On necessary optimality conditions in discrete control systems

The paper deals with a nonlinear discrete-time optimal control problem with a cost functional of terminal type. Using a new variation of the control and new properties of optimal controls, we prove the linearised optimality conditions extending such classical optimality conditions. Along with this, various optimality conditions of quasi-singular controls are obtained. Finally, the examples illustrating the rich content of the obtained results are illustrated.

[1]  Boban Marinkovic.  Sensitivity analysis for discrete optimal control problems , 2006, Math. Methods Oper. Res..

[2]  Vera Zeidan,et al.  Discrete Optimal Control: Second Order Optimality Conditions , 2002 .

[3]  H. Halkin.  A Maximum Principle of the Pontryagin Type for Systems Described by Nonlinear Difference Equations , 1966 .

[4]  Boban Marinković.  Optimality Conditions in Discrete Optimal Control Problems with State Constraints , 2007 .

[5]  Fang-Di Kong.  Optimality Conditions for Discrete Optimal Control Problems , 2017 .

[6]  V. Gorokhovik,et al.  First and second order necessary optimality conditions for a discrete-time optimal control problem with a vector-valued objective function , 2013 .

[7]  M. L. Chambers.  The Mathematical Theory of Optimal Processes , 1965 .

[8]  R. Vidal,et al.  The discrete-time maximum principle: a survey and some new results , 1984 .

[9]  H. Halkin,et al.  Discretional Convexity and the Maximum Principle for Discrete Systems , 1966 .

[10]  B. Mordukhovich.  Variational Analysis and Generalized Differentiation II: Applications , 2006 .

[11]  B. N. Pshenichnyi.  Necessary Conditions for an Extremum , 1971 .

[12]  B. Sh. Mordukhovich.  An approximate maximum principle for finite-difference control systems , 1989 .

[13]  R. V. Gamkrelidze,et al.  Theory of Optimal Processes , 1961 .

[14]  R. Jackson,et al.  On Discrete Analogues of Pontryagin's Maximum Principle† , 1965 .

[15]  Anatoly G. Kusraev.  Discrete maximum principle , 1983 .

[16]  R. Sridhar,et al.  A discrete optimal control problem , 1966 .

[17]  Rene Victor Valqui Vidal,et al.  On the connections between mathematical programming and discrete optimal control , 1986 .

[18]  F. Giannessi.  Variational Analysis and Generalized Differentiation , 2006 .

[19]  Sean R Eddy,et al.  What is dynamic programming? , 2004, Nature Biotechnology.

[20]  C. Ahlbrandt.  Equivalence of Discrete Euler Equations and Discrete Hamiltonian Systems , 1993 .

[21]  Juergen Manfred Harald Bruckner,et al.  Optimal Control of Discrete Systems , 1969 .

[22]  J. Tou.  Synthesis of discrete systems subject to control-signal saturation , 1964 .

[23]  B. W. Jordan,et al.  Theory of a Class of Discrete Optimal Control Systems , 1964 .

[24]  Jaroslav Dolezal.  Optimal control discrete-time systems , 1988 .

[25]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[26]  Tadeusz Styś,et al.  A discrete maximum principle , 1981 .