Related papers: $H_2$-Optimal Estimation of Linear Delayed and PDE…

A number of problems in quantum state and system identification are addressed. Specifically, it is shown that the maximum likelihood estimation (MLE) approach, already known to apply to quantum state tomography, is also applicable to…

We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…

The paper deals with the H2-norm and associated energy or power measurements for a class of processes known as CSVIU (Control and State Variation Increase Uncertainty). These are system models for which a stochastic process conveys the…

Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…

In this paper, a synthesis method for distributed estimation is presented, which is suitable for dealing with large-scale interconnected linear systems with disturbance. The main feature of the proposed method is that local estimators only…

The estimation of distributed parameters in partial differential equations (PDE) from measures of the solution of the PDE may lead to under-determination problems. The choice of a parameterization is a usual way of adding a-priori…

Approximate solutions of partial differential equations (PDEs) obtained by neural networks are highly affected by hyper parameter settings. For instance, the model training strongly depends on loss function design, including the choice of…

In this article, mixed finite element methods are discussed for a class of hyperbolic integro-differential equations (HIDEs). Based on a modification of the nonstandard energy formulation of Baker, both semidiscrete and completely discrete…

We deal with the problem of parameter estimation in stochastic differential equations (SDEs) in a partially observed framework. We aim to design a method working for both elliptic and hypoelliptic SDEs, the latters being characterized by…

This paper focuses on characterizing the fundamental performance limits that can be expected from an ideal decoder given a general model, ie, a general subset of "simple" vectors of interest. First, we extend the so-called notion of…

Physical processes evolving in both time and space are often modeled using Partial Differential Equations (PDEs). Recently, it has been shown how stability analysis and control of coupled PDEs in a single spatial variable can be more…

We consider an optimization problem related to semi-active damping of vibrating systems. The main problem is to determine the best damping matrix able to minimize influence of the input on the output of the system. We use a minimization…

This paper studies an optimization-based state estimation approach for discrete-time nonlinear systems under bounded process and measurement disturbances. We first introduce a full information estimator (FIE), which is given as a solution…

While the design of optimal peak-to-peak controllers/observers for linear systems is known to be a difficult problem, this problem becomes interestingly much easier in the context of interval observers because of the positive nature of the…

Stability perserving is an important topic in approximation of systems, e.g.\ model reduction. If the original system is stable, we often want the approximation to be stable. But even if an algorithm preserves stability the resulting system…

This paper investigates structure-preserving $H_2$-optimal model order reduction (MOR) for linear systems with quadratic outputs. Within a Petrov-Galerkin projection framework, the $H_2$-optimal MOR problem is first formulated as an…

In this paper, the synchronizability problem of dynamical networks is addressed, where better synchronizability means that the network synchronizes faster with lower-overshoot. The L2 norm of the error vector e is taken as a performance…

High fidelity models used in many science and engineering applications couple multiple physical states and parameters. Inverse problems arise when a model parameter cannot be determined directly, but rather is estimated using (typically…

This note addresses the question of optimally estimating a linear functional of an object acquired through linear observations corrupted by random noise, where optimality pertains to a worst-case setting tied to a symmetric, convex, and…

We consider parameter estimation for a linear parabolic second-order stochastic partial differential equation (SPDE) in two space dimensions driven by two types $Q$-Wiener processes based on high frequency data in time and space. We first…