Related papers: On a Class of Boundary Control Problems
Sets of bilinear constraints are important in various machine learning models. Mathematically, they are hyperbolas in a product space. In this paper, we give a complete formula for projections onto sets of bilinear constraints or hyperbolas…
A theoretical framework and numerical techniques to solve optimal control problems with a spatial trace term in the terminal cost and governed by regularized nonlinear hyperbolic conservation laws are provided. Depending on the spatial…
The purpose of this paper is to address a class of hybrid optimal control problems constrained with hyperelasticity and constant global volume. This type of problems can intervene for example in the mechanical aspects of cardiac activity.…
We study a nonlinear, non-autonomous feedback controller applied to boundary control systems. Our aim is to track a given reference signal with prescribed performance. Existence and uniqueness of solutions to the resulting closed-loop…
In the framework of a real Hilbert space we consider the problem of approaching solutions to a class of hierarchical variational inequality problems, subsuming several other problem classes including certain mathematical programs under…
We consider continuous-state and continuous-time control problems where the admissible trajectories of the system are constrained to remain on a union of half-planes which share a common straight line. This set will be named a junction. We…
Boundary feedback control design is studied for 1D hyperbolic systems with an in-domain disturbance and a boundary feedback controller under the effect of actuator saturation. Nonlinear semigroup theory is used to prove well-posedness of…
Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…
This paper is concerned with robust preconditioning of wave equations constrained linear inverse problems from boundary observation data. The main result of this paper is a concept for regularization parameter robust preconditioning.…
We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the…
We prove well posedness and stability in $\mathbf{L}^1$ for a class of mixed hyperbolic-parabolic non linear and non local equations in a bounded domain with no flow along the boundary. While the treatment of boundary conditions for the…
In this paper, we have stated some results about this concept. Furthermore, we introduce the notion of controlled $E$-frames and we characterize all controlled $E$-duals associated with a given controlled $E$-frame.
Symmetric spaces arise in wide variety of problems in Mathematics and Physics. They are mostly studied in Representation theory, Harmonic analysis and Differential geometry. As many physical systems have symmetric spaces as their…
This article deals with the boundary null controllability of some degenerate parabolic equations posed on a square domain, presenting the first study of boundary controllability for such equations in multidimensional settings. The proof…
We study a one-dimensional nonlinear hyperbolic-parabolic initial boundary value problem occurring in the theory of thermoelasticity. We prove existence and uniqueness of the local-in-time strong solution. Also, some global-in-time weak…
We consider parabolic equations on bounded smooth open sets $\Om\subset \R^N$ ($N\ge 1$) with mixed Dirichlet type boundary-exterior conditions associated with the elliptic operator $\mathscr{L} \coloneqq - \Delta + (-\Delta)^{s}$…
In this work we introduce the obstacle-mass constraint problem for a multidimensional scalar hyperbolic conservation law. We prove existence of an entropy solution to this problem by a penalization/viscosity method. The mass constraint…
This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties…
We study a family of initial boundary value problems associated to mixed hyperbolic-parabolic systems: v^{\epsilon} _t + A (v^{\epsilon}, \epsilon v^{\epsilon}_x ) v^{\epsilon}_x = \epsilon B (v^{\epsilon} ) v^{\epsilon}_{xx} The…
In this article, a notion of viscosity solutions is introduced for first order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent evolution equations in Hilbert space. We…