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Bayesian optimal control for a non-autonomous stochastic discrete time system

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  • Dassios, Ioannis K.
  • Szajowski, Krzysztof J.

Abstract

The main objective of this article is to develop Bayesian optimal control for a class of non-autonomous linear stochastic discrete time systems. By taking into consideration that the disturbances in the system are given by a random vector with components belonging to an exponential family with a natural parameter, we prove that the Bayes control is the solution of a linear system of algebraic equations. For the case that this linear system is singular, we apply optimization techniques to gain the Bayesian optimal control. Furthermore, we extend these results to generalized linear stochastic systems of difference equations and provide the Bayesian optimal control for the case where the coefficients of this type of systems are non-square matrices.

Suggested Citation

  • Dassios, Ioannis K. & Szajowski, Krzysztof J., 2016. "Bayesian optimal control for a non-autonomous stochastic discrete time system," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 556-564.
    • Handle: RePEc:eee:apmaco:v:274:y:2016:i:c:p:556-564
    DOI: 10.1016/j.amc.2015.11.002
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    References listed on IDEAS

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    1. Tesfatsion, Leigh S., 1982. "A Dual Approach to Bayesian Inference and Adaptive Control," Staff General Research Papers Archive 11213, Iowa State University, Department of Economics.
    2. Runggaldier, Wolfgang J., 1998. "Concepts and methods for discrete and continuous time control under uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 25-39, May.
    3. Ioannis Dassios & Alexandros Zimbidis & Charalambos Kontzalis, 2014. "The Delay Effect in a Stochastic Multiplier–Accelerator Model," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 3(1), pages 1-24, December.
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    Cited by:

    1. Fernando Ortega & Maria Filomena Barros, 2020. "The Samuelson macroeconomic model as a singular linear matrix difference equation," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 9(1), pages 1-10, December.
    2. Tharanidharan, V. & Sakthivel, R. & Ren, Yong & Marshal Anthoni, S., 2022. "Robust finite-time PID control for discrete-time large-scale interconnected uncertain system with discrete-delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 370-383.
    3. Maria Filomena Barros & Fernando Ortega, 2019. "An optimal equilibrium for a reformulated Samuelson economic discrete time system," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 8(1), pages 1-10, December.

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