Related papers: Backstepping Control Laws for Higher-Dimensional P…
The recently introduced DeepONet operator-learning framework for PDE control is extended from the results for basic hyperbolic and parabolic PDEs to an advanced hyperbolic class that involves delays on both the state and the system output…
This paper deals with the gradient extremum seeking control for static scalar maps with actuators governed by distributed diffusion partial differential equations (PDEs). To achieve the real-time optimization objective, we design a…
We consider the optimal control problem of a general nonlinear spatio-temporal system described by Partial Differential Equations (PDEs). Theory and algorithms for control of spatio-temporal systems are of rising interest among the…
State-dependent parameter identification, where unknown model parameters depend on one or more state variables in partial differential equations (PDEs) or coupled PDE systems, is fundamental to a wide range of problems in physics,…
We propose a new discretization method for PDEs on moving domains in the setting of unfitted finite element methods, which is provably higher-order accurate in space and time. In the considered setting, the physical domain that evolves…
Many physical systems are formulated on domains which are relatively large in some directions but relatively thin in other directions. We expect such systems to have emergent structures that vary slowly over the large dimensions. Common…
This technical note is concerned with boundary stabilization of multi-dimensional discrete-velocity kinetic models. By exploiting a certain stability structure of the models and adapting an appropriate Lyapunov functional, we derive…
An essential ingredient of a spectral method is the choice of suitable bases for test and trial spaces. On complex domains, these bases are harder to devise, necessitating the use of domain partitioning techniques such as the spectral…
The feedback exponential stabilization to trajectories for semilinear parabolic equations in a given bounded domain is addressed. The controls take values in a finite-dimensional space and are supported in a small region. Both internal and…
Mixed-dimensional partial differential equations arise in several physical applications, wherein parts of the domain have extreme aspect ratios. In this case, it is often appealing to model these features as lower-dimensional manifolds…
Symmetry in combinatorial problems is an extensively studied topic. We continue this research in the context of model expansion problems, with the aim of automating the workflow of detecting and breaking symmetry. We focus on local domain…
The existence of exponential dichotomies has been well-established as a powerful tool to study existence, stability, and bifurcations of coherent structures. Currently, the application of exponential dichotomies to elliptic problems posed…
High-dimensional Partial Differential Equations (PDEs) are a popular mathematical modelling tool, with applications ranging from finance to computational chemistry. However, standard numerical techniques for solving these PDEs are typically…
We introduce a control design and analysis framework for micro-macro, boundary control of large-scale, $n+m$ hyperbolic PDE systems. Specifically, we develop feedback laws for stabilization of hyperbolic systems at the micro level (i.e., of…
This paper is motivated by the problem of quantitatively bounding the convergence of adaptive control methods for stochastic systems to a stationary distribution. Such bounds are useful for analyzing statistics of trajectories and…
In this work, we consider the problem of boundary stabilization for a quasilinear 2X2 system of first-order hyperbolic PDEs. We design a new full-state feedback control law, with actuation on only one end of the domain, which achieves H^2…
We study the backstepping stabilization of higher order linear and nonlinear Schr\"odinger equations on a finite interval, where the boundary feedback acts from the left Dirichlet boundary condition. The plant is stabilized with a…
This paper addresses the problem of robust stabilization for linear hyperbolic Partial Differential Equations (PDEs) with Markov-jumping parameter uncertainty. We consider a 2 x 2 heterogeneous hyperbolic PDE and propose a control law using…
Forward and inverse models are used throughout different engineering fields to predict and understand the behaviour of systems and to find parameters from a set of observations. These models use root-finding and minimisation techniques…
This paper considers the backstepping state feedback and observer design for hyperbolic and parabolic PDEs, which are bidirectionally interconnected in a general coupling structure. Both PDE subsystems consist of coupled scalar PDEs with…