Domain Of Attraction Research Articles

Local set stability and target control of probabilistic Boolean networks

This paper analyzes the local set stability of probabilistic Boolean networks (PBNs), including local finite-time set stability with probability one (FSSPO) and local asymptotic set stability with probability one (ASSPO). Firstly, a necessary and sufficient condition is proposed for the local FSSPO of PBNs. Then, a reachable set with probability one is constructed, based on which, the largest domain of attraction for the local FSSPO of PBNs is determined. Secondly, by constructing two parameterized sets, the transition probability matrix of PBNs is properly partitioned, and the largest domain of attraction for the ASSPO is depicted. Finally, for PBNs which are locally stable, the target control is introduced to achieve the global FSSPO and global ASSPO of PBNs, respectively.

Computation and analysis of optimal disturbances of periodic solution of the hepatitis B dynamics model

Abstract Optimal disturbances of the periodic solution of the hepatitis B dynamics model corresponding to the chronic recurrent form of the disease are found. The dependence of the optimal disturbance on the phase of periodic solution is analyzed. Four phases of the solution are considered, they correspond to clinically different periods of development of the immune response and severity of the disease, namely, activation of antiviral immune reactions, attenuation of reactions, peak and minimum viral load. The possibility of using optimal disturbances to exit the domain of attraction of the considered periodic solution using minimal impact is studied. The components of disturbances that may underlie the phenomenon of spontaneous recovery from chronic hepatitis B observed in clinical practice are identified.

Chaos and attraction domain of fractional Φ6‐van der Pol with time delay velocity

This article investigates the chaotic analysis and attractive domain of a fractional‐order ‐van der Pol with time delay velocity under harmonic excitation. Firstly, eight different types of bifurcation states of the system under different parameters are calculated by using the undisturbed system. Secondly, the Melnikov method is used to explore the effect of time delay velocity on the threshold of chaos in the Smale horseshoe sense under the double‐well potential and three‐well potential of the system. Finally, through numerical analysis of the phase diagram, bifurcation diagram, and maximum Lyapunov exponent, the influence of time delay velocity on system chaos is studied. The results indicate that an increase in the delay velocity coefficient will lead to the system transitioning from a chaotic state to a periodic state, while an increase in the delay velocity term will lead to the system transitioning from a periodic state to a chaotic state. In the study of system bifurcation, it is found that the position of the equilibrium points of the system changes during periodic motion. Therefore, cell mapping is used to draw the attractive domain of the system is studying the influence of initial conditions on the equilibrium point of the system and the results show that there is a close relationship between the attraction domain and the process of chaos occurrence.

Site-Selective Access to Functionalized Pyrroloquinoxalinones via H-Atom Transfer from N═Csp2-H Bonds of Quinoxalinones.

Site-selective hydrogen atom transfer (HAT) from the N═Csp2-H bonds of quinoxaline-2(1H)-ones is a highly attractive but underdeveloped domain. Reported herein is a highly selective, practical, and economically efficient approach for facile assembly of pyrroloquinoxalinones by synergistic photocatalysis and HAT catalysis. The reaction proceeds through bromine radical-mediated HAT of quinoxalinones and imine radical addition to α-cyano-α,β-unsaturated ketones that establishes a cross-coupling/annulation cascade process, resulting in the synthesis of a series of functionalized pyrroloquinoxalinones. This protocol does not require transition metals or excess oxidants and uses easy-to-synthesize starting materials with excellent scalability and broad substrate scope. The establishment of N═Csp2 radical chemistry illustrates great potential for the synthesis of imine-containing molecules that are not possible with some traditional methods.

Flocking analysis and control of a nonlinear collective migration model

Abstract In this paper, we study a nonlinear collective migration model with the Cucker–Smale type weight, the nonlinear velocity coupling and the distributed network. Finite-time flocking tracking can be achieved by the alignment force gathering agents and the tracking force matching target. A trade-off existing between the two forces is established by the tracking strategy that can be viewed as a control. When the strategy is time-invariant, finite-time flocking tracking would occur for any initial state under the long-range weight, only for partial initial state under the short-range weight. An invariant set of the system is proposed and proved to be an attractive domain of the flocking state. Then two time-varying strategies, the average strategy and the maximum strategy, are designed to overcome the constraint of initial state under the short-range weight. The average strategy has to mobilize all agents simultaneously, but only causes once switch. The maximum strategy only mobilizes the agent with the largest velocity deviation, but produces more switches. Several numerical simulations are provided to observe the effects of the time-invariant and time-varying strategies.

Autonomous positioning, capturing, and grasping mechanism for robot end effectors based on the attraction domain relationship

Purpose This paper aims to solve the problem of uncertain position and attitude between unstructured terrain robot and grasped target and insufficient control accuracy in extreme environment, a grasping mechanism based on attraction domain relationship is proposed, which can realize autonomous positioning, capturing and grasping of robot under low control accuracy. Design/methodology/approach The grasping mechanism was designed, taking inspiration from fishing behavior this mechanism introduces attraction domains and flexible-elastic structures through the active and passive ends to achieve automatic positioning and capture. After the capture is completed, the grasping mechanism connects the active end and the passive end, simultaneously relying on the gravity of the target object to achieve locking and release between the robot and the target object. This paper adopts theoretical, simulation and experimental verification methods to conduct theoretical and simulation analysis on the autonomous positioning and grasping process of the mechanism, and produces grasping experimental prototypes with different positions and postures. Findings The experiment shows that the gripping mechanism designed in this paper can achieve automatic positioning capture and gripping of large deviation situations under low control accuracy, with a displacement deviation of up to 10 mm (about 1/6 diameter of the end of the mechanism) and an angle deviation of up to 3°. The scientific research task in the extremely high altitude environment has finally been successfully accomplished. Originality/value Inspired by fishing behavior, this paper proposes a positioning, capturing and grasping mechanism. The attraction area built with permanent magnets, coupled with the flexible connection, enables precise capture under low control, while the grasping mechanism can also rely on gravity to self-lock and release.

Stability analysis and stabilization of discrete-time switched nonlinear systems with mode-dependent average dwell time under nested actuator saturation

In this paper, the stability analysis and stabilization of a class of mode-dependent mean residence time-based discrete-time switching nonlinear systems are addressed. More specifically, under the mode-dependent average dwell time (MDADT) switching mode, combined with the practical problem, the nonlinear factor of nested actuator saturation (NAS) is introduced. Firstly, in order to ensure the system stability, based on the parameter-dependent discontinuous switching Lyapunov function and several basic lemmas, a state feedback controller is designed that makes the closed-loop system (CLS) achieve local exponential stability (LES) by solving the optimal problem in terms of linear matrix inequalities (LMIs). Secondly, the system considers the maximum attraction domain that can be achieved by the NAS system under the conditions. The simulation results show the effectiveness of the proposed design method. At the same time, the efficiency of the proposed method is verified via a water tank example.

Estimation of the domain of attraction for continuous-time saturated positive polynomial fuzzy systems based on novel analysis and convexification strategies

In this paper, the domain of attraction (DOA) of the continuous-time positive polynomial fuzzy systems subject to input saturation is estimated by using the level set of the linear copositive Lyapunov function. To relax the estimation of DOA, the restriction on the level set is removed by embedding the expression of the level set into the stability conditions and positivity conditions. Referring to the nonconvex terms caused by above novel analysis strategy, some polynomial inequality lemmas are proposed to handle them; the nonconvex terms caused by imperfect premise matching (IPM) nonlinear membership functions are dealt with by sector nonlinear methods and advanced Chebyshev membership-function-dependent (MFD) methods. In this advanced MFD method, the state space segmentation and polynomial order selection of the Chebyshev approximation method are improved based on breakpoints of the first derivative and curvature, respectively, which is helpful to reduce the conservatism and computational burden of the result. Thus, this advanced Chebyshev MFD method not only optimizes the convexification strategy, but also can further be extended to estimate the DOA when it is used to introduce the membership functions information for convex stability and positivity conditions. Finally, a numerical example and the lipoprotein metabolism and potassium ion transfer nonlinear model are presented to validate the effectiveness and feasibility of the aforementioned analysis and convexification strategies in the expansion of DOA estimation.

A Switching Memory-Based Event-Trigger Scheme for Synchronization of Lur'e Systems With Actuator Saturation: A Hybrid Lyapunov Method.

This article is concerned with the event-triggered synchronization of Lur'e systems subject to actuator saturation. Aiming at reducing control costs, a switching-memory-based event-trigger (SMBET) scheme, which allows a switching between the sleeping interval and the memory-based event-trigger (MBET) interval, is first presented. In consideration of the characteristics of SMBET, a piecewise-defined but continuous looped-functional is newly constructed, under which the requirement of positive definiteness and symmetry on some Lyapunov matrices is dropped within the sleeping interval. Then, a hybrid Lyapunov method (HLM), which bridges the gap between the continuous-time Lyapunov theory (CTLT) and the discrete-time Lyapunov theory (DTLT), is used to make the local stability analysis of the closed-loop system. Meanwhile, using a combination of inequality estimation techniques and the generalized sector condition, two sufficient local synchronization criteria and a codesign algorithm for the controller gain and triggering matrix are developed. Furthermore, two optimization strategies are, respectively, put forward to enlarge the estimated domain of attraction (DoA) and the allowable upper bound of sleeping intervals on the premise of ensuring local synchronization. Finally, a three-neuron neural network and the classical Chua's circuit are used to carry out some comparison analyses and to display the advantages of the designed SMBET strategy and the constructed HLM, respectively. Also, an application to image encryption is provided to substantiate the feasibility of the obtained local synchronization results.

Intrinsically Multi-Stable Spatial Linkages.

Multi-stable structures can be reconfigured with fewer, lightweight, and less accurate actuators. This is because the attraction domain in the multi-stable energy landscape provides both reconfiguration guidance and shape accuracy. Additionally, such structures can generate impulsive motion due to structural instability. Most multi-stable units are planar structures, while spatial linkages can generate complex 3D motion and hold a more promising potential for applications. This study proposes a generalized approach to design a type of intrinsically multi-stable spatial (IMSS) linkages with multiple prescriptible configurations, which are structurally compatible, and naturally stable at these states. It reveals that all over-constrained mechanisms can be transformed into multi-stable structures with the same design method. Single-loop bi-stable 4R and quadra-stable 6R spatial linkages modules with intrinsic non-symmetric stable states, which are transformed from fundamental kinematic linkage mechanisms unit such as Bennett and Bricard linkages, are designed to illustrate the basic idea and the superiority over the ordinary methods. Multi-loop assembly by these IMSS linkage modules shows potential for practical applications that are required for the deployability and impulsivity of reconfiguration. Two preliminary design cases of a deployable tube and an impulsive gripper are experimentally presented to validate this applicability. Further promisingly, this design method of IMSS linkages paves the way for morphing platforms with lightweight actuation, high shape accuracy, high stiffness, and prescribed impulsive 3Dmotion.

Resonance and attraction domain analysis of asymmetric duffing systems with fractional damping in two degrees of freedom

This article establishes a two degree of freedom asymmetric Duffing system model with fractional damping through the study of the Jeffcott rotor system with horizontal support, and analyzes the dynamic behavior of its resonance and attraction domain structures. The second-order approximate solution of the system equation is obtained using a multiscale method, and the slow flow modulation equations of both the amplitudes and phases are extracted. The comparison between approximate and numerical solutions has shown their high consistency and the Routh Hurwitz criterion is utilized to study the stability of the system. Finally, we explore the effect of fractional damping on the vibration behavior of the system using amplitude frequency curves, attractive watersheds, and time trajectory plots, including both negative and positive values of the nonlinear stiffness coefficient. The analysis shows that if the coefficient and order of the fractional damping term are reasonably selected, the horizontal and vertical displacements of the system vibration can be effectively controlled. The importance of this work lies in its application in rotor vibration, which has significant implications for the study of the system under investigation.

Cluster consensus for nonlinear multi‐agent systems restricted with input saturation by event triggered control

AbstractThis article studies the cluster consensus problem for the nonlinear multi‐agent systems subject to input saturation under the context of event triggered control. Taking ordinary consensus object as a special case, this article considers the problem of cluster consensus. The event triggered mechanism is designed and the Zeno phenomenon is ruled out. The sufficient conditions of control protocol and range estimation of domain of attraction are formulated by the linear matrix inequalities for the constraints of input saturation and nonlinear terms existed in the system dynamics. Finally, the proposed results are validated by one example in the background of spring damping system.

Estimation of the Attraction Domain for the Quantum Systems Based on the Schrödinger Equation

This paper investigates a quantum system described by the Schrödinger equation, utilizing the concept of the quantum Lyapunov function. The Lyapunov function is chosen based on the mean value of a virtual mechanical quantity, where different values of P, the mean value of the virtual mechanical quantity in the Lyapunov function, have an impact on the attractive domain of the quantum system. The selected primary optimization algorithms approximating matrix P are the particle swarm optimization (PSO) algorithm and the simulated annealing (SA) algorithm. This study examines the characteristics of the system’s attraction domain under these two distinct algorithms and establishes stability conditions for the nonlinear quantum system. We introduce a method to estimate the size of the attractive domain using the Lyapunov function approach, converting the attractive domain issue into an optimization challenge. Numerical simulations are conducted in various two-dimensional test systems and spin 1/2 particle systems.

Resilient sampled-data control for fractional-order PMVG-based WTS with actuator saturation and probabilistic faults using fuzzy Lyapunov function method

The goal of this study is to present a new fuzzy Lyapunov function-based resilient sampled-data control method for a fractional-order permanent magnet vernier generator (PMVG)-based wind turbine system (WTS) that addresses actuator saturation and probabilistic faults. To achieve this, we first model the dynamical fractional model of the PMVG-based WTS as a T-S fuzzy model. Next, we introduce a fuzzy Lyapunov function within a unified framework that incorporates actuator saturation, probabilistic faults, and uncertainty information from control gain matrices. We then present an actuator fault model that represents actuator faults as stochastic variables with a specific probability distribution. Subsequently, we formulate a robust asymptotic stability criterion for closed-loop systems using linear matrix inequality (LMI), which integrates the fuzzy Lyapunov function and membership function information with fractional integral inequality techniques based on sampling time. We also propose an LMI approach to identify the domain of attraction that meets the necessary actuator saturation criteria. Finally, we apply the proposed method to a PMVG-based WTS, demonstrating its superiority and practical applicability through a comparison with existing methods using a numerical example of a nonlinear truck trailer system.

Nonlinear Dynamics and Meshing State Transition Analysis of Spalling Defect Gears with Multi-Lubrication Conditions

The purpose of this paper is to analyze the dynamic characteristics and the meshing state transition characteristics of spalling defect gears under various lubrication conditions. The time-varying geometric parameters, motion parameters and load distribution of the gears in the state of positive meshing and reverse impact are analyzed. The time-varying meshing stiffness considering the time-varying friction coefficient under elastohydrodynamic lubrication (EHL), mixed lubrication and boundary lubrication are calculated, and the spalling defect is introduced in the stiffness calculation process. The equivalent lubrication model of the gear is established, the switching condition of the lubrication state is derived, and the distribution of the lubrication state in the torque-speed plane is discussed. The multimeshing state dynamic model of the spalling defect gear is established, and the evolution characteristics of the coexistence response and the transition of the meshing state under different lubrication conditions are simulated by using the attraction domain, phase trajectory, meshing force and bifurcation diagram. The results show that the phase trajectory of the gear with the spalling defect is deformed compared with that of the healthy gear. The change of lubrication state has little effect on the phase trajectory and attraction domain of the gear with spalling defect, but has a great influence on the meshing force. At the spalling boundary, the meshing force is changed abruptly, and the worse the lubrication state, the more obvious the mutation. Due to the influence of spalling on tooth stiffness, it will also affect the meshing force in the nonspalling area.

A novel saturation degree‐dependent adaptive event‐triggered control for systems with asymmetric saturation

AbstractThis paper investigates the control problem of systems with asymmetric saturation by the formulated saturation degree‐dependent event‐triggered mechanism. The subregion partition method is adopted to represent the asymmetric saturation as the symmetric saturation in each subregion. In order to further reduce the triggering number when the system is saturated and save the communication resources of the system, this paper establishes the saturation degree‐dependent adaptive event‐triggered condition. Then, the subregion‐related control law under the presented event‐triggered scheme is designed, and the asymptotic stabilization of the underlying system is realized. Moreover, an optimization algorithm is proposed to estimate the maximal domain of attraction. Finally, simulation examples are used to validate the theoretical results.

A control theoretic analysis of oscillator Ising machines

This work advances the understanding of oscillator Ising machines (OIMs) as a nonlinear dynamic system for solving computationally hard problems. Specifically, we classify the infinite number of all possible equilibrium points of an OIM, including non-0/π ones, into three types based on their structural stability properties. We then employ the stability analysis techniques from control theory to analyze the stability property of all possible equilibrium points and obtain the necessary and sufficient condition for their stability. As a result of these analytical results, we establish, for the first time, the threshold of the binarization in terms of the coupling strength and strength of the second harmonic signal. Furthermore, we provide an estimate of the domain of attraction of each asymptotically stable equilibrium point by employing the Lyapunov stability theory. Finally, we illustrate our theoretical conclusions by numerical simulation.

WITHDRAWN: Robust voltage regulation of DC-DC buck converter with ZIP load via an energy shaping control approach

ZIP loads (the parallel combination of constant impedance loads, constant current loads and constant power loads) exist widely in power system. In order to stabilize buck converter based DC distributed system with ZIP load, an adaptive energy shaping controller (AESC) is devised in this paper. Firstly, based on the assumption that the lumped disturbances are known, a full information controller is designed in the framework of the port Hamiltonian system via energy shaping technique. An obvious merit is that it is PI-type controller, which is easy to implement in practical application. Besides, using mathematical deductive method, an estimation of the domain of attraction is given to ensure the strict stability. Furthermore, to eliminate the influence of parameter perturbations on the system, a disturbance observer is proposed to reconstruct the lumped disturbances and then the estimated terms are introduced to above controller to form an adaptive control scheme. In addition, the strict stability analysis of the closed-loop system is given. Lastly, the simulation and experiment results are presented for assessing the designed controller.

Easy-to-actuate multi-compatible truss structures with prescribed reconfiguration

Multi-stable structures attract great interest because they possess special energy landscapes with domains of attraction around the stable states. Consequently, multi-stable structures have the potential to achieve prescribed reconfiguration with only a few lightweight actuators (such as shape-memory alloy springs), and do not need constant actuation to be locked at a stable state. However, most existing multi-stability designs are based on assembling bi-stable unit cells, which contain multitudes of distractive stable states, diminishing the feasibility of reconfiguration actuation. Another type is by introducing prestress together with kinematic symmetry or nonlinearity to achieve multi-stability, but the resultant structure often suffers the lack of stiffness. To help address these challenges, we firstly introduce the constraints that a truss structure is simultaneously compatible at multiple (more than two) prescribed states. Then, we solve for the design of multi-stable truss structures, named multi-compatible structures in this paper, where redundant stable states are limited. Secondly, we explore minimum energy paths connecting the designed stable states, and compute for a simple and inaccurate pulling actuation guiding the structure to transform along the computed paths. Finally, we fabricated four prototypes to demonstrate that prescribed reconfigurations with easy-actuation have been achieved and applied a quadra-stable structure to the design of a variable stiffness gripper. Altogether, our full-cycle design approach contains multi-stability design, stiffness design, minimum-energy-path finding, and pulling actuation design, which highlights the potential for designing morphing structures with lightweight actuation for practical applications.

Unveiling serotonergic dysfunction of obsessive-compulsive disorder on prefrontal network dynamics: a computational perspective.

Serotonin (5-HT) regulates working memory within the prefrontal cortex network, which is crucial for understanding obsessive-compulsive disorder. However, the mechanisms how network dynamics and serotonin interact in obsessive-compulsive disorder remain elusive. Here, we incorporate 5-HT receptors (5-HT1A, 5-HT2A) and dopamine receptors into a multistable prefrontal cortex network model, replicating the experimentally observed inverted U-curve phenomenon. We show how the two 5-HT receptors antagonize neuronal activity and modulate network multistability. Reduced binding of 5-HT1A receptors increases global firing, while reduced binding of 5-HT2A receptors deepens attractors. The obtained results suggest reward-dependent synaptic plasticity mechanisms may attenuate 5-HT related network impairments. Integrating serotonin-mediated dopamine release into circuit, we observe that decreased serotonin concentration triggers the network into a deep attractor state, expanding the domain of attraction of stable nodes with high firing rate, potentially causing aberrant reverse learning. This suggests a hypothesis wherein elevated dopamine concentrations in obsessive-compulsive disorder might result from primary deficits in serotonin levels. Findings of this work underscore the pivotal role of serotonergic dysregulation in modulating synaptic plasticity through dopamine pathways, potentially contributing to learned obsessions. Interestingly, serotonin reuptake inhibitors and antidopaminergic potentiators can counteract the over-stable state of high-firing stable points, providing new insights into obsessive-compulsive disorder treatment.