非线性系统平稳分岐解镇定的简化原理

Reduction principle of stationary bifurcation stabilization of nonlinear systems

研究了一类具有线性不可控模态的非线性系统平稳分岐解的镇定问题.假定系统参数不可测量.基于不变流形理论,从原非线性系统导出了一个一维的简化方程.从简化方程的性质导出了原系统能分岐镇定的一些充分和必要条件.并举例说明了此方法的有效性.

This paper studies the problem of stationary bifurcation stabilization of a class of nonlinear control systems, in which the parameter is not measurable. Based on the theory of invariant manifolds, a reduction system of one dimension is derived. Bifurcation stabilization of one dinensional nonlinear system is relatively easy to be solved. Some necessary conditions and sufficient conditions for bifurcation stabilization of the original nonlinear system are obtained from properties of the reduction system. An example is presented to illustrate the utility of the results.