一类高阶随机非线性系统的状态反馈镇定

State-feedback stabilization of a class of high-order stochastic nonlinear systems

针对一类既不可反馈线性化也不仿射于控制输入的高阶随机非线性系统,研究其状态反馈镇定问题.利用齐次占优和反推技术,所设计的状态反馈控制器使得整个闭环系统在[0,+∞)上几乎处处有唯一解,并使得闭环系统的平衡点是依概率全局渐近稳定的.主要贡献是完全取消了高阶系统的阶次限制,得到了新的结果.最后通过数值仿真验证了所提出控制方案的有效性.

For a class of high-order stochastic nonlinear systems, which are neither necessarily feedback linearizahle nor affine in the control input, this paper investigates the problem of state-feedback stabilization. By using the homogeneous domination and backstepping technique, a state-feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on [0, ＋oo）, and the equilibrium of the closed-loop system is globally asymptotically stable in probability. The main contribution lies in completely relaxing the power order restriction for high-order systems and leads to new results. A simulation example shows the effectiveness of the state-feedback controller.