Null Controllability Research Articles

A convex optimization based multistage wideband pattern accurate synthesis method for overlapping subarrays

Due to frequency variation and overlapping architecture, some overlapping subarrays may exhibit significant grating lobe problems in their wideband patterns. Furthermore, accurate synthesis methods for wideband patterns with subarray architecture are lacking in traditional approaches, as they cannot control sidelobe level (SLL) accurately while maintaining a narrow half-power beam width (HPBW). To address these challenges, this paper proposes a multistage control approach for achieving precise wideband pattern synthesis of subarray structures. Firstly, we propose a subarray pattern synthesis method based on multi-frequency null control (MNC) to address the grating lobe issue under specific overlapping architectures. Secondly, building on the MNC method, we introduce an improved approach called single-frequency null control (SNC) to enhance the array degrees of freedom utilization. Thirdly, we propose an array factor synthesis method based on multi-frequency minimum mainlobe width (M3W) to accurately control SLL and minimize HPBW. This method leverages the subarray pattern synthesis outcome and enforces the multi-frequency SLL constraint to minimize the mainlobe width. Finally, we validate our proposed methods by comparing wideband array patterns, integration array patterns, and traditional methods. The simulation results demonstrate that our methods offer superior GLL suppression, accurate SLL control, and HPBW minimization. Furthermore, the proposed techniques can be applied to arbitrary overlapping subarray systems without being affected by grating lobes, thus overcoming a limitation of traditional methods.

An explicit time for the uniform null controllability of a linear Korteweg-de Vries equation

An explicit time for the uniform null controllability of a linear Korteweg-de Vries equation

Null Controllability for Stochastic Parabolic Equations with Dynamic Boundary Conditions

Null Controllability for Stochastic Parabolic Equations with Dynamic Boundary Conditions

Sanguinarine-based isoquinoline alkaloids modulated the gut-brain axis and enhanced growth performance and gut integrity in natural heat stress broiler chickens

Persistent hot and humid tropical climate induces heat stress (HS), negatively impacting gut integrity with inflammation and tight junction degradation in broilers. As integrating operations of the digestive tract and hypothalamus in avian are regulated by feed intake, the effect of HS may be eased by feed supplementation. Herein, the effect of isoquinoline alkaloids (IQ) supplementation from Macleaya cordata on integrating gut-brain axis and gut integrity was assessed. 720 male broilers (Ross 308) were treated with IQ at null (control), 60 (IQ60), and 100 mg/kg (IQ100). They were reared in open production house between April and May in Southern Thailand with 33.0–38.0°C (average 35.0°C), 75–80% relative humidity (RH), and 160–200 heat stress index (HI). From day 1 to 42, IQ supplementation positively affected growth performance where body weight (BW), body weight gain (BWG), and feed intake (FI) were significantly higher in birds fed IQs than in the control group (P<0.05), and feed conversion ratio (FCR) was significantly lower in the IQ group (P<0.05). IQ improved gut integrity by reducing inflammation with significant down-regulation of nitric oxide synthase (iNOS), cytokines interferon gamma (IFN-γ), interleukin-4 (IL-4), tumor necrosis factor alpha (TNF-α), and nuclear factor κB (NF-κB) in the ileum (P<0.05). It strengthened tight junction by upregulates occludin (OCLD), claudin-1 (CLDN1), tight junction proteins-1 (TJP-1) and mucin-2 (MUC-2) in the jejunum (P<0.05). As a result, serum fluorescein isothiocyanate-dextran (FITC-d) and corticosterone levels were significantly lower (P<0.05). In terms of the gut-brain axis, IQ supplementation reduces ghrelin and cholecystokinin (CCK) mRNA expression in the jejunum and hypothalamus (P<0.05), which downregulated the expression of pro-opiomelanocortin (POMC), cocaine- and amphetamine-regulated transcript (CART), corticotropin-releasing hormone (CRH), and melanocortin four receptor (MC4R). It was the first evidence that IQ influences on modulating the gut-brain axis to suppress anorexigenic regulation in broilers with HS exposure.

Integrated analysis of whole blood oxylipin and cytokine responses after bacterial, viral, and T cell stimulation reveals new immune networks

Oxylipins are major immunomodulating mediators, yet studies of inflammation focus mainly on cytokines. Here, using a standardized whole-blood stimulation system, we characterized the oxylipin-driven inflammatory responses to various stimuli and their relationships with cytokine responses. We performed a pilot study in 25 healthy individuals using 6 different stimuli: 2 bacterial stimuli (LPS and live BCG), 2 viral stimuli (vaccine-grade poly I:C and live H1N1 attenuated influenza), an enterotoxin superantigen and a Null control. All stimuli induced a strong production of oxylipins but most importantly, bacterial, viral, and Tcell immune responses show distinct oxylipin signatures. Integration of the oxylipin and cytokine responses for each condition revealed new immune networks improving our understanding of inflammation regulation. Finally, the oxylipin responses and oxylipin-cytokine networks were compared in patients with active tuberculosis or with latent infection. This revealed different responses to BCG but not LPS stimulation highlighting new regulatory pathways for further investigations.

Qualitative and quantitative assessment of admittance controllers for hand-guiding surgical robots

Abstract When using redundant medical robots for hand-guiding heavy endoscopic tools, admittance control allows a completely defined tool and robot null space motion control. Although not a novel concept, comparative studies that help to design and implement admittance control are missing. In a user study, we compared four admittance controllers: one zero-torque controller that used measured joint torques and three others differently mapping forces/torques measured at the handle to tool tip velocity. We found that two of the four controllers (Dynamic Mass and Integrated Mass) outperformed the others.

Local null controllability for the thermistor problem

In this paper, we deal with the local null controllability of an initial boundary value problem for a thermistor equation. The control is distributed, locally in space. The main ingredients of the proof are suitable Carleman estimates for an adjoint system and Liusternik’s Inverse Mapping Theorem in Hilbert spaces. As a complement to the theoretical results, we present formulations and numerical simulations for the controllability problem, the results were obtained through the finite element method and a quasi-Newton method, simulated in the software Freefem++. Finally, large time null controllability, stabilization and others possible extensions and open problems concerning other systems are presented.

Boundary null controllability of convection-diffusion equations with constraints on the state and application to the identification of boundary pollution parameters

We study a null controllability problem for a convection-diffusion equation with the control contained in Fourier boundary condition to identify M parameters of pollution. The results are achieved by means of an observability inequality derived from new Carleman estimates for the boundary null controllability and the construction of a boundary sentinel to identify the parameters.

Inverse kinematics and multi-objective configuration optimization of the SSRMS manipulator

The Space Station Remote Manipulator System (SSRMS) type redundant manipulator with higher flexibility and foldability is widely used in the space environment. Inverse kinematics and multi-objective configuration optimization are analyzed in this paper. An arm angle parameterized inverse kinematics method using the approximate solution and error compensation scheme is proposed, which has the advantages of not requiring a selection of initial estimates of joint variables, being insensitive to Jacobian matrix singularities, having no pose error, and finding multiple solutions. In addition, Multiple Objective Particle Swarm Optimization (MOPSO) scheme is adopted to optimize the arm angle trajectory in null space, and the optimization index is set as joint torque and manipulability. Unlike traditional trajectory planning methods, we synthesize null space and configuration control to provide a novel perspective for trajectory planning. Finally, the experiments prove that the inverse kinematics algorithm is efficient and reliable, and the effectiveness of the configuration optimization method is verified by the numerical simulation of single objective and multi-objective optimization.

Summation method in an optimal control problem with delay

A summation procedure is described for the construction of the optimal solution in the null controllability problem for a differential equation with distributed delay.

Impulse controllability for the heat equation with inverse square potential and dynamic boundary conditions

Abstract In this paper, we investigate the null approximate impulse controllability of the heat equation with an inverse square potential subject to dynamic boundary conditions in the ball $B(0, R_{0})$ of radius $R_{0}=\left (\frac{4}{3}\right )^{\frac{3}{2}}$. To that purpose, we use the Carleman commutator approach to show a logarithmic convexity estimate traducing an observability inequality at one instant of time.

Targeting the Aspergillus flavus p2c gene through host-induced gene silencing reduces A. flavus infection and aflatoxin contamination in transgenic maize.

Aspergillus flavus is an opportunistic fungal pathogen that infects maize and produces aflatoxins. Using biocontrol or developing resistant cultivars to reduce aflatoxin contamination has only achieved limited success. Here, the A. flavus polygalacturonase gene (p2c) was targeted for suppression through host-induced gene silencing (HIGS) to reduce aflatoxin contamination in maize. An RNAi vector carrying a portion of the p2c gene was constructed and transformed into maize B104. Thirteen out of fifteen independent transformation events were confirmed to contain p2c. The T2 generation kernels containing the p2c transgene had less aflatoxin than those without the transgene in six out of eleven events we examined. Homozygous T3 transgenic kernels from four events produced significantly less aflatoxins (P ≤ 0.02) than the kernels from the null or B104 controls under field inoculation conditions. The F1 kernels from the crosses between six elite inbred lines with P2c5 and P2c13 also supported significantly less aflatoxins (P ≤ 0.02) than those from the crosses with null plants. The reduction in aflatoxin ranged from 93.7% to 30.3%. Transgenic leaf (T0 and T3) and kernel tissues (T4) were also found to have significantly higher levels of p2c gene-specific small RNAs. Further, homozygous transgenic maize kernels had significantly less fungal growth (27~40 fold) than the null control kernels 10 days after fungal inoculation in the field. The calculated suppression of p2c gene expression based on RNAseq data was 57.6% and 83.0% in P2c5 and P2c13 events, respectively. These results indicate clearly that the reduced aflatoxin production in the transgenic kernels is due to RNAi-based suppression of p2c expression, which results in reduced fungal growth and toxin production.

On the null controllability of integer order integro-differential equations

Abstract This paper is addressed to the study of the null controllability for integer order integro-differential equations. Unlike the known results for partial differential equations, we need to consider the equation involving a $\beta -$power of the Laplace operator $(-\varDelta )^\beta $ and an integral term. The key point is to construct a suitable state space of the controlled system at the final time. We first discuss a class of hyperbolic integro-differential equation. We prove that the controlled system is null controllable by an Ingham-type estimate. Also, the controllability time is given. On the other hand, by reduction to absurdity, we deduce that the null controllability property fails for a class of parabolic integro-differential equation with $\beta \in \mathbb{N}^+$.

Observability and control of parabolic equations on networks with loops

Network theory can be useful for studying complex systems such as those that arise, for example, in physical sciences, engineering, economics and sociology. In this paper, we prove the observability of parabolic equations on networks with loops. By using a novel Carleman inequality, we find that the observability of the entire network can be achieved under certain hypothesis about the position of the observation domain. The main difficulty we tackle, due to the existence of loops, is to avoid entering into a circular fallacy, notably in the construction of the auxiliary function for the Carleman inequality. The difficulty is overcome with a careful treatment of the boundary terms on the junctions. Finally, we use the observability to prove the null controllability of the network and to obtain the Lipschitz stability for an inverse problem consisting on retrieving a stationary potential in the parabolic equation from measurements on the observation domain.

Fractional Stochastic Evolution Inclusions with Control on the Boundary

Symmetry in systems arises as a result of natural design and provides a pivotal mechanism for crucial system properties. In the field of control theory, scattered research has been carried out concerning the control of group-theoretic symmetric systems. In this manuscript, the principles of stochastic analysis, the fixed-point theorem, fractional calculus, and multivalued map theory are implemented to investigate the null boundary controllability (NBC) of stochastic evolution inclusion (SEI) with the Hilfer fractional derivative (HFD) and the Clarke subdifferential. Moreover, an example is depicted to show the effect of the obtained results.

The effects of short messages encouraging prevention behaviors early in the COVID-19 pandemic.

Effectively addressing public health crises like the COVID-19 pandemic requires persuading the mass public to change their behavior in significant ways. Many efforts to encourage behavior change-such as public service announcements, social media posts, and billboards-involve short, persuasive appeals, yet the effectiveness of these messages is unclear. Early in the COVID-19 pandemic, we tested whether short messages could increase intentions to comply with public health guidelines. To identify promising messages, we conducted two pretests (n = 1,596) in which participants rated the persuasiveness of 56 unique messages: 31 based on the persuasion and social influence literatures and 25 drawn from a pool of crowdsourced messages generated by online respondents. The four top-rated messages emphasized: (1) civic responsibility to reciprocate the sacrifices of health care workers, (2) caring for the elderly and vulnerable, (3) a specific, sympathetic victim, and (4) limited health care system capacity. We then conducted three well-powered, pre-registered experiments (total n = 3,719) testing whether these four top-rated messages, and a standard public health message based on language from the CDC, increased intentions to comply with public health guidelines, such as masking in public spaces. In Study 1, we found the four messages and the standard public health message significantly outperformed a null control. In Studies 2 and 3, we compared the effects of persuasive messages to the standard public health message, finding that none consistently out-performed the standard message. This is in line with other research showing minimal persuasive effects of short messages after the very early stages of the pandemic. Across our studies, we found that (1) short messages can increase intentions to comply with public health guidelines, but (2) short messages featuring persuasive techniques from the social science literature did not substantially outperform standard public health messages.

Null Controllability of Nonlinear Mixed Integro-differential Systems

The present paper investigates the existence of mild solutions and provides sufficient conditions for the null controllability of nonlinear mixed integrodifferential systems with unbounded linear operators in Banach spaces. It is observed that, if the linear system is controllable, then the nonlinear equivalence is also controllable by subjecting certain smooth conditions on the perturbation function. The results are obtained using semi group of linear operators, fractional powers of operators and the Schauder fixed point theorem.

Controllability Criteria on Discrete-Time Impulsive Hybrid Systems With Input Delay

Due to the importance of the hybrid systems, the controllability for linear discrete-time impulsive hybrid systems with input delay (DIHSID) is investigated by resorting to the geometric and algebraic analytical methods in this article. First, the null reachability and controllability geometric conditions are studied. Specifically, the null reachable set and controllable set for every impulsive and switching sequence are obtained by the properties of the invariant subspace. Besides, a new subspace sequence is constructed to analyze the null reachability and controllability of DIHSID. Second, the complete controllability of DIHSID is investigated by algebraic methods. In the form of Gramian matrices, several sufficient complete controllability conditions for DIHSID are established without assuming the nonsingularity of all impulsive matrices. Furthermore, a less conservative complete controllability criterion that is necessary and sufficient is developed by introducing a row matrix of some Gramian matrices. Finally, two illustrating examples show the effectiveness of the developed controllability theory.

Global Controllability of the Boussinesq System with Navier-Slip-with-Friction and Robin Boundary Conditions

In this paper, we deal with the global exact controllability to the trajectories of the Boussinesq system posed in 2D or 3D smooth bounded domains. The velocity field of the fluid must satisfy a Navier-slip-with-friction boundary condition, and a Robin boundary condition is imposed to the temperature. We assume that one can act on the velocity and the temperature on a small part of the boundary. For the proof, we first transform the boundary control problem into a distributed control problem. Then, we prove a global approximate controllability result by adapting the strategy of Coron, Marbach, and Sueur [J. Eur. Math. Soc. (JEMS), 22 (2020), pp. 1625–1673]; this relies on the controllability properties of the inviscid Boussinesq system and the analysis of appropriate asymptotic boundary layer expansions. Finally, we conclude with a local controllability result; as in many other cases, this can be established as a consequence of the null controllability of a linearized system through a fixed-point argument. Our contribution can be viewed as an extension of the results in [J. Eur. Math. Soc. (JEMS), 22 (2020), pp. 1625–1673], where thermal effects were not considered. Thus, we prove that the ideas behind the controllability properties of the Euler system and the well-prepared dissipation technique can be adapted to the present situation. Furthermore, we cover all the classical boundary conditions for the temperature, that is, those of the Robin, Neumann, and Dirichlet kinds.

Lebeau–Robbiano Inequality for Heat Equation with Dynamic Boundary Conditions and Optimal Null Controllability

Lebeau–Robbiano Inequality for Heat Equation with Dynamic Boundary Conditions and Optimal Null Controllability