Related papers: Finite-dimensional control of the heat equation: D…
Recently, a constructive method was suggested for finite-dimensional observer-based control of 1D linear heat equation, which is robust to input/output delays. In this paper, we aim to extend this method to the 2D case with general…
Recently a constructive method was introduced for finite-dimensional observer-based control of 1D parabolic PDEs. In this paper we present an improved method in terms of the reduced-order LMIs (that significantly shorten the computation…
Finite-dimensional observer-based controller design for PDEs is a challenging problem. Recently, such controllers were introduced for the 1D heat equation, under the assumption that one of the observation or control operators is bounded.…
We study global finite-dimensional observer-based stabilization of a semilinear 1D heat equation with globally Lipschitz semilinearity in the state variable. We consider Neumann actuation and point measurement. Using dynamic extension and…
We prove an exact controllability result for a one-dimensional heat equation with delay in both lower and highest order terms and nonhomogeneous Dirichlet boundary conditions. Moreover, we give an explicit representation of the control…
This paper investigates the output feedback boundary control of reaction-diffusion equations with either distributed or boundary measurement by means of a finite-dimensional observer. A constructive method dealing with the design of…
The primary focus of this paper is to establish the internal null controllability for the one-dimensional heat equation featuring dynamic boundary conditions. This achievement is realized by introducing a new Carleman estimate and an…
In this paper, a quadratic optimal control problem is considered for second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in which the "point" control function (depending only on time) constitutes a source term. These…
We study null controllability for linear heat-type systems in finite dimensions that incorporate both memory and time-delay effects. A strengthened notion of controllability, referred to as delay and memory-type null controllability, is…
The aim of this work is to present some strategies to solve numerically controllability problems for the two-dimensional heat equation, the Stokes equations and the Navier-Stokes equations with Dirichlet boundary conditions. The main idea…
An in-domain finite dimensional controller for a class of distributed parameter systems on a one-dimensional spatial domain formulated under the port-Hamiltonian framework is presented. Based on [25] where positive feedback and a late…
Given one open-loop measured trajectory of a single-input single-output discrete-time linear time-invariant system, we present a framework for data-driven controller design for closed-loop finite-horizon dissipativity. First, we parametrize…
We consider a fully-discrete approximations of 1-D heat equation with dynamic boundary conditions for which we provide a controllability result. The proof of this result is based on a relaxed observability inequality for the corresponding…
This paper investigates the output feedback setpoint regulation control of a reaction-diffusion equation by means of boundary control. The considered reaction-diffusion plant may be open-loop unstable. The proposed control strategy consists…
This paper provides a complete characterization of the Dirichlet boundary outputs that can be exactly tracked in the one-dimensional heat equation with Neumann boundary control. The problem consists in describing the set of boundary traces…
For mechanical systems we present a controller able to track an unknown smooth signal, converging in finite time and by means of a continuous control signal. The control scheme is insensitive against unknown perturbations with bounded…
Recent work has introduced the concept of finite-time scaling to characterize bifurcation diagrams at finite times in deterministic discrete dynamical systems, drawing an analogy with finite-size scaling used to study critical behavior in…
This paper addresses sampled-data control of 2D Kuramoto-Sivashinsky equation over a rectangular domain. We suggest to divide the 2D rectangular into N sub-domains, where sensors provide spatially averaged or point state measurements to be…
In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…
In this paper, we consider simultaneous reconstruction of the diffusion coefficient and initial state for a one-dimensional heat equation through boundary control and measurement. The boundary measurement is known to make the system exactly…