Related papers: A different look at controllability
We develop a functional-analytic characterization of output tracking controllability for finite-dimensional linear systems. By formulating tracking as the surjectivity of the control-to-output map on suitable trajectory spaces, we show that…
In this paper we study partial-approximate controllability of semilinear nonlocal fractional evolution equations in Hilbert spaces. By using fractional calculus, variational approach and approximating technique, we give the approximate…
Model Predictive Control (MPC) is often tuned by trial and error. When a baseline linear controller exists that is already well tuned in the absence of constraints and MPC is introduced to enforce them, one would like to avoid altering the…
We construct least squares formulations of PDEs with inhomogeneous essential boundary conditions, where boundary residuals are not measured in unpractical fractional Sobolev norms, but which formulations nevertheless are shown to yield a…
Given the full shift over a countable state space on a countable amenable group, we develop its thermodynamic formalism. First, we introduce the concept of pressure and, using tiling techniques, prove its existence and further properties…
We consider a linear nonlocal heat equation in a bounded domain $\Omega\subset\mathbb{R}^d$ with Dirichlet boundary conditions. The non-locality is given by the presence of an integral kernel. We analyze the problem of controllability when…
In this paper, we recover the boundary null controllability for the degenerate heat equation by analyzing the asymptotic behavior of an eligible family of state-control pairs $((u_{\varepsilon}, h_{\varepsilon}))_{\varepsilon >0}$ solving…
We investigate the theory of thermodynamic formalism from the perspective of computable analysis, with a special focus on the computability of equilibrium states. Specifically, we develop two complementary general approaches to verify the…
Backward parabolic equations, such as the backward heat equation, are classical examples of ill-posed problems where solutions may not exist or depend continuously on the data. In this work, we study a least squares finite element method to…
In this paper, we consider a structurally damped elastic equation under hinged boundary conditions. Fully-discrete numerical approximation schemes are generated for the null controllability of these parabolic-like PDEs. We mainly use finite…
A joint characterisation of the controllability and observability of a particular kind of discrete system has been developed. The key idea of the procedure can be reduced to a correct choice of the sampling sequence. This freedom, owing to…
Using a compactness-uniqueness approach, we show that the Fattorini criterion implies the exact controllability of general compactly perturbed controlled linear systems. We then apply this perturbation result to obtain new controllability…
This paper investigates a minimal time control problem for the heat equation with multiple impulse controls. We first establish the maximum principles for this problem and then prove the equivalence between the minimal time impulse control…
Control properties of the Kawahara equation are considered when the equation is posed on an unbounded domain. Precisely, the paper's main results are related to an approximation theorem that ensures the exact (internal) controllability in…
Let us consider a nonlinear degenerate reaction-diffusion equation with application to climate science. After proving that the solution remains nonnegative at any time, when the initial state is nonnegative, we prove the approximate…
We give the solution to the minimum-energy control problem for linear stochastic systems. The problem is as follows: given an exactly controllable system, find the control process with the minimum expected energy that transfers the system…
This work is devoted to prove the pointwise controllability of the Bernoulli-Euler beam equation. It is obtained as a limit of internal controllability of the same type of equation.
We present a finite element (FE) scheme for the numerical approximation of the solution to a non-local Poisson equation involving the one-dimensional fractional Laplacian $(-d_x^2)^s$ on the interval $(-L,L)$. In particular, we include the…
How can humans stay in control of advanced artificial intelligence systems? One proposal is corrigibility, which requires the agent to follow the instructions of a human overseer, without inappropriately influencing them. In this paper, we…
We consider the probability measure minimizing a free energy functional equal to the sum of a Coulomb interaction, a confinement potential and an entropy term, which arises in the statistical mechanics of Coulomb gases. In the limit where…