Design Methods And Performance Analysis Of Nonlinear Observer

The present paper focuses on the investigation of the observer design for nonlinear systems. Luenberger type observer, H_∞partial-state observer and adaptive observer are designed for several different classes of nonlinear systems, respectively, and it has also been provided with the existence conditions or the methods of solving gain matrix of the observers. Moreover, it has been analyzed that the convergence property and disturbance attenuation property, etc. of the designed observers. The main contents of this paper are composed of the following three parts:(Ⅰ) Observer design for more general Lipschitz nonlinear systemsIn this part, the Luenberger type observer design is investigated for a class of more general Lipschitz nonlinear systems. The problem of asymptotically convergent observer design is changed into that of solving the corresponding gain matrix. The sufficient conditions that the gain matrix satisfies are given, and the method of solving gain matrix is also presented. Firstly, under certain detectability that the system satisfies, the sufficient conditions are presented for the asymptotic convergence of the observer error by using the singular value theory, and the method of solving gain matrix is presented based on the Riccati equation. Secondly, when the system does not satisfy such detectability but satisfies other conditions, there is a gain matrix ensuring the asymptotic convergence of the observer error, and the sufficient conditions and the method of solving gain matrix are obtained similarly.(Ⅱ) H_∞partial-state observer design for nonlinear systemsIn this part, the robust partial-state observer design is investigated for a class of nonlinear systems with L₂ (i.e. square integrable) disturbance. A novel H_∞state observer is designed to reconstruct the partial-state of nonlinear systems. Firstly, the restricted conditions and the detailed expressions are given for the partial-state observer design matrices. Then, the L₂ disturbance attenuation problem is investigated for the observer error by analyzing the observer error dynamics, and the sufficient conditions are given for the existence of the H_∞partial-state observer based on the LMI method. Theoretical analysis turns out that this observer designed can realize the asymptotic reconstruction for the states to be estimated when no disturbance, and the observer error is attenuation to the L₂ disturbance when disturbance exists.(Ⅲ) Adaptive observer design for nonlinear systems and its robustness analysisIn this part, the adaptive observer design is investigated for a class of nonlinear systems with unknown parameters and L₂ disturbance, and a new robust adaptive state observer is designed to reconstruct the system states. Firstly, when no disturbance, the method of obtaining observer gain matrix is presented for the asymptotic convergence of the observer error by solving some Riccati equation. Secondly, when disturbance exists but is bounded, there is a gain matrix ensuring the asymptotic convergence of the observer error, and the method of solving the gain matrix is obtained similarly.The three parts above also give the corresponding simulation examples, respectively, to illustrate the effectiveness and feasibility of the observer design methods.