Adaptive Parameter Estimation-based Observer Design for Nonlinear Systems

In this paper, alternative adaptive observers are developed for nonlinear systems to achieve state observation and parameter estimation of nonlinear systems simultaneously. The proposed observers are derived from the perspective of adaptive parameter estimation method, which leads to the reduced-order observers to deal with partially unknown system states and unknown parameters. To be specific, the nonlinear parametric function of unknown states to be identified is first transformed into a cascade form, which is linearly independent of unknown constant parameters. This transformation is achieved by finding an unmeasurable injective mapping function. Then, the functions related to measurable states are injected into a set of low- pass filters to derive the relationship between the mapping function and unknown parameters. In this line, the observer design problem is transformed into an equivalent parameter estimation problem. Consequently, we further exploit a recently proposed parameter estimation method that differs from the classical gradient descent algorithm to estimate the mapping function and unknown constant parameters. Finally, the unknown system states can be reconstructed by inverting this mapping function. A simulation example of DC-DC Cuk converter illustrates the effectiveness of proposed method.