Global Stabilization Research Articles

Damping Turning Rule of Virtual Synchronous Generator for Global Stability

In this paper, it is interesting to find that the virtual synchronous generator (VSG) with sufficient damping can exhibit the global stability phenomenon, i.e., the grid-connected VSG keeps asymptotically stable irrespective of the fault clearing time. The expression of the dissipated energy induced by damping is first derived from the energy conservation law. The dissipated energy equals the damping factor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{D}$</tex-math></inline-formula> times the area in the phase plane encircled by the system trajectory and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> -axis. Accordingly, a simple approach to realizing global stabilization is proposed by tuning the damping of the grid-connected VSG. It is proved that once the constant potential energy decrement over every period is less than one minimal dissipated energy, the kinetic energy at the unstable equilibrium point (UEP) of each period drops gradually, and the global stability can be achieved. Furthermore, an equal energy surface composed by the potential energy of the UEP is constructed to estimate the minimal dissipated energy, yielding an analytical and conservative damping tuning rule of VSGs for global stability. Simulation studies based on PSCAD/EMTDC have validated the correctness of the proposed global stability condition and the effectiveness of the damping tuning method of VSGs.

Adaptive Prescribed-Time Control of Time-Delay Nonlinear Systems via a Double Time-Varying Gain Approach.

This article studies the global prescribed-time stabilization problem for a class of time-delay nonlinear systems with uncertain parameters. First, we design two time-varying gains with special properties, in which one is introduced into virtual controllers to achieve prescribed-time convergence and the other one is used to construct the Lyapunov-Krasovskii (L-K) functional and Lyapunov function to handle the nonlinear time-delay term and unknown parameters, respectively. Then, by utilizing double time-varying gains and the scaling-free backstepping design approach, a dynamic state feedback controller is constructed, which guarantees that all state variables reach zero within a prescribed time, and the prescribed time can be specified in advance. Then, based on new functionals and regular differential inequality, we figure out the explicit expression for the upper bound of all variables, which plays an important role in proving the boundedness of all system variables. Final, a simulation example is given to demonstrate the effectiveness of the proposed method.

Sufficient conditions for uniform global asymptotic stabilization of affine discrete-time systems with periodic coefficients

Sufficient conditions for uniform global asymptotic stabilization of affine discrete-time systems with periodic coefficients

Global rational stabilization of a class of nonlinear time-delay systems

The present paper is mainly aimed at introducing a novel notion of stability of nonlinear time-delay systems called Rational Stability. According to the Lyapunov-type, various sufficient conditions for rational stability are reached. Under delay dependent conditions, we suggest a nonlinear time-delay observer to estimate the system states, a state feedback controller and the observer-based controller rational stability is provided. Moreover, global rational stability using output feedback is given. Finally, the study presents simulation findings to show the feasibility of the suggested strategy.

Green technologies, government stability, and green energy transition in a globalized world: evidence from E-7 nations.

Unsustainable development and rising environmental degradation are major challenges for emerging nations that tend to promote human welfare by expanding economic development. Green energy transition (GETR) can help these nations to continue their development, reduce fossil fuel utilization, and achieve environmental sustainability. However, previous literature overlooks the importance of green technologies, government stability, and economic globalization in the GETR process. Accordingly, this research takes a step forward and assesses the impacts of green technologies (GT), government stability (GOV), and economic globalization (EGL) on green energy transition including population density (POP) and economic growth (GDP) in emerging seven (E-7) countries from 1992 to 2020. The research applied the "continuously updated fully modified (CuP-FM)" methodology to acquire the long-run findings robust to endogeneity stationary regressors, autocorrelation, and cross-sectional dependence (CD). The results highlighted that green technologies can be enhanced to accelerate the energy transition process since GETR and green technologies are positively connected. Also, government stability and economic globalization support the green energy transition. However, both population density and economic growth obstruct the energy transition process. The Emirmahmutoğlu and Kose test unveiled that green technologies, economic globalization, and government stability Granger cause the green energy transition. Based on these findings, policies are directed to promote the GETR by enhancing green technologies, economic globalization, and government stability for achieving ecological sustainability.

Global classical solvability and stabilization in a two-dimensional chemotaxis–fluid system with sub-logarithmic sensitivity

In this paper, we consider the following system: [Formula: see text] in a smoothly bounded domain [Formula: see text] with [Formula: see text] and a given function [Formula: see text] with [Formula: see text] It is proved that if [Formula: see text] then for appropriately small initial data an associated no-flux/no-flux/Dirichlet initial-boundary value problem is globally solvable in the classical sense, and that if [Formula: see text] then under a different but still suitable smallness restriction of the initial data, a corresponding initial-boundary value problem subject to no-flux/no-flux/Dirichlet boundary conditions admits a unique classical solution which is globally bounded and approaches a constant equilibria [Formula: see text] in [Formula: see text] as [Formula: see text] with [Formula: see text]

Global regularity and asymptotic stabilization for the incompressible Navier–Stokes-Cahn–Hilliard model with unmatched densities

We study an initial-boundary value problem for the incompressible Navier–Stokes–Cahn–Hilliard system with non-constant density proposed by Abels, Garcke and Grün in 2012. This model arises in the diffuse interface theory for binary mixtures of viscous incompressible fluids. This system is a generalization of the well-known model H in the case of fluids with unmatched densities. In three dimensions, we prove that any global weak solution (for which uniqueness is not known) exhibits a propagation of regularity in time and stabilizes towards an equilibrium state as t→∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t \\rightarrow \\infty $$\\end{document}. More precisely, the concentration function ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} is a strong solution of the Cahn–Hilliard equation for (arbitrary) positive times, whereas the velocity field u\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{{u}}}$$\\end{document} becomes a strong solution of the momentum equation for large times. Our analysis hinges upon the following key points: a novel global regularity result (with explicit bounds) for the Cahn–Hilliard equation with divergence-free velocity belonging only to L2(0,∞;H0,σ1(Ω))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2(0,\\infty ; {\ extbf{H}}^1_{0,\\sigma }(\\Omega ))$$\\end{document}, the energy dissipation of the system, the separation property for large times, a weak-strong uniqueness type result, and the Lojasiewicz–Simon inequality. Additionally, in two dimensions, we show the existence and uniqueness of global strong solutions for the full system. Finally, we discuss the existence of global weak solutions for the case of the double obstacle potential.

Global Finite-Time Stabilization of First-Order Systems With Bounded Controls

This paper addresses the global finite-time stabilization problem for systems with bounded controls. First, based on the bounded functions of tanh(∙) and arctan(∙), two classes of bounded global finite-time controllers are proposed to stabilize single integrator systems and the saturation level of the control input can be prescribed. In addition, for each proposed controller, the upper-bound estimate for closed-loop settling time is provided explicitly, which is closely related to a parameter reflecting the initial state location. Finally, the effectiveness of the proposed controllers is verified through simulation.

Homogeneous Domination Approach to Global Stabilization of Stochastic Continuous Nonlinear Time-Delay Systems With SISS-Like Conditions

This article aims to investigate the global stabilization for a class of stochastic continuous time-delay nonlinear systems involved with unknown control coefficients and stochastic-input-to-state-stable-like conditions. Without involving the traditional adaptive compensation approach, a dominate gain is adopted to deal with uncertain nonlinearities, which not only include unmeasurable state but also involve input and state delays. On account of homogeneous domination manner and stochastic stability theory, a delay-independent controller is developed to guarantee that the closed-loop system is globally asymptotically stable in probability. Finally, a simulation example is supplied to show the virtue of the devised strategy.

Global Stabilization of a Chain of Integrators by Event-triggered Control With a Two-gain Selection Algorithm

Global Stabilization of a Chain of Integrators by Event-triggered Control With a Two-gain Selection Algorithm

Noisy prediction-based control leading to stability switch

Applying Prediction-Based Control (PBC) xn+1=(1−αn)f(xn)+αnxn with stochastically perturbed control coefficient αn=α+ℓξn+1, n∈N, where ξ are bounded identically distributed independent random variables, we globally stabilize the unique equilibrium K of the equation xn+1=f(xn) in a certain domain. In our results, the noisy control α+ℓξ provides both local and global stability, while the mean value α of the control does not guarantee global stability, for example, the deterministic controlled system can have a stable two-cycle, and non-controlled map be chaotic. In the case of unimodal f with a negative Schwarzian derivative, we get sharp stability results generalizing Singer’s famous statement ‘local stability implies global’ to the case of the stochastic control. New global stability results are also obtained in the deterministic settings for variable αn and, generally, continuous but not differentiable at K map f.

Topological description of the non-covalent interactions present within 2-(2-Hydroxyphenyl)benzothiazole analogues: An “Atoms in Molecules” investigation

“Atoms in Molecules” formalism has been exploited to highlight the non-covalent interactions present within the molecular frameworks of a series of compounds structurally analogous to 2-(2-Hydroxyphenyl)benzothiazole and to critically assess the energetics of the interaction lines towards the conformational preference as well as the global stabilization of the said structures. Moreover, for a comprehensive scrutiny of the regulatory role of the aromatic stabilization of the rings present within the frameworks in governing the preferred conformation as well as to study its modulations in the presence of the non-covalent communications; Nucleus independent chemical shift (NICS) descriptor has also been employed. The hydrogen bonds associated with the Closed conformations of the concerned structures are distinguished by closed shell synergy with a credible degree of covalency and the corresponding energetics is found to have no discernible dependence on the substitutions in the aromatic nuclei. On the other hand, the Open conformations are found to have either an H····H or an N····H interaction lines; topologically identified as closed-shell interaction. For the systems with an N12 substitution (vide Scheme 1), the difference between the energies of the Closed and the Open conformations is found to significantly decrease which has been attributed to the enhanced stability of the N12 and the Hd atoms in the Open conformations, corroborated by a marginal increase in the aromaticity of the allied Open conformations as compared to the Closed conformations.

Robust Approach for Global Stabilization of a Class of Underactuated Mechanical Systems in Presence of Uncertainties

Underactuated mechanical systems offer complex dynamic behavior and poses control challenges, especially in the presence of uncertainties in the system. To cope with such systems, control mechanisms are required, which needs to be robust. In this research, an algorithm based on sliding mode control (SMC) is presented. The algorithm design offer a methodical way to handle underactuation, while the robustness properties of SMC suppresses the effect of norm bounded uncertainties and external disturbances. To proceed with the design, an underactuated system is converted into cascaded subsystems, a linear one and reduced-order nonlinear subsystem. The proposed SMC design is backed by rigorous mathematical presentation and based on Lyapunov theory, so that the global stabilization of overall system is ensured. Numerical simulations are performed, on the laboratory test bench underactuated systems (Inertial Wheel, Furuta Pendulum, TORA, and an Overhead Crane), to validate the efficacy of the proposed design. In addition, a novel sliding surface is presented for Inertial Wheel and Furuta Pendulum to achieve swingup control and global stabilization subjected to uncertainties.

Weighted pseudo [formula omitted]-almost periodic sequence solution and guaranteed cost control for discrete-time and discrete-space stochastic inertial neural networks

This article considers the dual hybrid influences of both discrete spatial diffusions and discrete time in a stochastic inertial neural networks via the methods of exponential Euler difference and second order central finite difference. Based on a non-decomposed constant variation formula, and the theories of semi-flow and metric dynamical systems, the existence of a unique weighted pseudo θ-almost periodic sequence solution is addressed to the discrete space and time stochastic inertial neural networks. Further, a guaranteed cost controller is designed to complete a global exponential stabilization for this discrete networks by establishing a framework of drive, response and error networks. Meanwhile, global exponential stability in the sense of mean square is achieved as well. This discussion is pioneering in considering discrete spatial diffusions in inertial neural networks and offers the studying bases for future researches.

Global adaptive stabilization via more efficient event‐triggered feedback for uncertain nonlinear systems

AbstractThis paper typically concerns more efficient event‐triggered implementation, and specifically establishes an adaptive event‐triggered framework to achieve global stabilization for a class of uncertain nonlinear systems while reducing both sensor‐to‐controller and controller‐to‐actuator communication (rather than only one‐side communication). First, a novel switching event‐triggering mechanism is proposed to determine when to transmit information and adjust parameters. Particularly, with the switching varying mechanism incorporated, not only large uncertainties (whose bounds are unknown) but also inherent nonlinearities can be effectively dealt with. Then, a linear simple controller, rather than a complicated nonlinear one as in the related literature, is designed based on the switching event‐triggering mechanism. It turns out that the closed‐loop system states converge to zero while no infinitely fast sampling/execution or infinite switchings occur. Notably, just owing to the linearity of controller function, the controller signal is kept from entering the event‐triggering mechanism, which enables the sensor‐to‐controller event‐triggered communication. Besides, by strengthening the switching varying mechanism, an explicit pre‐evaluation is derived for the lower bound of inter‐execution intervals, in order to ensure moderate communication rates for reliable implementation of the event‐triggered controller.

Non-linear effect of manufacturing on an environmental pollution index in Latin America.

Manufacturing is one of the primary sources of environmental pollution due to the emission of polluting gases and waste generation. This research aims to examine the manufacturing industry's effect on an environmental pollution index in nineteen Latin American countries using non-linear methods. The youth population, globalization, property rights, civil liberties, the unemployment gap, and government stability moderate the relationship between the two variables. The research has a temporal coverage between 1990 and 2017 and uses threshold regressions to verify the hypotheses. In order to obtain more specific inferences, we group countries according to the trade block and geographic region to which they belong. Our findings indicate that manufacturing has limited explanatory power for environmental pollution. This finding is supported by the fact that the manufacturing industry in the region is scarce. In addition, we find a threshold effect on the youth population, globalization, property rights, civil liberties, and government stability. Consequently, our results highlight the importance of institutional factors in designing and applying environmental mitigation mechanisms in developing regions.

Global Finite-Time Stabilization of Spacecraft Attitude With Disturbances via Continuous Nonlinear Controller

In this paper, a robust continuous controller is investigated to solve the global finite-time attitude stabilization problem of rigid spacecraft system subject to multiple disturbances. The system order is firstly increased by derivation and the derivative of the actual torque is regarded as the virtual control law to be designed. Then, a super-twisting differentiator is constructed to provide finite-time angular acceleration estimations. Finally, based on the estimated angular accelerations, a discontinuous set stabilization control law is designed as the virtual controller. The actual continuous controller is obtained by integrating the discontinuous one. Rigorous proof and stability analysis are presented based on Lyapunov analysis. Compared with most of the existing finite-time control approaches in spacecraft systems, the proposed continuous control scheme guarantees the finite-time set stability of the closed-loop system. Moreover, the system states can converge to the equilibria even in the presence of derivative-bounded disturbances. Simulation studies of the proposed controller are illustrated to demonstrate the strong disturbance rejection ability, fast convergence rate, and high steady-state precision.

Global exponential stabilization of the linearized Korteweg-de Vries equation with a state delay

Abstract In this paper, well-posedness and global boundary exponential stabilization problems are studied for the one-dimensional linearized Korteweg-de Vries equation (KdV) with state delay, which is posed in bounded interval $[0,2\pi ]$ and actuated at the left boundary by Dirichlet condition. Based on the infinite-dimensional backstepping method for the delay-free case, a linear Volterra-type integral transformation maps the system into another homogeneous target system, and an explicit feedback control law is obtained. Under this feedback, we prove the well-posedness of the considered system in an appropriate Banach space and its exponential stabilization in the topology of $L^{2}(0,2\pi )$-norm by the use of an appropriate Lyapunov–Razumikhin functional. Moreover, under the same feedback law, we get the local exponential stability for the non-linear KdV equation. A numerical example is provided to illustrate the result.

Re-expansion of vertebral compression fractures in patients with multiple myeloma with percutaneous vertebroplasty using spinejack implants: a preliminary and retrospective study.

To retrospectively evaluate the feasibility and effectiveness of vertebroplasty using Spinejack implantation for the treatment and stabilization of painful vertebral compression fractures, in patients diagnosed with Multiple Myeloma (MM), to allow both an effective pain reduction and a global structural spine stabilization. From July 2017 and May 2022 thirty-nine patients diagnosed MM, with forty-nine vertebral compression fractures underwent percutaneous Vertebroplasty using Spinejack Implants. We analyzed the feasibility and complications of the procedure, the decrease in pain using visual analogue scale (VAS) and Functional Mobility Scale (FMS). The technical success rate was 100%. No procedure-related major complications or death occurred. In the 6-month follow-up, the mean VAS score decreased from 5.4 ± 1.0 to 0.2 ± 0.5 with a mean reduction of 96.3%. FMS decreased from 2.3 ± 0.5 vs. 1.2 ± 0.4 with a mean reduction of -47.8%. There were no major complications related to incorrect positioning of the Expandable Titanium SpineJack Implants. In five patients, a cement leak was observed with no associated clinical manifestations. The average length of hospital stay was 6-8 Hours6.6 ± 1.2 h. No new bone fractures or local disease recurrence occurred during a median contrast-enhanced CT follow-up of 6 months. Our results suggest that vertebroplasty, using Spinejack implantation for the treatment and stabilization of painful vertebral compression fractures, secondary to Multiple Myeloma is a safe and effective procedure with long - term pain relief and restoration of vertebral height.

On 2D incompressible Boussinesq systems: Global stabilization under dynamic boundary conditions

This paper studies the stability of large data solutions to the 2D fully/partially dissipative Boussinesq systems on the unit square subject to various types of boundary conditions, including dynamic Couette flow. It is shown that under suitable conditions on the boundary data, solutions starting in H3 exist globally in time and the differences between the solutions and their corresponding boundary data converge to zero in certain topology as time goes to infinity. There is no smallness restrictions on initial data.