Guaranteed error estimation in uncertain systems

In this paper bounding estimators for uncertain systems are developed using the concept of Fuzzy Dynamic Programming. The estimator gives an upper bound to the error for any allowed system parameter variation. A dynamic system is considered where the uncertainty in initial state, additive plant disturbance, measurement errors are modeled as unknown but bounded (UBB). It is further assumed that there is a UBB uncertainty in the system parameters. The estimation problem for a non-linear system with parameter uncertainty is first formulated as a constrained optimization problem and then using Fuzzy Dynamic Programming the class of bounding estimators is derived. The results are applied to obtain a linear estimator for linear uncertain system. It is shown that such an estimator is precomputable and that it reduces to the optimum filter for a linear system with additive disturbances as the model uncertainty vanishes.