期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 68, 期 3, 页码 1685-1691出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2022.3151195
关键词
Numerical stability; Stability criteria; Asymptotic stability; Optimal control; Lyapunov methods; Steady-state; Nonlinear dynamical systems; Bellman theory; discrete-time systems; finite-time stability; finite-time stabilization; optimal control
This article presents a framework for addressing the problem of optimal nonlinear analysis and feedback control for finite-time stability and finite-time stabilization for nonlinear discrete-time controlled dynamical systems. The finite-time stability of the closed-loop nonlinear system is guaranteed by satisfying a difference inequality involving fractional powers and a minimum operator. The Lyapunov function used in this framework can be seen as the solution to a difference equation corresponding to a steady-state form of the Bellman equation, ensuring both finite-time stability and optimality. Finally, a numerical example demonstrates the effectiveness of the proposed framework.
Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Sufficient conditions for finite-time stability have recently been developed in the literature for discrete-time dynamical systems. In this article, we build on these results to develop a framework for addressing the problem of optimal nonlinear analysis and feedback control for finite-time stability and finite-time stabilization for nonlinear discrete-time controlled dynamical systems. Finite-time stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that satisfies a difference inequality involving fractional powers and a minimum operator. This Lyapunov function can clearly be seen to be the solution to a difference equation that corresponds to a steady-state form of the Bellman equation, and hence, guaranteeing both finite-time stability and optimality. Finally, a numerical example is presented to demonstrate the efficacy of the proposed finite-time discrete stabilization framework.
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