Exact Controllability Research Articles

Controllability of Hilfer fractional Langevin evolution equations

The existence of fractional evolution equations has attracted a growing interest in recent years. The mild solution of fractional evolution equations constructed by a probability density function was first introduced by El-Borai. Inspired by El-Borai, Zhou and Jiao gave a definition of mild solution for fractional evolution equations with Caputo fractional derivative. Exact controllability is one of the fundamental issues in control theory: under some admissible control input, a system can be steered from an arbitrary given initial state to an arbitrary desired final state. In this article, using the (α, β) resolvent operator and three different fixed point theorems, we discuss the control problem for a class of Hilfer fractional Langevin evolution equations. The exact controllability of Hilfer fractional Langevin systems is established. An example is also discussed to illustrate the results.

Exact controllability of the transmission string–beam equations with a single boundary control

We consider the exact controllability of a transmission system which models a flexible beam with one end clamped and the other end linked to a string. The control only acts on the free end of the string. Using the multiplier method, we prove that the full energy of transmission system can be estimated by the boundary data of string. Finally, by using the HUM method, we deduce that the transmission system is exactly controllable at the time of control .

High-temperature reactivity of vanadium oxide clusters in methane activation: Vibrational degrees of freedom matter.

Understanding the properties of small particles working under high-temperature conditions at the atomistic scale is imperative for exact control of related processes, but it is quite challenging to achieve experimentally. Herein, benefitting from state-of-the-art mass spectrometry and by using our newly designed high-temperature reactor, the activity of atomically precise particles of negatively charged vanadium oxide clusters toward hydrogen atom abstraction (HAA) from methane, the most stable alkane molecule, has been measured at elevated temperatures up to 873K. We discovered the positive correlation between the reaction rate and cluster size that larger clusters possessing greater vibrational degrees of freedom can carry more vibrational energies to enhance the HAA reactivity at high temperature, in contrast with the electronic and geometric issues that control the activity at room temperature. This finding opens up a new dimension, vibrational degrees of freedom, for the simulation or design of particle reactions under high-temperature conditions.

Control of Kawahara equation with overdetermination condition: The unbounded cases

In this manuscript, we consider the internal control problem for the fifth‐order KdV type equation, commonly called the Kawahara equation, on unbounded domains. Precisely, under certain hypotheses over the initial and boundary data, we can prove that there exists an internal control input such that solutions of the Kawahara equation satisfy an integral overdetermination condition. This condition is satisfied when the domain of the Kawahara equation is posed in the real line, left half‐line, and right half‐line. Moreover, we are also able to prove that there exists a minimal time in which the integral overdetermination condition is satisfied. Finally, we show a type of exact controllability associated with the “mass” of the Kawahara equation posed in the half‐line.

Hierarchical exact controllability of hyperbolic equations and Dunford-Pettis' theorem

This paper deals with the Stackelberg-Nash strategies for boundary control problems for linear and semilinear wave equations. Assuming that we can act on the system through a hierarchy of controls, to each leader, we associate a Nash equilibrium (two followers) corresponding to a bi-objective optimal control problem. Then we look for a leader that solves an exact boundary controllability problem. We mainly consider the case of a semilinear hyperbolic PDE where all the controls (leader and followers) act on small parts of the boundary. In view of the lack of regularity, the arguments usually invoked to prove controllability do not work here. Accordingly, we carry out a fixed-point approach based on weak compactness in $L^1$. To this purpose, we apply Dunford-Pettis' Theorem. We also consider the case where the followers act in small subsets of the domain.

Study for Bonding Technology by Electroplated Nano porous Cu Structure

The various kinds of the packaging technologies such as 2.nD, 2.5D, 3D are highly studied with the rapid development of miniaturization and high density of semiconductor packaging. This trend increases the importance of fine pitch interconnect. To achieve fine pitch interconnect, Cu-Cu direct bonding or hybrid bonding which has no solder in bonding layer is the promising technologies. There are some difficulties in the solderless bonding such as the control of bump uniformity, high accuracy CMP (Chemical Mechanical Polishing) process and so on. In particular, the exact surface shape control is the essential issue. To solve these problems, we are proposing Nano porous (NP) Cu materials for interconnect material. One of the technical challenges is the process for formation of NP Cu µ-bump structure. We are focusing on electroplating process for µ-bump formation. Firstly, we developed the plating chemicals for formation of NP Cu structure. We consider two types of plating chemicals for NP Cu formation, de-alloying and direct porous plating process. For de-alloying process, Cu-Zn alloy bumps were plated, and NP Cu bumps were obtained by de-alloying the Cu-Zn alloy. For direct porous plating process, NP Cu bumps were plated by using unique additives which can form NP structure directly. By using electroplated NP Cu, we studied its various properties, and carried out bonding tests. As the results, NP Cu structure shows unique properties such as electrical conductivity and the hardness, and we consider that these unique properties should widen the bonding process margin. We would like to present our recent research of NP Cu which is promising materials for advanced bonding technology.

Stability and controllability of nonautonomous neutral system with two delays

This article investigates the exact and approximate controllability, finite time stability, and –Hyers–Ulam–Rassias stability of a neutral impulsive system of differential equations with two delays. Fixed point theory is associated in the analysis of controllability of the system. The stability analysis is carried out with the help of Grönwall type inequality.

Relatively exact controllability for fractional stochastic delay differential equations of order [formula omitted

In this paper, our main purpose is to study a class of fractional stochastic delay differential equations (FSDDEs) of order κ∈(1,2]. Firstly, we present a concept of delay Grammian matrix involving delayed matrix functions of sine. Subsequently, the relatively exact controllability of linear FSDDEs is obtained by using Grammian matrix. Furthermore, based on Krasnoselskii’s fixed point theorem, we explore the relatively exact controllability of the nonlinear addressed equations. In addition, with the aid of delay Grönwall inequality, Jensen inequality and Itô isometry, existence of optimal control for the Lagrange problem is derived. Finally, the theoretical conclusions are supported through two examples.

Global nonlinear exact impact time control guidance design based on error dynamics

Global nonlinear exact impact time control guidance design based on error dynamics

Exact Controllability of Wave Equations with Interior Degeneracy and One-Sided Boundary Control

Exact Controllability of Wave Equations with Interior Degeneracy and One-Sided Boundary Control

External and internal dual-controls: Tunable cavity and Ru–O–Co bond bridge synergistically accelerate the RuCoCu-MOF/CF nanorods for urea-assisted energy-saving hydrogen production

Currently, there are still many limitations in the research of conductive metal-organic frameworks (MOFs) in the field of electrocatalysis. On the one hand, most MOFs have a solid construction, seriously hindering their mass transfer process. On the other hand, innate bonding is not conducive to the optimization of electronic structures and the excitation of intrinsic active sites. Therefore, external/internal dual-control of MOFs is urgently needed to break the shackles of their activity. Herein, the hollow RuCoCu-MOF/CF nanorods with tunable cavities are directionally constructed by a self-sacrificial template method. Benefiting from the exact morphological control and the unique Ru–O–Co bond bridge, RuCoCu-MOF/CF exhibits superior performances for alkaline hydrogen evolution reaction (HER) and urea oxidation reaction (UOR). Surprisingly, a record-breaking voltage of 1.402 V drives a current density of 10 mA cm−2 for urea-assisted overall water splitting under alkaline conditions, greatly promoting the development of energy-efficient hydrogen production technology. This work firstly constructed the MOF-based self-supporting electrode with ultra-high urea-assisted hydrogen production and urea degradation performances via the dual controls of the cavity size and chemical bond bridge. This points out the direction for the development of unique integrated electrodes for both hydrogen production and decontamination.

Computer-Generated Holography Methods for Data Page Reconstruction Using Phase-Only Medium

Achievements in the field of high-speed spatial modulation electrooptic components provide the possibility to create perspective optical-digital diffractive systems for information storage and processing that outperform modern electronic counterparts by utilizing throughput, energy efficiency, and reliability. This work presents a study of computer-generated holography methods that allow the formation of spatially-modulated information signals (data pages) with high accuracy using phase-only spatial light modulators. Computer-generated Fourier hologram fringe patterns were formed using bipolar intensity and double-phase coding. Numerical and experimental results of both methods’ implementation are compared. It was determined that bipolar intensity holograms provide higher data density on the data page if complex digital modulation methods such as multilevel amplitude and phase or quadrature modulation are used to represent data points. Double-phase coding can offer perspective for multilevel amplitude or multilevel intensity modulated data page reconstruction; however, exact control of phase modulation characteristics is required to obtain high reconstruction quality.

Machine Learning for Halide Perovskite Materials ABX3 (B = Pb, X = I, Br, Cl) Assessment of Structural Properties and Band Gap Engineering for Solar Energy

The exact control of material properties essential for solar applications has been made possible because of perovskites' compositional engineering. However, tackling efficiency, stability, and toxicity at the same time is still a difficulty. Mixed lead-free and inorganic perovskites have lately shown promise in addressing these problems, but their composition space is vast, making it challenging to find good candidates even with high-throughput approaches. We investigated two groups of halide perovskite compound data with the ABX3 formula to investigate the formation energy data for 81 compounds. The structural stability was analyzed over 63 compounds. For these perovskites, we used new library data extracted from a calculation using generalized-gradient approximation within the Perdew-Burke-Ernzerhof (PBE) functional established on density functional theory. As a second step, we built machine learning models, based on a kernel-based naive Bayes algorithm that anticipate a variety of target characteristics, including the mixing enthalpy, different octahedral distortions, and band gap calculations. In addition to laying the groundwork for observing new perovskites that go beyond currently available technical uses, this work creates a framework for finding and optimizing perovskites in a photovoltaic application.

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.

Carbon nanotube pathogenicity conforms to a unified theory for mesothelioma causation by elongate materials and fibers

The purpose of this review is to elucidate how dimensional and durability characteristics of high aspect ratio nanomaterials (HARN), including carbon nanotubes (CNT) and metal nanowires (MeNW), contribute to understanding the fiber pathogenicity paradigm (FPP), including by explaining the structure-activity relationships (SAR) of a diverse range of natural and synthetic elongate materials that may or may not contribute to mesothelioma development in the lung. While the FPP was originally developed to explain the critical importance of asbestos and synthetic vitreous fiber length, width, aspect ratio and biopersistence in mesothelioma development, there are a vast number of additional inhalable materials that need to be considered in terms of pathogenic features that may contribute to mesothelioma or lack thereof. Not only does the ability to exert more exact control over the length and biopersistence of HARNs confirm the tenets of the FPP, but could be studied by implementating more appropriate toxicological tools for SAR analysis. This includes experimentation with carefully assembled libraries of CNTs and MeNWs, helping to establish more precise dimensional features for interfering in lymphatic drainage from the parietal pleura, triggering of lysosomal damage, frustrated phagocytosis and generation of chronic inflammation. The evidence includes data that long and rigid, but not short and flexible multi-wall CNTs are capable of generating mesotheliomas in rodents based on an adverse outcome pathway requiring access to pleural cavity, obstruction of pleural stomata, chronic inflammation and transformation of mesothelial cells. In addition to durability and dimensional characteristics, bending stiffness of CNTs is a critical factor in determining the shape and rigidity of pathogenic MWCNTs. While no evidence has been obtained in humans that CNT exposure leads to a mesothelioma outcome, it is important to monitor exposure levels and health effect impacts in workers to prevent adverse health outcomes in humans.

Relatively exact controllability of fractional stochastic delay system driven by Lévy noise

In this article, we consider the relatively exact controllability of fractional stochastic delay system (FSDS) driven by Lévy noise. First, we derive the solution of linear FSDS via delayed matrix functions of Mittag–Leffler (M‐L). Subsequently, by virtue of the controllability Grammian matrix, we explore the relatively exact controllability of linear FSDS. In addition, with the aid of Jensen's inequality, Hölder's inequality, and Itô's isometry, the existence and uniqueness of the considered nonlinear FSDS are investigated by employing Banach contraction principle. Thereafter, the relatively exact controllability of nonlinear FSDS is discussed. Finally, the theoretical results are supported through examples.

Exact Controllability of Hilfer Fractional Differential System with Non-instantaneous Impluleses and State Dependent Delay

Exact Controllability of Hilfer Fractional Differential System with Non-instantaneous Impluleses and State Dependent Delay

Deep Reinforcement Learning-Based Control of Stewart Platform With Parametric Simulation in ROS and Gazebo

AbstractThe Stewart platform is an entirely parallel robot with mechanical differences from typical serial robotic manipulators, which has a wide application area ranging from flight and driving simulators to structural test platforms. This work concentrates on learning to control a complex model of the Stewart platform using state-of-the-art deep reinforcement learning (DRL) algorithms. In this regard, to enhance the reliability of the learning performance and to have a test bed capable of mimicking the behavior of the system completely, a precisely designed simulation environment is presented. Therefore, we first design a parametric representation for the kinematics of the Stewart platform in Gazebo and robot operating system (ROS) and integrate it with a Python class to conveniently generate the structures in simulation description format (SDF). Then, to control the system, we benefit from three DRL algorithms: the asynchronous advantage actor–critic (A3C), the deep deterministic policy gradient (DDPG), and the proximal policy optimization (PPO) to learn the control gains of a proportional integral derivative (PID) controller for a given reaching task. We chose to apply these algorithms due to the Stewart platform’s continuous action and state spaces, making them well-suited for our problem, where exact controller tuning is a crucial task. The simulation results show that the DRL algorithms can successfully learn the controller gains, resulting in satisfactory control performance.

The dynamics of directional transport of a droplet in programmable electrowetting channel

Directional fluid transport by electrowetting is an effective method for fluid management both on Earth and in the space environment. Exact control of the process is always hard because the fundamental dynamics of fluid flow and interface are not well understood. In this study, we examine the process of a sensible droplet transported directionally in an electrowetting channel. The electrodes of the channel are programmed to actuate the droplet at the most effective manner. We build a numerical model based on the phase field method, and a dynamic contact angle model is incorporated in the model. Based on simulated results, the basic process of droplet deformation and motion is explained. Three different stages are observed when the droplet starts to move in the electrowetting channel. The droplet can be transported at a high velocity of 17 mm/s at a voltage of V = 80 V. A wide range of influence factors, including voltage, droplet size, friction factor, pinning force, channel height, gravity level, and tilted angle of the channel, are considered. The contact line friction increases almost linearly with the contact line friction coefficient and the pinning force, both retarding the motion of the droplet at parabolic relations. With an increase in the gravity level, the transport velocity of large droplet decreases. However, the droplet smaller than the capillary length shows quite good anti-gravity capability, which can be transported smoothly even when the channel is tilted by 90° in a normal gravity.

A Method Based on Phase-shifting Carrier for Reducing DC-link Current Harmonics in Dual Three-phase PMSM Drive under Open-phase Conditions

The All-Electric of modern military equipment has become an important trend, in the field of aircraft the traditional servo control focus on the exact control of the motor. With the development of power electronics technology, a high-power motor has expanded into a multiphase kind which cast off the limitation of traditional three-phase motors. The multiphase motor has more control resources and fault-tolerant control ability under the fault condition, which has practical meaning for high safety and high-reliability applications in an airborne environment. The multiphase motor can be controlled by a series of phase-shift carriers, which can reduce DC current ripple more effectively than the traditional carrier-based pulse width modulation, but it needs to find the optimal phase shift angle. In this paper, the optimal carrier phase shift angle is analyzed mathematically which can be used for both under health and single open-phase fault of a dual three-phase motor, and the simulation result illustrates that the carrier phase shift method used in this paper has the DC current ripple optimization effect.