Nonlinear Quadratic Estimator with selective error state weighting

Abstract

A new approach for optimal observer design of nonlinear systems, the so-called Nonlinear Quadratic Estimator is proposed. This approach employs the minimisation of a quadratic cost functional, thereby comprising two design parameters: Selective weighting of specific error state components and estimated upper bound minimisation. The new approach works without dual system transformation, achieving significant error state minimisation with optimised error dynamics and enabling a selective error state minimisation. Within this proceeding the observer and estimator design method, respectively, is derived from a Lyapunov stability condition of nonlinear, time-continuous systems in Takagi-Sugeno model structure, solved with linear matrix inequalities. Its capability is illustrated for an academical example of a nonlinear system with observer based stabilisation.