Dissipativity, inverse optimal control, and stability margins for nonlinear discrete-time stochastic feedback regulators

Haddad, Wassim M.; Lanchares, Manuel

doi:10.1080/00207179.2022.2085178

Cited by 5 publications

(1 citation statement)

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“…Expanding on the findings of [15,16,18,19], this paper introduces a framework for analyzing and designing feedback controllers for nonlinear stochastic dynamical systems. Specifically, it addresses a feedback stochastic optimal control problem with a nonlinearnonquadratic performance measure over an infinite horizon.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Optimal Control for Stochastic Dynamical Systems

Lanchares,

Haddad

2024

Mathematics

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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.

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Section: Introductionmentioning

confidence: 99%