Abstract
This paper deals with finite time inverse optimal stabilization for stochastic nonlinear systems. A concept of the stochastic finite time control Lyapunov function (SFT-CLF) is presented, and a control law for finite time stabilization for the closed-loop system is obtained. Furthermore, a sufficient condition is developed for finite time inverse optimal stabilization in probability, and a control law is designed to ensure that the equilibrium of the closed-loop system is finite time inverse optimal stable. Finally, an example is given to illustrate the applications of theorems established in this paper.
Highlights
In many engineering fields, it is desirable that trajectories of a dynamical system converge to an equilibrium in finite time
The stochastic finite time control Lyapunov function is defined as follows
An explicit feedback control law is designed such that the equilibrium x = 0 of the closed-loop system is globally finite time stable in probability
Summary
It is desirable that trajectories of a dynamical system converge to an equilibrium in finite time. Florchinger [16] proved that the feedback control law defined in [15] can globally asymptotically stabilize stochastic nonlinear systems. This result was extended when the drift as well as the controlled part was corrupted by a noise in the works of Chabour and Oumoun [17]. After considering the finite time stabilization of stochastic systems, an important problem is how to further design a stabilizing controller which is optimal with respect to meaningful cost functionals, that is, the inverse optimal control. We consider the finite time inverse optimal controller design. The effectiveness of the proposed design technique is illustrated by an example
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