Work

Finite Time Stability and Optimal Control for Stochastic Dynamical Systems

Year: 2025

Type: article

Abstract: In real-world applications, finite time convergence to a desired Lyapunov stable equilibrium is often necessary. This notion of stability is known as finite time stability and refers to systems in which the state trajectory reaches an equilibrium in finite time. This paper explores the notion of finite time stability in probability within the context of nonlinear stochastic dynamical systems. Specifically, we introduce sufficient conditions based on Lyapunov methods, utilizing Lyapunov functions that satisfy scalar differential inequalities involving fractional powers for guaranteeing finite time stability in probability. Then, we address the finite time optimal control problem by developing a framework for designing optimal feedback control laws that achieve finite time stochastic stability of the closed-loop system using a Lyapunov function that also serves as the solution to the steady-state stochastic Hamilton–Jacobi–Bellman equation.

Source: Axioms

DOI: 10.3390/axioms14100767

Authors: Ronit Chitre, Wassim M. Haddad

Institution: Georgia Institute of Technology

Language: English

Topic: Stability and Control of Uncertain Systems

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Air Force Office of Scientific Research