一类不确定高阶随机非线性系统的自适应镇定

通过状态反馈和自适应技术解决了一类不确定高阶随机非线性系统的全局镇定问题.尽管对于确定性系统的类似问题已有大量研究,但由于存在随机干扰的影响,研究该问题同样具有重要意义,并且,更难以找到合适的二次连续可微的控制李亚普诺夫函数.通过引入新的控制李亚普诺夫函数并利用增加幂积分的方法,成功地设计了自适应连续状态反馈控制器,使得原系统的状态在概率意义下全局渐近稳定,而其他闭环系统状态在概率意义下全局稳定.仿真算例验证了控制器设计方法的有效性.

Adaptive stabilization for a class of uncertain high-order stochastic nonlinear systems

This paper is devoted to solvingthe global stabilization problem viastate feedback and adaptive technique for a class of uncertain high order stochastic nonlinear systems. Although much effort has been made for deterministic ones, the problem is significant and deserves attention since it involves the effects caused by the stochastic disturbance and, for which, an appropriate control Lyapunov  function should be twice continuously differentiable and hence is moredifficult to find. By introducing a novel control Lyapunov  function and using the method of adding a power integrator, an adaptive state feedback continuous controller is successfully designed, which guarantees that the original system states are globally asymptotically stable in probability while the other closed loop signals are globally stable in probability. A simulation example is provided to illustrate the effectiveness of the proposed approach. 