly I.	Siberian Federal University	ai-rouban@mail.ru

Всего: 1

References

Rouban, A.I. (2002) Coefficients and Functional of Sensitivity for dynamic Systems described by integral Equations with dead Time. AMSE Jourvajs, Series Advances C. 57(3). pp. 15-34.

Rouban, A.I. (2000) Coefficients and functionals of sensitivity for continuous many-dimensional dynamic systems described by integral equations with delay time. 5th International Conference on Topical Problems of Electronic Instrument Engineering. Proceedings APEIE-2000. Vol. 1. Novosibirsk: Novosibirsk State Technical University. pp. 135-140.

Rouban, A.I. (1999) Sensitivity coefficients for many-dimensional continuous and discontinuous dynamic systems with delay time. AMSE Jourvajs, Series Advances A. 36(2). pp. 17-36.

Rouban, A.I. (1999) Coefficients and functionals of sensitivity for multivariate systems described by integral and integro-differetial equations. AMSE Jourvajs, Series Advances A. 35(1). pp. 25-34.

Rouban, A.I. (2017) The sensitivity functionals in the Bolts's problem for multivariate dynamic systems described by ordinary integral equations. Vestnik Tomskogo gosudarstvennogo universiteta. Upravlenie, vychislitel'naya tekhnika i informatika -Tomsk State University Journal of Control and Computer Science. 38. pp. 30-36. DOI: 10.17223/19988605/38/5

Ruban, A.I. (1982) Identification and Sensitivity of Complex Systems. Tomsk: Tomsk State University.

Tsikunov, A.M. (1984) Adaptive Control of Objects with Delay Time. Moscow: Nauka.

Haug, E.J., Choi, K.K. & Komkov, V. (1988) Design Sensitivity Analysis of Structural Systems. Moscow: Mir.

Afanasyev, V.N., Kolmanovskiy, V.B. & Nosov, V.R. (1998) The Mathematical Theory of Designing of Control Systems. Moscow: Vysshaya shkola.

Voronov, A.A. (1979) Stability, controllability, observability. Moscow: Nauka.

Rosenvasser, E.N. & Yusupov, R.M. (1981) Sensitivity of Control Systems. Moscow: Nauka.

Kostyuk, V.I. & Shirokov, L.A. (1981) Automatic Parametrical Optimization of Regulation Systems. Moscow: Energoizdat.

Ruban, A.I. (1975) Nonlinear Dynamic Objects Identification on the Base of Sensitivity Algorithm. Tomsk: Tomsk State University.

Bedy, Yu.A. (1976) About asymptotic properties of decisions of the equations with delay time. Differential Equations. 12(9). pp. 1669-1682

Rosenvasser, E.N. & Yusupov, R.M. (1977) Sensitivity Theory and Its Application. Vol. 23. Moscow: Svyaz.

Mishkis, A.D. (1977) Some problems of the differential equations theory with deviating argument. Successes of Mathematical Sciences. 32(2). pp. 173-202

Gekher, K. (1973) Theory of Sensitivity and Tolerances of Electronic Circuits. Moscow: Sovetskoe radio.

Speedy, C.B., Brown, R.F. & Goodwin, G.C. (1973) Control Theory: Identification and Optimal Control. Moscow: Mir.

Bryson, A.E. & Ho, Ju-Chi. (1972) Applied Theory of Optimal Control. Moscow: Mir.

Gorodetsky, V.I., Zacharin, F.M., Rosenvasser, E.N. & Yusupov, R.M. (1971) Methods of Sensitivity Theory in Automatic Control. Leningrad: Energiya.

Krutyko, P.D. (1969) The decision of a identification problem by a sensitivity theory method. News of Sciences Academy of the USSR. Technical Cybernetics. 6. pp. 146-153.

Petrov, B.N. & Krutyko, P.D. (1970) Application of the sensitivity theory in automatic control problems. News of Sciences Academy of the USSR. Technical Cybernetics. 2. pp. 202-212.

Rosenvasser, E.N. & Yusupov, R.M. (1969) Sensitivity of automatic control sysiems. Leningrad: Energiya.

Ostrovsky, G.M. & Volin, Yu.M. (1967) Methods of optimization of chemical reactors. Moscow: Khimiya.

Bellman, R. & Kuk, K.L. (1967) Differential-difference equation. Moscow: Mir.