基于全驱系统方法的输入饱和非线性切换系统鲁棒控制

Robust Control of Input-saturated Nonlinear Switched Systems Based on the Fully Actuated Approach

  • 摘要: 针对一类受输入饱和、参数不确定性及状态不可测多重约束影响的非线性切换系统,本文基于全驱系统方法,提出了一种适用于输入饱和切换系统的鲁棒控制策略。该方法的主要优势是能够消除系统的非线性,从而获得一个特征极点可自由配置的线性定常闭环系统,简化了控制器的设计过程。首先,建立了输入饱和切换系统的全驱系统模型。然后,设计了扩展状态观测器,以同步估计不可测状态及非线性项,同时采用凸包方法处理输入饱和项。针对每个子系统,利用全驱系统方法设计控制器,并通过参数化设计方法与线性矩阵不等式求解确定控制器参数。最后,借助多重李雅普诺夫函数、线性矩阵不等式及平均驻留时间策略,推导并确立了闭环切换系统的稳定性条件,并通过数值仿真验证了该控制方法的有效性。

     

    Abstract: For a class of nonlinear switched systems subject to multiple constraints including input saturation, parametric uncertainties, and unmeasurable states, we propose a robust control strategy for input-saturated switched systems based on the fully actuated system approach. The main advantage of this method is its ability to cancel out inherent nonlinearities, which ensures that the closed-loop dynamics exhibit linear time-invariant characteristics with freely assignable eigenvalue poles and simplifies the controller design process. Firstly, a fully actuated system model is established for the input-saturated switched system. Secondly, an extended state observer is designed to simultaneously estimate the unmeasurable states and nonlinear terms, while the convex hull approach is employed to handle the input saturation. For each subsystem, a controller is designed using the fully actuated system method, with its parameters determined through parametric design and linear matrix inequality (LMI) solutions. Finally, by leveraging the construction of multiple Lyapunov functions, linear matrix inequalities and the average dwell time strategy, the stability conditions for the closed-loop switched system are derived and established. Furthermore, numerical simulations verify the effectiveness of the proposed control scheme.

     

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