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 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

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... 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. In this paper we consider the estimation of state variables and parameters for nonlinear, continuous-time systems in a bounded-error context. This problem was first addressed by Jaulin, 1 though other versions of the problem (e.g., with linear models and/or discrete time) have also been studied. 2-5 Jaulin 1 proposed an algorithm for state estimation based on interval analysis 6 and consistency (constraint propagation) techniques. 7 A first-order method was used to get a guaranteed enclosure of the solution of the ordinary differential equations (ODEs) describing the system. Consistency techniques then were used to contract the domains for the state variables by pruning parts that are inconsistent with the measured output. However, the large wrapping effect associated with the first-order method leads to very pessimistic results. Raïssi et al. 8 provided a technical improvement by using a more accurate interval computation of the solution of the ODEs. Use of a high-order Taylor series method, together with other techniques proposed by Rihm, 9 made it possible to obtain a better enclosure of the solution to the ODE system. This approach was also used to provide a method for guaranteed parameter estimation. These approaches rely on the use of interval methods 6 (also called validated or verified methods) for solving the initial value problem (IVP) for ODEs. When the parameters and/or initial states are not known with certainty and are given by intervals, traditional approximate solution methods for ODEs are not useful, since, in essence, they would have to solve infinitely many systems to determine an enclosure of the solutions. In contrast, interval methods not only can determine a guaranteed error bound on the true solution, but can also verify that a unique solution to the problem exists. An excellent review of interval methods for IVPs has been given by Nedialkov et al. 10 For addressing this problem, there are various packages available, including AWA, 11 VNODE, 12 and COSY VI, 13 all of which consider uncertainties in initial state only. In this study, we use a new package named VSPODE (Validating Solver for Parametric ODEs), described by Lin and Stadtherr, 14 for computing a validated enclosure of all solutions of an ODE system with interval-valued parameters and/or initial state. The method is based on a traditional interval approach, 10 but involves a novel use of Taylor models 15,16 to address the dependency