Skip to main content
SpringerLink
Log in

Algorithms for solving discrete optimal control problems with infinite time horizon and determining minimal mean cost cycles in a directed graph as decision support tool

  • Original Paper
  • Published:
Central European Journal of Operations Research Aims and scope Submit manuscript

Abstract

Time-discrete systems with a finite set of states are considered. Discrete optimal control problems with infinite time horizon for such systems are formulated. We introduce a certain graph-theoretic structure to model the transitions of the dynamical system. Algorithms for finding the optimal stationary control parameters are presented. Furthermore, we determine the optimal mean cost cycles. This approach can be used as a decision support strategy within such a class of problems; especially so-called multilayered decision problems which occur within environmental emission trading procedures can be modelled by such an approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bellman R (1959) Functional equations in the theory of dynamic programming, XI-Limit theorems. Rand Circolo Math Palermo 8(3): 343–345

    Article  Google Scholar 

  • Bellman R, Kalaba R (1965) Dynamic programming and modern control theory. Academic Press, New York

    Google Scholar 

  • Christofides N (1975) Graph theory: an algorithmic approach. Academic Press, New York

    Google Scholar 

  • Karp R (1978) A characterization of the minimum cycle mean in a digraph. Discret Math 23(3): 309–311

    Article  Google Scholar 

  • Khachian L (1982) On an exact solution of the system of linear inequalities and linear programming problems USSR. Comput Math Math Phys 22: 999–1002

    Google Scholar 

  • Lawler E (1996) Optimal cycles in doubly weighted directed linear graphs. International symposium on theory of graphs. Dunod, Paris, p 209

  • Lozovanu D (1991) Extremal-combinatorial problems and algorithms for its solving. Kishinev, Stiinta (in Russian)

  • Lozovanu D, Petic C (1998) Algorithms for finding the minimum cycle mean in the weighted directed graph. Comput Sci J Moldova 6, n. 1(26)

    Google Scholar 

  • Lozovanu D, Pickl S (2005) Nash equilibria for multiobjective control of time-discrete systems and polynomial-time algorithms for k-partite networks. Central Eur J Oper Res 13(2): 127–146

    Google Scholar 

  • Lozovanu D, Pickl S (2006) An approach for an algorithmic solution of discrete decision problems and their game-theoretical extension. Central Eur J Oper Res 14(4): 357–375

    Article  Google Scholar 

  • Lozovanu D, Pickl S (2007) Algorithms and the calculation of Nash equilibria for multi-objective control of time-discrete systems and polynomial-time algorithms for dynamic c-games on networks. Eur J Oper Res 181: 1214–1232

    Article  Google Scholar 

  • Lozovanu D, Pickl S (2009) Optimization and multiobjective Control of time-discrete systems and dynamical games: dynamic networks and multilayered structures. Springer, 300 p

  • Romanovski I (1967) Optimization of stationary control of discrete deterministic processes. Cybernetics 2: 66–78

    Google Scholar 

  • Weber G-W, Alparslan G, Söyler B (2007) A new mathematical approach in environmental and life sciences: gene-environment networks and their dynamics. To appear in environmental modeling and assessment. doi:10.1007/s10666-007-9137-z

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Academy of Sciences, Academy str., 5, 2028, Chisinau, Moldova

    Dmitrii Lozovanu

  2. Institut für Theoretische Informatik, Mathematik und Operations Research, Fakultät für Informatik, Universität der Bundeswehr, Munich, Germany

    Stefan Pickl

Authors
  1. Dmitrii Lozovanu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stefan Pickl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dmitrii Lozovanu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lozovanu, D., Pickl, S. Algorithms for solving discrete optimal control problems with infinite time horizon and determining minimal mean cost cycles in a directed graph as decision support tool. Cent Eur J Oper Res 17, 255–264 (2009). https://doi.org/10.1007/s10100-009-0090-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10100-009-0090-6

Keywords

Search

Navigation