On Hamilton–Jacobi formalism in time-delay control systems
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 5, pp. 269-277
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

For control problems under disturbances in time-delay systems, methods of defining the value of optimal guaranteed result and optimal control strategies are considered on the basis of generalized solutions of appropriate functional equations of the Hamilton–Jacobi type.
Keywords: time-delay systems, control theory, differential games, dynamic programming, Hamilton–Jacobi equations, minimax solutions, viscosity solutions.
@article{TIMM_2010_16_5_a30,
     author = {N. Yu. Lukoyanov},
     title = {On {Hamilton{\textendash}Jacobi} formalism in time-delay control systems},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {269--277},
     year = {2010},
     volume = {16},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2010_16_5_a30/}
}
TY  - JOUR
AU  - N. Yu. Lukoyanov
TI  - On Hamilton–Jacobi formalism in time-delay control systems
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2010
SP  - 269
EP  - 277
VL  - 16
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/TIMM_2010_16_5_a30/
LA  - en
ID  - TIMM_2010_16_5_a30
ER  - 
%0 Journal Article
%A N. Yu. Lukoyanov
%T On Hamilton–Jacobi formalism in time-delay control systems
%J Trudy Instituta matematiki i mehaniki
%D 2010
%P 269-277
%V 16
%N 5
%U http://geodesic.mathdoc.fr/item/TIMM_2010_16_5_a30/
%G en
%F TIMM_2010_16_5_a30
N. Yu. Lukoyanov. On Hamilton–Jacobi formalism in time-delay control systems. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 5, pp. 269-277. http://geodesic.mathdoc.fr/item/TIMM_2010_16_5_a30/

[1] Krasovskii N. N., Subbotin A. I., Game-Theoretical Control Problems, Springer-Verlag, Berlin, 1988 | MR | Zbl

[2] Krasovskii N. N., “Differential games. Approximation and formal models”, Mat. Sbornik, 107(149):4 (1978), 541–571 | MR | Zbl

[3] Krasovskii N. N., Stability of Motion. Applications of Lyapunov's Second Method to Differential Systems and Equations with Delay, Stanford Univ. Press, 1963 | MR | Zbl

[4] Osipov Yu. S., “Differential games of systems with aftereffect”, Dokl. Akad. Nauk SSSR, 196:4 (1971), 779–782 | MR | Zbl

[5] Subbotin A. I., “Generalization of the main equation of the differential game theory”, Dokl. Akad. Nauk SSSR, 254:2 (1980), 293–297 | MR | Zbl

[6] Kim A. V., Functional Differential Equations. Application of $i$-Smooth Calculus, Kluwer, Dordrecht, 1999 | MR

[7] Krasovskii N. N., “To problem of unification of differential games”, Dokl. Akad. Nauk SSSR, 226:6 (1976), 1260–1263 | MR

[8] Subbotin A. I., Generalized Solutions of First-Order PDEs: The Dynamical Optimization Perspective, Birkhäuser, Boston etc., 1995 | MR

[9] Crandall M. G., Lions P.-L., “Viscosity solutions of Hamilton–Jacobi equations”, Trans. Amer. Math. Society, 277:1 (1983), 1–42 | DOI | MR | Zbl

[10] Lukoyanov N. Yu., “Functional Hamilton–Jacobi type equations in ci-derivatives for systems with distributed delays”, Nonlinear Funct. Anal. and Appl., 8:3 (2003), 365–397 | MR | Zbl

[11] Lukoyanov N. Yu., “Functional Hamilton–Jacobi type equations with ci-derivatives in control problems with hereditary information”, Nonlinear Funct. Anal. and Appl., 8:4 (2003), 535–556 | MR

[12] Lukoyanov N. Yu., “On optimality conditions for the guaranteed result in control problems for time-delay systems”, Trudy Inst. Mat. Mekh. UrO RAN, 15, no. 3, 2009, 158–169

[13] Lukoyanov N. Yu., “Minimax and viscosity solutions in optimization problems for hereditary systems”, Trudy Inst. Mat. Mekh. UrO RAN, 15, no. 4, 2009, 183–194

[14] Aubin J. P., Haddad G., “History path dependent optimal control and portfolio valuation and management”, Positivity, 6 (2002), 331–358 | DOI | MR | Zbl

[15] Garnysheva G. G., Subbotin A. I., “Strategies of minimax aiming in the direction of quasigradient”, Prikl. Mat. Mekh., 58:4 (1994), 5–11 | MR | Zbl

[16] Soner H. M., “On the Hamilton–Jacobi–Bellman equations in Banach spaces”, J. Optim. Theory and Appl., 57:3 (1988), 429–437 | DOI | MR | Zbl