持续有界扰动系统的嵌套不变椭圆集鲁棒控制

Nested Invariant Ellipse Sets Robust Control for the System with Persistent Bounded Disturbances

为了抑制外部持续有界扰动和模型不确定性对系统稳定性控制的影响,通过不变集理论,采用嵌套不变椭圆集鲁棒控制算法实现系统的快速稳定控制。控制算法分为离线算法和在线算法两部分。离线时根据公式得到一维状态变量序列,通过线性矩阵不等式方法优化得到嵌套不变椭圆集。在线时,根据系统状态变量在嵌套不变椭圆集的位置,构建新的不变椭圆集并计算得到系统的控制律。给出新的不变椭圆集满足系统控制要求的理论证明。通过与不变单椭圆集控制算法进行仿真比较,结果验证了上述算法的有效性,为持续有界扰动下模型不确定性系统的稳定控制,提供一种有效的控制方法。

In order to suppress the influence of external persistent bounded disturbances and system model uncertainty disturbances on system stability control, we used the nested invariant ellipse sets robust control algorithm to achieve the stable and quick control of the system through invariant set theory. The control algorithm is divided into offline algorithm and online algorithm. When offline, it selected the one-dimensional state variable sequence by the formula. The linear matrix inequality method was used to optimize the nested invariant ellipse sets. When online, according to the position of the system state variables in the nested invariant ellipse sets, the new invariant ellipse set was constructed and the control law of the system was calculated. The theoretical proof is given, that the new invariant ellipse set can meet the system control requirements. The effectiveness of the algorithm is verified by simulation comparison with the invariant single ellipse set control algorithm. It provides an effective control method for the stability control of the model uncertainty system with persistent bounded disturbances.