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Nonlinear Optimal Control for Stochastic Dynamical Systems

Author

Listed:
  • Manuel Lanchares

    (School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150, USA)

  • Wassim M. Haddad

    (School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150, USA)

Abstract

This paper presents a comprehensive framework addressing optimal nonlinear analysis and feedback control synthesis for nonlinear stochastic dynamical systems. The focus lies on establishing connections between stochastic Lyapunov theory and stochastic Hamilton–Jacobi–Bellman theory within a unified perspective. We demonstrate that the closed-loop nonlinear system’s asymptotic stability in probability is ensured through a Lyapunov function, identified as the solution to the steady-state form of the stochastic Hamilton–Jacobi–Bellman equation. This dual assurance guarantees both stochastic stability and optimality. Additionally, optimal feedback controllers for affine nonlinear systems are developed using an inverse optimality framework tailored to the stochastic stabilization problem. Furthermore, the paper derives stability margins for optimal and inverse optimal stochastic feedback regulators. Gain, sector, and disk margin guarantees are established for nonlinear stochastic dynamical systems controlled by nonlinear optimal and inverse optimal Hamilton–Jacobi–Bellman controllers.

Suggested Citation

  • Manuel Lanchares & Wassim M. Haddad, 2024. "Nonlinear Optimal Control for Stochastic Dynamical Systems," Mathematics, MDPI, vol. 12(5), pages 1-30, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:647-:d:1344064
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    References listed on IDEAS

    as
    1. Chang,Fwu-Ranq, 2009. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521541947.
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