Set membership state and parameter estimation for systems described by nonlinear differential equations

This paper investigates the use of guaranteed methods to perform state and parameter estimation for nonlinear continuous-time systems, in a bounded-error context. A state estimator based on a prediction-correction approach is given, where the prediction step consists in a validated integration of an initial value problem for an ordinary differential equation (IVP for ODE) using interval analysis and high-order Taylor models, while the correction step uses a set inversion technique. The state estimator is extended to solve the parameter estimation problem. An illustrative example is presented for each part.