Robust H_infinity Filter Design for Lipschitz Nonlinear Systems via Multiobjective Optimization
It provides a more robust observer design for nonlinear systems with Lipschitz dynamics, which is important for control and estimation applications.
This paper proposes a new LMI-based H_infinity observer design for Lipschitz nonlinear systems that guarantees exponential convergence and robustness against disturbances and nonlinear uncertainty, while simultaneously optimizing the admissible Lipschitz constant and disturbance attenuation level via multiobjective optimization.
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.