Structural-parametrical Design Method of Adaptive Observers for Nonlinear Systems

The structural-parametrical method for design of adaptive observers (AO) for nonlinear dynamic systems under uncertainty is proposed. The design of AO is consisting of two stages. The structural stage allowed identifying a class of nonlinearity and its structural parameters. The solution of this task is based on an estimation of the system structural identifiability (SI). The method and criteria of the system structural identifiability are proposed. Effect of an input on the SI is showed. We believe that the excitation constancy condition is satisfied for system variables. Requirements to the input at stages of structural and parametrical design of AO differ. The parametrical design stage AO uses the results obtained at the first stage of the adaptive observer construction. Two cases of the structural information application are considered. The main attention is focused on the case of the insufficient structural information. Adaptive algorithms for tuning of parameters AO are proposed. The uncertainty estimation procedure is proposed. Stability of the adaptive system is proved. Simulation results confirmed the performance of the proposed approach.