具有扰动输入的不确定性非线性系统的输出调节极限性能

本文研究了一类具有扰动输入的不确定性非线性系统的输出调节问题, 给出了该类系统在最差的不确定性参数和扰动输入情况下系统输出调节的极限性能. 所讨论的非线性系统是可镇定非最小相位系统, 并且该系统的零动态由“鲁棒输入对状态稳定(robust input-to-state stable)部分”和“不稳定但可镇定部分”组成. 假设系统的不确定性参数和扰动输入分别以非线性函数和仿射形式同时出现在系统零动态的鲁棒输入对状态稳定部分和系统的可线性化部分, 而且其可线性化部分的不确定性具有下三角形结构形式. 该系统输出调节问题的性能以其输出信号能量作为度量. 对于上述非线性系统, 在最差的不确定性参数和扰动输入情况下, 输出调节问题的极限性能只取决于镇定其零动态“不稳定部分”所需的最小能量.

Performance limits in output regulation of an uncertain nonlinear system under disturbances

The attainable performance of the output regulation is studied for an uncertain nonlinear system under disturbances. The nonlinear system is a stabilizable nonminimum phase system with zero dynamics consisting of a robust input-to-state stable component and an unstable but stabilizable component. It is assumed that the uncertain parametervector and disturbances only enter the robust input-to-state stable component of the zero dynamics and the linearizable part of the system. Furthermore, the function of the uncertain parameter-vector forms a lower triangular structure in the linearizable part of the system. The performance of this problem is measured by the energy of the output of the system. It is shown that the attainable performance of output regulation under the worst uncertain parameter-vector and disturbances for the nonlinear system is determined only by the minimum energy required for stabilizing the unstable part of its zero dynamics.