大规模离散线性系统的分散饱和反馈镇定(英文)

Stabilization of Discrete-time Large-scale Linear Systems under Actuator Saturation by Decentralized Feedback

考虑了具有执行器饱和的大规模离散时间线性系统分散控制器的设计。首先进行了在执行器幅值饱和的情形下的研究,然后延伸到执行器具有多层饱和的情况,例如,幅值和速率同时存在饱和或通过多层神经元网络近似的执行器非线性。在这2种情况下,给出了闭环系统在分散状态反馈律的作用下,椭球收敛不变性的条件。基于这些条件,可取得大吸引域的分散状态反馈控制律的设计可以归结为具有双线性矩阵不等式(BM I)约束的优化问题。对这些双线性约束优化问题提出了数值算法。数值算例显示了所提出的设计方法的有效性。

The design of decentralized controllers for discrete-time large-scale linear systems under actuator saturation is considered. The development is first carried out in the situation when on actuator magnitude saturation is presented and then extended to the situation where the actuators are subject to nested saturation, which represents, for example, simultaneous actuator magnitude and rate saturation and approximation of actuator nonlinearities by muhi-layer neural networks. In both situations, for the closed-loop system under a saturating decentralized state feedback law, conditions are identified under which an ellipsoid is contractively invariant and thus within the domain of attraction. Based on these conditions, the design of decentralized state feedback laws that achieve large domains of attraction can be formulated as optimization problems with bilinear matrix inequality（BMI） constraints. Numerical algorithms are developed to solve these BMI problems. Numerical examples are used to demonstrate the effectiveness of design method.