Set-Membership Filter for Discrete-Time Nonlinear Systems Using State-Dependent Coefficient Parameterization

In this article, a recursive set-membership filtering algorithm for discrete-time nonlinear dynamical systems subject to unknown but bounded process and measurement noises is proposed. The dynamics are represented in pseudolinear form using the state-dependent coefficient (SDC) parameterization. Matrix Taylor expansions utilized expand matrices about state estimates. Upper bounds on norms of remainders matrix calculated online nonadaptive random search at each time step. Utilizing these upper ellipsoidal set description uncertainties, two-step filter derived that utilizes “correction–prediction” structure standard Kalman variants. At step, correction prediction ellipsoids constructed contain true system by solving corresponding semidefinite programs. Finally, simulation example included illustrate effectiveness proposed approach.