Related papers: Sampled-Data Control of the Stefan System
In this paper, we explore the conditions for asymptotic stability of the hybrid closed-loop system resulting from the interconnection of a nonlinear plant, an intelligent sensor that generates finite-time convergent estimates of the plant…
A range of optimization cases of two-dimensional Stefan problems, solved using a tracking-type cost-functional, is presented. A level set method is used to capture the interface between the liquid and solid phases and an immersed boundary…
This note is concerned with the study of the initial boundary value problem for systems of conservation laws from the point of view of control theory, where the initial data is fixed and the boundary data are regarded as control functions.…
We show uniqueness of solutions to the two-phase Stefan problem which have signed measures as initial data.
We study multi-phase Stefan problem with increasing Riemann initial data and with generally negative latent specific heats for the phase transitions. We propose the variational formulation of self-similar solutions, which allows to find…
We introduce and analyze a nonlocal version of the one-phase Stefan problem in which, as in the classical model, the rate of growth of the volume of the liquid phase is proportional to the rate at which energy is lost through the…
In this paper, a novel control strategy namely disturbance observer-based control is first applied to stabilization and disturbance rejection for an anti-stable stochastic heat equation with Neumann boundary actuation and unknown boundary…
Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving phase change material as well as temperature dependent thermal coefficients. Existence of at least one similarity solution is proved imposing a…
Most heat transfer models for bulk crystal growth rely on the classical Stefan formulation to evaluate interface motion during phase change. However, when the interface is non-smooth the use of the classical Stefan formulation may lead to…
We show that if a linear infinite-dimensional system is exponentially stabilizable by compact feedback, it is also stabilizable by means of a sampled-data feedback that is fed through a globally Lipschitz nonlinearity, provided that the…
We consider a general linear control system and a general quadratic cost, where the state evolves continuously in time and the control is sampled, i.e., is piecewise constant over a subdivision of the time interval. This is the framework of…
We study the regularity and well-posedness of physical solutions to the supercooled Stefan problem. Assuming only that the initial temperature is integrable, we prove that the free boundary, known to have jump discontinuities as a function…
We study a one-dimensional one-phase Stefan problem with a Neumann boundary condition on the fixed part of the boundary. We construct the unique self-similar solution, and show that starting from arbitrary initial data, solution orbits…
In this paper, we propose a novel sampling control framework based on the emulation technique where the sampling error is regarded as an auxiliary input to the emulated system. Utilizing the supremum norm of sampling error, the design of…
We develop a mathematical model for a three-phase free boundary problem in one dimension that involves the interactions between gas, water and ice. The dynamics are driven by melting of the ice layer, while the pressurized gas also…
Motivated by applications in economics and finance, in particular to the modeling of limit order books, we study a class of stochastic second-order PDEs with non-linear Stefan-type boundary interaction. To solve the equation we transform…
In this paper, we study the dynamics of a linear control system with given state feedback control law in the presence of fast periodic sampling at temporal frequency $1/\delta$ ($0 < \delta \ll 1$), together with small white noise…
This paper discusses the boundary feedback stabilization of a reaction-diffusion equation with Robin boundary conditions and in the presence of a time-varying state-delay. The proposed control design strategy is based on a…
We prove the global-time existence of weak solutions to the supercooled Stefan problem. Our result holds in general space dimensions and with a general class of initial data. In addition, our solution is maximal in the sense of a certain…
We consider two implicit approximation schemes of the one-dimensional supercooled Stefan problem and prove their convergence, even in the presence of finite time blow-ups. All proofs are based on a probabilistic reformulation recently…