On the need for switched-gain observers for non-monotonic nonlinear systems
On the need for switched-gain observers for non-monotonic nonlinear systems
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DOI：
10.1016/j.automatica.2020.108814
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
R. Rajamani;Woongsun Jeon;H. Movahedi;A. Zemouche
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文献类型：
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作者：
R. Rajamani;Woongsun Jeon;H. Movahedi;A. Zemouche
本文主要研究非单调非线性系统的观测器设计问题。考虑一类非线性系统，其中过程动力学方程和输出方程均由状态的标量组合的非线性向量函数组成。假定非线性函数的导数有界可微。提出了一种只需要求解单个线性矩阵不等式的指数收敛状态估计观测器设计算法。该算法在涉及的非线性函数是单调的情况下能够有效地工作。然而，当系统的全部或部分函数是非单调的时，它就失效了。数值计算和解析结果表明，当所有输出函数或所有过程动力学函数均为非单调时，观测器设计LMI均无可行解。此外，当所涉及的非线性函数都是非单调的时，无论非线性的Lipschitz常数或Jacobian界有多小，文献中其他基于恒定增益lmi的观测器设计方法也会失败。这一限制在以前的观察者设计文献中没有被认识到。为了克服这一限制，开发了一种在多个恒定观测器增益之间切换的混合观测器，该观测器可以为具有非单调非线性函数的系统提供全局渐近稳定性。具有切换增益的混合观测器使现有的观测器设计方法能够用于具有有限局部极值的非单调非线性函数。最后给出了混合观测器在道路车辆位置跟踪问题和工业执行器活塞位置估计问题两种运动估计中的应用。
This paper focuses on the challenges in observer design for nonlinear systems which are non-monotonic. A class of nonlinear systems is considered in which the process dynamics and output equations are both composed of nonlinear vector functions of scalar combinations of the states. The nonlinear functions are assumed to be differentiable with bounded derivatives. An observer design algorithm that requires solving just a single linear matrix inequality for exponentially convergent state estimation is developed. The developed algorithm works effectively when the involved nonlinear functions are monotonic. However, it fails when all or even some of the system functions are non-monotonic. Both numerical computation and analytical results show that the observer design LMI has no feasible solutions when either all output functions or all process dynamics functions are non-monotonic. Further, other constant gain LMI-based observer design methods from literature also fail when the involved nonlinear functions are all non-monotonic, no matter how small the Lipschitz constant or the Jacobian bounds of the nonlinearities. This limitation has not previously been recognized in observer design literature. To overcome this limitation, a hybrid observer that switches between multiple constant observer gains is developed that can provide global asymptotic stability for systems with non-monotonic nonlinear functions. Hybrid observers with switched gains enable existing observer design methods to be utilized for non-monotonic nonlinear functions with finite local extrema. The application of the developed hybrid observer to two motion estimation applications, one a vehicle position tracking problem on roads and another a piston position estimation problem for an industrial actuator, are demonstrated.