Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter esti...

This paper introduces new methods for estimating parameters and their uncertainty in the context of inverse problems. The new techniques are capable of dealing with both measurement and modelling errors but also with uncertainty in parameters of the model that are assumed known. All the uncertain quantities are taken as unknown but bounded. In such a bounded-error context, reliable set-membersh...

We consider the bit-probe complexity of the set membership problem, where a set S of size at most n from a universe of size m is to be represented as a short bit vector in order to answer membership queries of the form “Is x in S?” by adaptively probing the bit vector at t places. Let s(m,n, t) be the minimum number of bits of storage needed for such a scheme. Several recent works investigate s...

Interval methods have been shown to be efficient, robust and reliable to solve difficult set-membership localization problems. However they are unsuitable in a probabilistic context, where the approximation of an unbounded probability density function by a set cannot be accepted. This paper proposes a new probabilistic approach which makes possible to use classical set-membership localization m...

We present a method, known in control theory, to give set-membership estimates for the states of a population in which an infectious disease is spreading. An estimation is reasonable due to the fact that the parameters of the equations describing the dynamics of the disease are not known with certainty. We discuss the properties of the resulting estimations. These include the possibility to det...

In this paper, security of lattice-quantization data hiding is considered under a cryptanalytic point of view. Security in this family of methods is implemented by means of a pseudorandom dither signal which randomizes the codebook, preventing unauthorized embedding and/or decoding. However, the theoretical analysis shows that the observation of several watermarked signals can provide sufficien...

The goal is to estimate {πi, 1 ≤ i ≤ n} (i.e., membership estimation). We model the network with the degree-corrected mixed membership (DCMM) model [8]. Since for many natural networks, the degrees have an approximate power-law tail, we allow severe degree heterogeneity in our model. For any membership estimation {π̂i, 1 ≤ i ≤ n}, since each πi is a probability mass function, it is natural to me...

The present paper deals with combined estimation of the state and of the system model for a continuous-time system under uncertain perturbations which may arise not only in the inputs but also in the system parameters. This produces model uncertainty of the multiplicative type. The uncertain items are assumed either unknown but bounded by hard or soft bounds or bounded with unspecified bound. T...

In this paper, the robust fault detection problem for non-linear systems considering both bounded parametric modelling errors and measurement noises is addressed. The non-linear system is monitored by using a state estimator with bounded modelling uncertainty and bounded process and measurement noises. Additionally, time-variant and time-invariant system models are taken into account. Fault det...