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Lyapunov’s stability analysis for first degree polynomial systems, subject to risk-sensitive control

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  • Hernandez-Castorena, Gerardo Armando
  • Alcorta-Garcia, Maria Aracelia
  • Saenz-Esqueda, Jose Armando
  • Mendez, Gerardo Maximiliano

Abstract

This work presents a novel methodology to verify the stability of first-degree stochastic polynomial systems under a Risk-Sensitive (RS) optimal control using Lyapunov’s stability analysis theory. The so-called Lyapunov’s indirect method is applied to prove its stability when it is combined with the dynamics of Riccati’s gain equation. The proposed methodology guarantees both the exponential stability of deterministic systems and the robustness of stochastic systems. Simulation results demonstrate the robustness, the effectiveness and the feasibility of this proposal.

Suggested Citation

  • Hernandez-Castorena, Gerardo Armando & Alcorta-Garcia, Maria Aracelia & Saenz-Esqueda, Jose Armando & Mendez, Gerardo Maximiliano, 2024. "Lyapunov’s stability analysis for first degree polynomial systems, subject to risk-sensitive control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 464-473.
    • Handle: RePEc:eee:matcom:v:226:y:2024:i:c:p:464-473
    DOI: 10.1016/j.matcom.2024.07.006
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    References listed on IDEAS

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    1. Ronald A. Howard & James E. Matheson, 1972. "Risk-Sensitive Markov Decision Processes," Management Science, INFORMS, vol. 18(7), pages 356-369, March.
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