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Original Articles

On necessary optimality conditions in discrete control systems

, &
Pages 2097-2106 | Received 08 Oct 2014, Accepted 24 Mar 2015, Published online: 29 Apr 2015

References

  • Ahlbrandt, C.D. (1993). Equivalence of discrete Euler equations and discrete Hamiltonian systems. Journal of Mathematical Analysis and Applications, 180(1), 498–517.
  • Arutyunov A.V., & Marinkovic, B. (2005). Necessary conditions for optimality in discrete optimal control problems [in Russian]. Vestnik MGU Seriya, 15, 43–48.
  • Ashchepkov, L.T. (1972). To necessary optimality conditions of higher order for singular controls in discrete systems [in Russian]. Differential Equations, 8(10), 1857–1867.
  • Ashchepkov, L.T. (1973). Multipoint optimality conditions of discrete systems [in Russian]. Collection: Differential and integral equations, 1, 37–46.
  • Ashchepkov, L.T. (1987). Optimal control with discontinuous systems [in Russian]. Moscow: Nauka.
  • Bellman, R. (2003). Dynamic programming. Mineola, NY: Dover Publications.
  • Boltyanskii, V.G. (1978). Optimal control of discrete systems. New York, NY: Wiley.
  • Butkovskii, A.G. (1963). On necessary and sufficient optimality conditions for impulse control systems. Avtomatika i telemekhanika, 24(8), 1056–1064.
  • Dolezal, J. (1988) Optimal control discrete-time systems ( Lecture Notes in Control and Information Sciences). New York, NY: Springer.
  • Dubovitskii, A.Ya. (1978). Discrete maximum principle. Automation and Remote Control, 10(1), 55–71.
  • Dzyuba, N.N., & Pshenichniy, B.N. (1975). On discrete maximum principle [in Russian]. Kibernetika, 2, 25–36.
  • Fan, Lian-Chen, & Wan, Chu-Sen. (1967). Discrete maximum principle [in Russian]. Moscow: Mir.
  • Ferreira, J.A.S., & Vidal, R.V.V. (1986). On the connections between mathematical programming and discrete optimal control ( Lecture Notes in Control and Information Sciences). New York, NY: Springer.
  • Gabasov, R. (1968). On the theory of optimal processes in discrete systems [in Russian]. Žhurnal Vyčhislitel'noi Matemaki i Matematicheskoi Fiziki, 8, 780–796.
  • Gabasov, R., & Gusakova, M.L. (1971). Maximum principle for general discrete systems. Differencialnye Uravnenija, 7, 1581–1590.
  • Gabasov, R., & Kirillova, F.M. (1969). Theory of necessary conditions for optimality for discrete systems. Automation and Remote Control, 12, 1921–1928.
  • Gabasov, R., Kirillova, F.M., & Mordukhovich, B.S. (1973). A discrete maximum principle [in Russian]. Doklady Akademii Nauk SSSR, 213, 19–22.
  • Gabasov, R., Kirillova, F.M., & Mordukhovich, B.S. (1993). ϵ-maximum principle for suboptimal controls [in Russian]. Doklady Akademii Nauk SSSR, 268, 525–529.
  • Gaishun, I.V. (1996). Multiparameter control systems. Minsk: Navuka i Tèkhnika.
  • Gaishun, I.V. (2001). Systems with discrete time [in Russian]. Minsk: National Academy of Sciences of Belarus, Institute of Mathematics.
  • Gorokhovik, S.Ya. (1985). Necessary optimality conditions for singular controls in discrete systems with terminal constraints [in Russian]. Izvestija Akademii Nauk BSSR, Ser. fiz.-mat. 3, 35–40.
  • Gorokhovik, V.V., Gorokhovik, S.Ya., & Marinković, B. (2009). Necessary optimality conditions for a smooth discrete-time optimal control problem with vector-valued objective function [in Russian]. Proceedings of Institute of Mathematics (Minsk), 17, 27–40.
  • Gorokhovik, V.V., Gorokhovik, S.Ya., & Marinković, B. (2013). First and second order necessary optimality conditions for a discrete-time optimal control problem with a vector-valued objective function. Positivity, 17, 483–500.
  • Gorokhovik, V.V., & Simonov, A.Yu. (1998). Optimality conditions for the input of a discrete-time system in the control problem with respect to the preference relation [in Russian]. Izvestija Akademii Nauk BSSR, Ser. fiz.-mat. 4, 41–46.
  • Gurman, V.I. (1976). Optimization of discrete systems [in Russian]. Irkutsk State University: ISU.
  • Halkin, H. (1966). A maximum principle of the Pontryagin type for systems described by nonlinear difference equations. SIAM Journal on Control, 4, 90–111.
  • Hilscher, R., & Zeidan, V. (2002). Discrete optimal control: Second order optimality conditions. Journal of Difference Equations and Applications, 8, 875–896.
  • Holtzman, J.M., & Halkin, H. (1966). Directional convexity and the maximum principle for discrete systems. SIAM Journal on Control, 4, 2, 213–275.
  • Jakson, R., & Horn, F. (1965). On discrete analoques of Pontryagins maximum principle. International Journal of Control, 1 389–395.
  • Jordan, B.W., & Polak, E. (1964). Theory of a class of discrete optimal control systems. Journal of Electronics and Control, 17, 697–711.
  • Krasovsky, N.N. (1957). On a problem of optimal control [in Russian]. Prikladnaya matematika I mekhanika, 21, 670–677.
  • Malanowski, K. (1991). Stability and sensitivity analysis of discrete optimal control problems. Problems of Control and Information Theory, 28, 187–200.
  • Mansimov, K.B. (2013). Discrete systems [in Russian]. Baku: Elm.
  • Mardanov, M.J., & Melikov, T.K. (2014). On necessary optimality conditions for discrete control systems [in Russian]. In Proceedings of the International Conference devoted to 55 years of the Institute of Mathematics and Mechanics (pp. 242–245). Baku: Elm.
  • Marinković, B. (2006). Sensitivity analysis for discrete optimal control problems. Mathematical Methods of Operations Research, 63, 513–524.
  • Marinković, B. (2007). Optimality conditions for discrete optimal control problems. Optimization Methods and Software, 22, 959–969.
  • Marinković, B. (2008). Optimality conditions in discrete optimal control problems with state constraints. Numerical Functional Analysis and Optimization, 28, 945–955.
  • Melikov, T.K. (1979). To necessary optimality conditions for distributed parameters systems. Dep. in VINITI, AS of the USSR, 2637-79, 31.
  • Minchenko, L.I. (1976). On necessary optimality conditions for some classes of discrete control systems [in Russian]. Differencialnye Uravnenija, 12(7), 1211–1218.
  • Moiseev, N.N. (1975). Elements of theory of optimal systems [in Russian]. Moscow: Nauka.
  • Mordukhovich, B.S. (1973). On optimal control of discrete systems [in Russian]. Differencialnye Uravnenija, 9(4), 727–734.
  • Mordukhovich, B.S. (1988a). Approximate maximum principle for finite difference control systems. USSR Computational Mathematics and Mathematical Physics, 28, 106–114.
  • Mordukhovich, B.S. (1988b). Approximation methods in problems of optimization and control [in Russian]. Moscow: Nauka.
  • Mordukhovich, B.S. (2005a). Variational analysis and generalized differentiation. I: General theory. Berlin: Springer.
  • Mordukhovich, B.S. (2005b). Variational analysis and generalized differentiation. II: Applications. Berlin: Springer.
  • Nahorski, Z., Ravn, H.F., & Vidal R.V.V., (1984). A discrete-time maximum principle: A survey and some new results. International Journal of Control, 40, 533–554.
  • Pearson, J.D. Jr, & Sridhar, R. (1966). A discrete optimal control problem. IEEE Transactions on Automatic Control, 11, 171–174.
  • Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., & Mishchenko, E.F. (1962). Mathematical theory of optimal processes. New York, NY: Wiley.
  • Propoi, A.I. (1973). Elements of the theory of optimal discrete processes [in Russian]. Moscow: Nauka.
  • Pshenichnyi, B.N. (1971) Necessary conditions for an extremum. New York, NY: Marcel Dekker.
  • Rozonoer, L.I. (1959). L.S. Pontryagin's maximum principle in theory of optimal systems [in Russian]. Avtomatika i telemekhanika, 20, 1320–1334.
  • Tou, J.T. (1964). Synthesis of discrete systems subject to control-signal saturation. Journal of the Franklin Institute, 277, 401–413.
  • Vasilev, F.P. (1981). Methods for solving extremal problems [in Russian]. Moscow: Nauka.
  • Wells, C.H. (1967). Minimun norm control of discrete systems. IEEE International Convention Record, 3, 55–64.

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