基于多目标优化的Lipschitz非线性系统鲁棒H_infinity滤波器设计
Robust H_infinity Filter Design for Lipschitz Nonlinear Systems via Multiobjective Optimization
AI总结：
提出一种基于LMI优化的H_infinity观测器设计方法，同时优化可容许Lipschitz常数和干扰衰减水平，保证指数收敛和对非线性不确定性的鲁棒性。
摘要：
本文提出了一种新的Lipschitz非线性系统H_infinity观测器设计方法，形式化为LMI优化问题。所提出的观测器具有保证的衰减率（指数收敛），并且对未知外部干扰具有鲁棒性。此外，由于所提出的LMI在可容许Lipschitz常数上的线性性，可以通过LMI优化最大化该常数。这为观测器增加了一个额外的重要特性，即对非线性不确定性的鲁棒性。推导了可容忍的非线性不确定性的显式界限。新的LMI公式还允许对干扰衰减水平（H_infinity代价）进行优化。然后，通过LMI多目标优化同时优化H_infinity滤波器的可容许Lipschitz常数和干扰衰减水平。
英文摘要：
In this paper, a new method of H_infinity observer design for Lipschitz nonlinear systems is proposed in the form of an LMI optimization problem. The proposed observer has guaranteed decay rate (exponential convergence) and is robust against unknown exogenous disturbance. In addition, thanks to the linearity of the proposed LMIs in the admissible Lipschitz constant, it can be maximized via LMI optimization. This adds an extra important feature to the observer, robustness against nonlinear uncertainty. Explicit bound on the tolerable nonlinear uncertainty is derived. The new LMI formulation also allows optimizations over the disturbance attenuation level (H_infinity cost). Then, the admissible Lipschitz constant and the disturbance attenuation level of the H_infinity filter are simultaneously optimized through LMI multiobjective optimization.
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