**ABSTRACT**

In this paper the Single Particle Model is used to describe the behavior of a Li-ion battery. The main goal is to design a feedback input current in order to regulate the State of Charge (SOC) to a prescribed reference trajectory. In order to do that, we use the boundary ion concentration as output. First, we measure it directly and then we assume the existence of an appropriate estimator, which has been established in the literature using voltage measurements. By applying backstepping and Lyapunov tools, we are able to build observers and to design output feedback controllers giving a positive answer to the SOC tracking problem. We provide convergence proofs and perform some numerical simulations to illustrate our theoretical results.

**ABSTRACT**

**ABSTRACT**

We describe a “discretize-then-relax” strategy to *globally* minimize integral functionals over functions 𝑢𝑢 in a Sobolev space subject to Dirichlet boundary conditions. The strategy applies whenever the integral functional depends polynomially on 𝑢𝑢 and its derivatives, even if it is nonconvex. The “discretize” step uses a bounded finite element scheme to approximate the integral minimization problem with a convergent hierarchy of polynomial optimization problems over a compact feasible set, indexed by the decreasing size ℎℎ of the finite element mesh. The “relax” step employs sparse moment-sum-of-squares relaxations to approximate each polynomial optimization problem with a hierarchy of convex semidefinite programs, indexed by an increasing relaxation order 𝜔𝜔. We prove that, as 𝜔→∞𝜔→∞ and ℎ→0, solutions of such semidefinite programs provide approximate minimizers that converge in a suitable sense (including in certain 𝐿𝑝𝐿𝑝 norms) to the global minimizer of the original integral functional if it is unique. We also report computational experiments showing that our numerical strategy works well even when technical conditions required by our theoretical analysis are not satisfied.

**ABSTRACT**

Use of generative models and deep learning for physics-based systems is currently dominated by the task of emulation. However, the remarkable flexibility offered by data-driven architectures would suggest to extend this representation to other aspects of system analysis including model inversion and identifiability. We introduce InVAErt (pronounced *invert*) networks, a comprehensive framework for data-driven analysis and synthesis of parametric physical systems which uses a deterministic encoder and decoder to represent the forward and inverse solution maps, a normalizing flow to capture the probabilistic distribution of system outputs, and a variational encoder designed to learn a compact latent representation for the lack of bijectivity between inputs and outputs. We formally analyze how changes in the penalty coefficients affect the stationarity condition of the loss function, the phenomenon of posterior collapse, and propose strategies for latent space sampling, since we find that all these aspects significantly affect both training and testing performance. We verify our framework through extensive numerical examples, including simple linear, nonlinear, and periodic maps, dynamical systems, and spatio-temporal PDEs.

**ABSTRACT**

Wildland–urban interface (WUI) regions are particularly vulnerable to wildfires due to their proximity to both nature and urban developments, posing significant risks to lives and property. To enhance our understanding of the risk profiles in WUI areas, we analysed seven fire case studies in central Chile. We developed a mixed-method approach for conducting local-scale analyses, which involved field surveys, remote-sensing through satellite and drone imagery, and GIS-based analysis of the collected data. The methodology led to the generation of a georeferenced dataset of damaged and undamaged dwellings, including 16 variables representing their physical characteristics, spatial arrangement, and the availability of fire suppression resources. A binary classification model was then used to assess the relative importance of these attributes as indicators of vulnerability. The analysis revealed that spatial arrangement factors have a greater impact on damage prediction than the structural conditions and fire preparedness of individual units. Specifically, factors such as dwelling proximity to neighbours, distance to vegetation, proximity to the border of dwelling groups, and distance from the origin of the fire substantially contribute to the prediction of fire damage. Other structural attributes associated with less affluent homes may also increase the likelihood of damage, although further data are required for confirmation. This study provides insights for the design, planning, and governance of WUI areas in Chile, aiding the development of risk mitigation strategies for both built structures and the broader territorial area.

**ABSTRACT**

This paper is about the stabilization of a cascade system of $n$ linear Korteweg--de Vries equations in a bounded interval. It considers an output feedback control placed at the left endpoint of the last equation, while the output involves only the solution to the first equation. The boundary control problems investigated include two cases: a classical control on the Dirichlet boundary condition and a less standard one on its second-order derivative. The feedback control law utilizes the estimated solutions of a high-gain observer system, and the output feedback control leads to stabilization for any $n$ for the first boundary conditions case and for $n=2$ for the second one.

**ABSTRACT**

This paper studies the exponential stabilization of a Boussinesq system describing the two-way propagation of small amplitude gravity waves on the surface of an ideal fluid, the so-called Boussinesq system of the Korteweg–de Vries type. We use a Gramian-based method introduced by Urquiza to design our feedback control. By means of spectral analysis and Fourier expansion, we show that the solutions of the linearized system decay uniformly to zero when the feedback control is applied. The decay rate can be chosen as large as we want. The main novelty of our work is that we can exponentially stabilize this system of two coupled equations using only one scalar input.

Edificio de Innovación UC, Piso 2

Vicuña Mackenna 4860

Macul, Chile

Vicuña Mackenna 4860

Macul, Chile