基于状态相关系数系统的非线性控制

Nonlinear Control Based on State-dependent Coefficient Systems

针对非线性仿射系统的镇定问题,将待镇定系统表达成相应的状态相关系数系统。在短时段内,可以用一个线性定常系统逼近该状态相关系数系统,将该线性定常系统的镇定控制器用来控制原非线性系统。该设计方法的优点是:设计简单,只用到线性定常系统的控制方法,无需构造复杂的李亚普诺夫函数;扩展容易,可以结合各种线性系统设计方法进行控制器设计。在状态相关系数矩阵满足可换性条件时,可以保证闭环系统的稳定性。对小车倒立摆的仿真结果表明:用该设计方法构造的控制器可以很好地镇定系统。

The nonlinear affine systems were represented by state -dependent coefficient systems. In a short time interval, the state - dependent coefficient systems could be approximated by linear systems, with which linear stabilizing controllers were designed and used to stabilize the original nonlinear affine systems. The stability of the closed - loop systems was ascertained under the condition that the coefficients matrices were commutative. The design approach can be combined with many design methodologies for linear systems, and has the advantages of simplicity and avoiding the construction of complex Lyapunov functions. Simulation of the cart pendulum system shows the effectiveness of the design method.