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Finite-Time Stabilization and Optimal Feedback Control
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DOI：10.1109/TAC.2015.2454891.png)
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摘要
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Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Since finite-time convergence implies nonuniqueness of system solutions in reverse time, such systems possess non-Lipschitzian dynamics. Sufficient conditions for finite-time stability have been developed in the literature using continuous Lyapunov functions. In this technical note, we develop a framework for addressing the problem of optimal nonlinear analysis and feedback control for finite-time stability and finite-time stabilization. Finite-time stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that satisfies a differential inequality involving fractional powers. This Lyapunov function can clearly be seen to be the solution to a partial differential equation that corresponds to a steady-state form of the Hamilton-Jacobi-Bellman equation, and hence, guaranteeing both finite-time stability and optimality.
Keyword:
Differential inequalities
finite-time stability
finite-time stabilization
Hamilton-Jacobi-Bellman theory
optimal control
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7
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1.3W
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6.7W
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分享收藏Finite-time stability and instability of stochastic nonlinear systems随机非线性系统的有限时间稳定性和不稳定性.png)
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