Null Controllability Research Articles

Null controllability for backward stochastic parabolic convection-diffusion equations with dynamic boundary conditions

Null controllability for backward stochastic parabolic convection-diffusion equations with dynamic boundary conditions

Perturbation-Based Nulling Control Beamforming With Measured Element Radiation Patterns for MU-mMIMO

Perturbation-Based Nulling Control Beamforming With Measured Element Radiation Patterns for MU-mMIMO

Study approximate controllability and null controllability of neutral delay Hilfer fractional stochastic integrodifferential system with Rosenblatt process

In this paper, we investigate the sufficient conditions for approximate controllability and null controllability of neutral delay stochastic Hilfer fractional integrodifferential system with Rosenblatt process are established. The required results are obtained based on a fixed point technique, fractional calculus and stochastic analysis. Finally, an example is given to illustrate the obtained results.

Null controllability of KdV equation in a star-shaped network

Null controllability of KdV equation in a star-shaped network

Quantitative Rapid and Finite Time Stabilization of the Heat Equation

The finite time stabilizability of the one dimensional heat equation is proved by Coron-Nguyên [J.-M. Coron and H.-M. Nguyen, Arch. Ration. Mech. Anal. 225 (2017) 993–1023], while the same question for multidimensional spaces remained open. Inspired by Coron-Trélat [J.-M. Coron and E. Trélat, SIAM J. Control Optim. 43 (2004) 549–569] we introduce a new method to stabilize multidimensional heat equations quantitatively in finite time and call it Frequency Lyapunov method. This method naturally combines spectral inequality [G. Lebeau and L. Robbiano, Comm. Partial Diff. Equ. 20 (1995) 335–356] and constructive feedback stabilization. As application this approach also yields a constructive proof for null controllability, which gives sharing optimal cost CeC/T with explicit controls and works perfectly for related nonlinear models such as Navier–Stokes equations [S. Xiang, Ann. Inst. H. Poincaré C Anal. Non Lineaire 40 (2023) 1487–1511.].

Null controllability of the advection-dispersion equation with respect to the dispersion parameter using the Fokas method

We investigate the null controllability of the linear advection-dispersion (LAD) equation posed on a finite interval. To this end, we employ the Fokas method to determine boundary controls and the controlled solutions concerning varying dispersion parameters and final times. By employing the Fokas method for the LAD equation, which provides an explicit integral representation of the solution, we enable a comprehensive analysis of null controllability. Consequently, we derive a boundary control input that effectively steers the solution from its initial state to the zero state within a given final time. The proposed approach offers a straightforward means to achieve the null controllability for the LAD equation, even as the dispersion parameter and the final time vary. Importantly, the effectiveness of this approach can be extended to various types of boundary control problems, thereby enhancing its broader applicability and potential impact.

The Cost of Null Controllability for a Backward Stochastic Degenerate Parabolic Equation in the Vanishing Viscosity Limit

The Cost of Null Controllability for a Backward Stochastic Degenerate Parabolic Equation in the Vanishing Viscosity Limit

Modulation of seed amylose content in durum wheat through mutagenesis of starch synthase IIa (SSIIa) and its effect on milling and semolina quality

The elimination of Starch Synthase IIa (SSIIa) in durum wheat seeds increases amylose and protein but decreases starch and seed size. To mitigate the negative impact of increased amylose upon seed size we identified partially functional SSIIa alleles and combined them with SSIIa null alleles. The first step was to mutagenize durum with ethyl methanesulfonate (EMS) and select SSIIa-A1 and SSIIa-B1 missense alleles and combine them by crossing with SSIIa null alleles. Segregating lines possessing a SSIIa null mutation in one genome and a missense mutation in the other genome were compared to single SSIIa null mutant sister lines over two field seasons. Lines that carried one SSIIa null and one missense allele showed elevated amylose compared to single null sister lines and controls. In most SSIIa haplotypes tested, increased amylose content was negatively correlated with seed size and starch content. However, two SSIIa missense alleles were identified that increased amylose to 34 % when combined with a SSIIa null allele. Thus, moderate amylose increases are possible if a small amount of SSIIa activity remains in developing wheat seeds without negatively impacting seed size or starch.

Global exact controllability of the viscous and resistive MHD system in a rectangle thanks to the lateral sides and to distributed phantom forces

We consider the 2-D incompressible viscous and resistive magnetohydrodynamics (MHD) system in a rectangle, with controls on the lateral sides. The velocity satisfies Dirichlet boundary conditions, while the magnetic field follows perfectly conducting wall boundary conditions on the remaining, uncontrolled part of the boundary. We extend the small-time global exact null controllability result of Coron et al. in [Ann PDE 5(2):1-49, 2019] from Navier-Stokes equations to MHD equations, with a little help of distributed phantom forces, which can be chosen arbitrarily small in any given Sobolev spaces. Our analysis relies on Coron’s return method, the well-prepared dissipation method, long-time nonlinear Cauchy-Kovalevskaya estimates and Badra’s local exact controllability result.

The Null Boundary Controllability for a Fourth-Order Parabolic Equation with Samarskii–Ionkin-Type Boundary Conditions

The Null Boundary Controllability for a Fourth-Order Parabolic Equation with Samarskii–Ionkin-Type Boundary Conditions

Null controllability and Stackelberg–Nash strategy for a $2\times 2$ system of parabolic equations

This paper is dedicated to solving a multi-objective control problem for a 2\times2 system of parabolic equations. Here, we have many objectives, possibly conflictive, and we adopt a concept of hierarchy for the controls. We have the leader control, responsible for objectives of controllability type, and the follower controls which intend to be a Nash-equilibrium with respect to some given cost functionals. The novelty here is that we formulate this problem for systems of parabolic equations, meaning that we have many variables and naturally much more objectives to accomplish.

Sharp uniqueness and stability of solution for an inverse source problem for the Schrödinger equation

This article is concerned with the uniqueness and the stability for an inverse source problem of determining a spatially varying factor f(x) of a source term given by with suitably given R(t) of the Schrödinger equation with time independent coefficients. In order to establish these results, for the Schrödinger equation, we prove (i) a logarithmic conditional stability estimate for a Cauchy problem attached with the zero Dirichlet boundary conditions on the whole boundary, (ii) the unique continuation for the Cauchy problem from an arbitrary small part of a lateral boundary. We do not assume any constraints on the geometry of the subboundary and an observation time length. The key is an integral transform with a kernel solving a null controllability problem for the one-dimensional Schrödinger equation, which transforms a solution of the Schrödinger equation to a solution of an elliptic equation.

Exact Null Controllability of a One-Dimensional Wave Equation with a Mixed Boundary

In this paper, exact null controllability of one-dimensional wave equations in non-cylindrical domains was discussed. It is different from past papers, as we consider boundary conditions for more complex cases. The wave equations have a mixed Dirichlet–Neumann boundary condition. The control is put on the fixed endpoint with a Neumann boundary condition. By using the Hilbert Uniqueness Method, exact null controllability can be obtained.

Impulse controllability for degenerate singular parabolic equations via logarithmic convexity method

Abstract In this paper, we study null approximate controllability of degenerate singular parabolic equations under the action of an impulsive control. To this aim, we prove an observation estimate at one point in time for the problems associated to the operators: $$ \begin{align*}& u_{t} -(x^{\alpha} u_{x})_{x} - \dfrac{\mu}{x^{\beta}} u = 0, \qquad x \in \left(0, 1\right), \end{align*} $$ where the parameters $\alpha \geq 0$, $\beta , \mu \in \mathbb{R}$ satisfy suitable assumptions. The method of proof combines both the logarithmic convexity and the Carleman commutator.

Ground state solitary waves local controllability for the nonlinear focusing Schrödinger equation in the mass critical and mass slightly subcritical case

In this paper, we prove the boundary exact local controllability around ground state solitary waves with different scaling for the mass critical and mass slightly subcritical nonlinear Schrödinger equation. More precisely, we prove that there exists a control driving the solution from the vicinity of Qλ1 to the vicinity of Qλ2, for λ1,λ2>0, with a minimal time of controllability. In the mass slightly subcritical case, we also prove the null controllability for initial data starting in a neighborhood of the ground state Qλ, for λ>0, with a minimal time of controllability. The control strategy deployed in this article is non-destructive as the solution remains close to the ground state for all time.

Exact controllability to the trajectories of the one-phase Stefan problem

This paper deals with the boundary exact controllability to the trajectories of the one-phase Stefan problem in one spatial dimension. This is a free-boundary problem that models solidification and melting processes. We prove the local exact controllability to (smooth) trajectories. To this purpose, we first reformulate the problem as the local null controllability of a coupled PDE-ODE system with distributed controls. Then, a new Carleman inequality for the adjoint of the linearized PDE-ODE system, coupled on the boundary through nonlocal in space and memory terms, is presented. This leads to the null controllability of an appropriate linear system. Finally, the result is obtained via local inversion, by using Lyusternik-Graves' Theorem. As a byproduct of our approach, we find that some parabolic equations which contains memory terms located on the boundary are null-controllable.

Carleman estimate and null controllability for a degenerate parabolic equation with a slightly superlinear reaction term

Carleman estimate and null controllability for a degenerate parabolic equation with a slightly superlinear reaction term

Effectiveness of a Novel Tablet Application in Reducing Guideline Deviations During Pediatric Cardiac Arrest

Deviations from international resuscitation guidelines during the management of pediatric cardiac arrest are frequent and affect clinical outcomes. An interactive tablet application (app), PediAppRREST, was developed to reduce guideline deviations during pediatric cardiac arrest. To assess the effectiveness of PediAppRREST in improving the management of simulated in-hospital pediatric cardiac arrest. This multicenter 3-group simulation-based randomized clinical trial was conducted from September 2020 to December 2021 at 4 Italian university hospitals (Padua, Florence, Rome, Novara). Participants included residents in pediatrics, emergency medicine, and anesthesiology. Analyses were conducted as intention-to-treat. Data were analyzed from January to June 2022. Teams were randomized to 1 of 3 study groups: an intervention group that used the PediAppRREST app; a control group that used a paper-based cognitive aid, the Pediatric Advanced Life Support (PALS) pocket card; and a control group that used no cognitive aids. All the teams managed the same standardized simulated scenario of nonshockable pediatric cardiac arrest. The primary outcome was the number of deviations from guidelines, measured by a 15-item checklist based on guideline recommendations. The main secondary outcomes were quality of chest compressions, team clinical performance (measured by the Clinical Performance Tool), and perceived team leader's workload. Study outcomes were assessed via video reviews of the scenarios. Overall 100 teams of 300 participants (mean [SD] age, 29.0 [2.2] years; 195 [65%] female) were analyzed by intention-to-treat, including 32 teams randomized to the PediAppRREST group, 35 teams randomized to the PALS control group, and 33 teams randomized to the null control group. Participant characteristics (210 pediatric residents [70%]; 48 anesthesiology residents [16%]; 42 emergency medicine residents [14%]) were not statistically different among the study groups. The number of deviations from guidelines was significantly lower in the PediAppRREST group than in the control groups (mean difference vs PALS control, -3.0; 95% CI, -4.0 to -1.9; P < .001; mean difference vs null control, -2.6; 95% CI, -3.6 to -1.5; P < .001). Clinical Performance Tool scores were significantly higher in the PediAppRREST group than control groups (mean difference vs PALS control, 1.4; 95% CI, 0.4 to 2.3; P = .002; mean difference vs null control, 1.1; 95% CI, 0.2 to 2.1; P = .01). The other secondary outcomes did not significantly differ among the study groups. In this randomized clinical trial, the use of the PediAppRREST app resulted in fewer deviations from guidelines and a better team clinical performance during the management of pediatric cardiac arrest. ClinicalTrials.gov Identifier: NCT04619498.

A Gain-Enhanced Differential-Fed Stacked Circular Patch Antenna With Simultaneously Controllable E-Plane and H-Plane Radiation Nulls

In this work, a differential-fed three-layer stacked circular patch antenna with enhanced gain performance is theoretically investigated for the simultaneous control of radiation nulls over both <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> -plane and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> -plane patterns. First, the bottom layer patch is meticulously designed based on a modified TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> mode to meet the matching conditions. Then, the structures of the parasitic layer patches are contrived to form similar peripheral radiative current distributions compared with the bottom one, aiming to simplify the analysis process. After that, the three-layer patches are stacked in a capacitively coupled fashion, which guarantees the out-of-phase scheme between the middle layer patch and the other two-layer patches. By means of the cavity-model theorem, further investigations on the multilayer distributions of the equivalent magnetic currents for the three radiators have successfully demonstrated that the destructive interference among the currents will result in the emergence of radiation nulls for both <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> -plane and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> -plane patterns. As a result, the beamwidth of the antenna in the two principal planes can be narrowed, which contributes to a significant improvement in the overall gain performance. Furthermore, a thorough array factor analysis on the flexible control of the radiation nulls is highlighted with both theoretical predictions and full-wave quantitative verifications. Finally, an experimental prototype is fabricated and measured to prove its validity. Compared with other stacked antennas with approximately the same longitudinal profiles, this design features the highest measured peak gain of 13.9 dBi, with an attractive increment of 8.0 dB pronounced.

Exact Null Controllability of a Wave Equation with Dirichlet–Neumann Boundary in a Non-Cylindrical Domain

In this paper, by applying the Hilbert Uniqueness Method in a non-cylindrical domain, we prove the exact null controllability of one wave equation with a moving boundary. The moving endpoint of this wave equation has a Neumann-type boundary condition, while the fixed endpoint has a Dirichlet boundary condition. We derived the exact null controllability and obtained an exact controllability time of the wave equation.