Guaranteed State and Parameter Estimation for Nonlinear Continuous-Time Systems with Bounded-Error Measurements

Abstract

A strategy for state and parameter estimation in nonlinear, continuous-time systems is presented. The method provides guaranteed enclosures of all state and parameter values that are consistent with bounded-error output measurements. Key features of the method are the use of a new validated solver for parametric ordinary differential equations (ODEs), which is used to produce guaranteed bounds on the solutions of nonlinear dynamic systems with interval-valued parameters and initial states, and the use of a constraint propagation strategy on the Taylor models used to represent the solutions of the dynamic system. Numerical experiments demonstrate the use and computational efficiency of the method.