一类不确定非线性系统的鲁棒调节控制

摘要

The regulation control for the nonlinear uncertain systems is a central topic in robust control theory.This paper studies the robust regulation control problem for a class of nonlinear uncertain systems with unmodeled dynamics, uncertain nonlinearities, and unknown time-varying control coefficients.A robust regulation control scheme is presented using the changing supply rates technique,Nussbaum function gain as well as local small-gain conditions,and then the stability is analyzed.The simulation example verifies its efficacy.The results show that he proposed control scheme is robust against the unmodeled dynamics,uncertain nonlinearities,and unknown control coefficients;the changing supply rates technique could overcome the possible instability because of the unmodeled dynamic subsystem;Nussbaum function gain could effectively handle serious uncertainties in systems such as the unknown control direction,time-varying unknown control coefficients and so on;local small-gain conditions could well address the unmeasured states growth problems.%非线性不确定系统的调节控制是鲁棒控制理论的重要内容。文章研究一类带有未建模动态的控制系数完全未知的不确定非线性系统的鲁棒调节控制问题，应用改变供能函数率的方法、Nussbaum函数增益及局部小增益型条件，提出了鲁棒调节控制方案；分析了其稳定性；并对所提出的鲁棒调节控制方案进行了仿真验证。结果表明：所提出的控制方案对未建模动态、不确定非线性及时变未知控制系数具有良好的鲁棒性；应用改变供能函数率的方法能够克服未建模动态子系统可能导致的系统不稳定性；Nussbaum函数增益能够有效处理控制方向未知、时变的未知控制系数等严重的系统不确定性；局部小增益型条件可以有效解决不可测状态不确定性的增长问题。