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This paper presents a new approach to bounded-error state estimation involving time uncertainties. For a given bounded\ud observation of a continuous-time non-linear system, it is assumed that neither the values of the observed data nor their\ud acquisition instants are known exactly. For systems described by state-space equations, we prove theoretically and demonstrate\ud by simulations that the proposed constraint propagation approach enables the computation of bounding sets for the systems’\ud state vectors that are consistent with the uncertain measurements. The bounding property of the method is guaranteed even\ud if the system is strongly non-linear. Compared with other existing constraint propagation approaches, the originality of the\ud method stems from our definition and use of bounding tubes which enable to enclose the set of all feasible trajectories inside\ud sets. This method makes it possible to build specific operators for the propagation of time uncertainties through the whole\ud trajectory. The efficiency of the approach is illustrated on two examples: the dynamic localization of a mobile robot and the\ud correction of a drifting clock.

This paper proposes a new observer for estimating the state vector of a nonlinear system. This observer, which is robust with respect to outliers, assumes that the measurement errors, as well as the number of outliers that could occur within a given time window, are bounded. The principle of the approach is to use interval analysis to deal properly with the nonlinearities involved in the system (without any linearization or approximation) and to propagate through the time, in a forward and backward manner, the assumptions made about outliers. A test case related to the localization and control of an underwater robot is also proposed to illustrate the efficiency of the approach.

In the context of bounded-error estimation, it is customary to assume that the error between the model output and output data should lie between some known prior bounds. In this paper, it is also assumed that the factors characterizing the experiments that have been carried out (e.g., measurement times) are uncertain, with known prior bounds. An algorithm based on interval analysis is used to characterize the set of all values of the parameter vector to be estimated that are consistent with these hypotheses. This is performed in a guaranteed way, even when the model output is a nonlinear function of the parameters and factors characterizing the experiments.

Proving that an uncertain parametric model is stable amounts to prove the inclusion of two sets: the set A of all feasible parameters and the set B of all parameters for which the model is stable. In this paper, a new algorithm, able to decide whether or not A is included in B, is presented. The method is based on interval analysis which is a numerical tool able to deal with inequalities in a global and guaranteed way. Convergence properties of the algorithm are provided. The algorithm is then applied to the robust stability of a discrete-time model where the information on the parameters is given through bounded-error data. The behavior of the algorithm with respect to the number of parameters is illustrated on a continuous-time model.

Many design problems, e.g. in control theory, amount to tuning a parameter vector c so as to guarantee that specifications are met for all feasible values of some unknown perturbation vector p. A new prototype algorithm for solving this guaranteed-tuning problem is proposed, and its convergence properties are established. It applies when the design specifications translate into a finite number of (possibly nonlinear) inequalities. Three test cases taken from the field of control are considered, namely the design of a PID controller robust to structured uncertainty, the control of a nonlinear discrete-time model with uncertain parameters and initial state, and a problem of motion planning, with obstacles to be avoided.

In the context of bounded-error estimation, one is interested in characterizing the set of all the values of the parameters to be estimated that are consistent with the data in the sense that the errors between the data and model outputs fall within prior bounds. While the problem can be considered as solved when the model output is linear in the parameters, the situation is far less advanced in the general nonlinear case. In this paper, the problem of nonlinear bounded-error estimation is viewed as one of set inversion. An original algorithm is proposed, based upon interval analysis, that makes it possible to characterize the feasible set for the parameters by enclosing it between internal and external unions of boxes. The convergence of the algorithm is proved and the algorithm is applied to two test cases. The results obtained are compared with those provided by signomial analysis.