A nonlinear robust observer has been developed by combining the advantages of the variable structure systems (VSS) theory with those of the self-tuning fuzzy logic algorithm. The observer does not require an exact knowledge of the system dynamics or the construction of a rule-based expert fuzzy inference system. Instead, it requires the upper bounds on the modeling imprecision to be known. The observer design involves the derivation of inequality conditions that must be satisfied by the tuning parameters in order to ensure the convergence of the estimation process.
The observer has been applied to estimate the state variables of an under-actuated marine vessel. The simulation results demonstrated the capabilities of the observer in providing accurate estimates of the state variables in spite of considerable modeling imprecision and significant environmental disturbances.