Conditions For Stability Of Systems Research Articles

Multi-agent behavioral evolutionary game analysis of digital twin technology adoption in manufacturing enterprises

ABSTRACT Digital twin technology is crucial in breaking through the bottleneck of integrating the physical and information worlds in the manufacturing industry. However, manufacturing enterprises lack sufficient economic motivation and subjective willingness to adopt due to concerns about technological challenges and cost inputs. To elucidate the mechanisms that influence the adoption of digital twin technology, this study establishes an evolutionary game model from a stakeholder perspective, dynamically analyzes the strategy selection and system stability conditions of each participant and conducts numerical simulations. The findings reveal that the adoption process of digital twin technology in manufacturing enterprises occurs in phases. The coefficient of product attribute enhancement emerges as a key factor in promoting adoption. Government financial and consumption subsidies further encourage the adoption of digital twin technology and enhance customer preference for twin products and derivative services. The customer digital collaboration coefficient and demand matching coefficient significantly affect customers’ perceived utility benefits, which in turn influence manufacturing enterprises’ decisions to adopt digital twin technology by converting them into spillover benefits. Finally, this study provides targeted recommendations to various stakeholders to further promote the adoption of digital twin technology.

Stability and Hopf Bifurcation Analysis of Fractional Double-Delay Prey–Predator Model Under PDα Control

A fractional-order proportional-derivative controller is designed to address bifurcation issues in a dual-time-delay fractional-order predator–prey model, achieving anti-control of Hopf bifurcation at equilibrium of the system. By selecting different delays as bifurcation parameters, the stability and Hopf bifurcation conditions of the controlled system are derived. The results show that the fractional-order, delays and control parameters play an important role in determining the stability and Hopf bifurcation of the system. By selecting reasonable system parameters (fractional-order, delays, and control parameters), effective system control strategies can be devised. Finally, the key findings of this study are verified through numerical examples. The research in this paper has potential application value for the management of natural ecosystems.

Novel Sufficient Conditions for Stabilization of Linear Positive Discrete-Time Systems Using Event-Triggered Control

Novel Sufficient Conditions for Stabilization of Linear Positive Discrete-Time Systems Using Event-Triggered Control

MATHEMATICAL MODELING OF OPERATIONAL RELIABILITY OF GROUND-BASED NAVIGATION SYSTEMS

The theoretical justification for improving the effectiveness of vibration isolation for navigation equipment by reducing the natural frequency of the elastic suspension through the use of an additional electromagnetic loading system on the moving part is presented. An overview of the main elements of primary sensors and vibration protection systems for reproducing vibrations is provided. It is emphasized that vibration isolation of navigation equipment in the low-frequency disturbance range, typical for terrestrial carriers, is a crucial component in preventing emergency situations on airborne and marine vessels. A detailed calculation scheme for a vibration test stand using vertically installed flat springs is presented. Relationships between the natural frequency of the suspension and the system parameters are determined. One method for reducing the natural frequency of an elastic suspension on flat springs is analyzed. The calculation scheme for the suspension with vertically installed elastic springs is outlined. The stability conditions of the linear system, which depend on the amplitude of oscillations, are analytically investigated. It is emphasized that there is no translational movement of the suspension other than the chosen one. It is proposed to consider the calculation scheme of the suspension in the absence of dry friction. The structural component of the magnetic system is analyzed. The system of dispersive fluxes and their concentration in the air gap is outlined. An analysis of the compensatory nonlinearity of the stiffness characteristic of elastic elements is carried out. The reduction of distortions in the shape of the moving oscillations of the moving platform in the horizontal plane is analyzed. Stiffness characteristics of the suspension with a magnet for several actual values of kkk and δ\deltaδ are provided. Experimental calculations demonstrate that this vibration isolation system for navigation equipment leads to a significant reduction in the natural frequency of the suspension, ensuring its operational reliability and maximum prevention of low-frequency horizontal vibrations.

Fault-Tolerant Time-Varying Formation Trajectory Tracking Control for Multi-Agent Systems with Time Delays and Semi-Markov Switching Topologies

The fault-tolerant time-varying formation (TVF) trajectory tracking control problem is investigated in this paper for uncertain multi-agent systems (MASs) with external disturbances subject to time delays under semi-Markov switching topologies. Firstly, based on the characteristics of actuator faults, a failure distribution model is established, which can better describe the occurrence of the failures in practice. Secondly, switching the network topologies is assumed to follow a semi-Markov stochastic process that depends on the sojourn time. Subsequently, a novel distributed state-feedback control protocol with time-varying delays is proposed to ensure that the MASs can maintain a desired formation configuration. To reduce the impact of disturbances imposed on the system, the H∞ performance index is introduced to enhance the robustness of the controller. Furthermore, by constructing an advanced Lyapunov–Krasovskii (LK) functional and utilizing the reciprocally convex combination theory, the TVF control problem can be transformed into an asymptotic stability issue, achieving the purpose of decoupling and reducing conservatism. Furthermore, sufficient conditions for system stability are obtained through linear matrix inequalities (LMIs). Eventually, the availability and superiority of the theoretical results are validated by three simulation examples.

Model Reference Control for Reducing Pilot-Induced Oscillation Tendencies

Lags between pilot inputs and aircraft responses may lead to a pilot–vehicle system entering into a pilot-induced oscillation. A model reference control element can compensate for these lags, avoiding pilot-induced oscillations and improving tracking performance. Neural network compensation drives the combined controller–plant system to exhibit a closed-loop response similar to that of an idealized system, immune to the factors that trigger pilot-induced oscillations. Actuator rate limiting has been a historically ubiquitous cause of pilot-induced oscillations; meanwhile, aeroelastic effects pose a threat to future lightweight, flexible aircraft designs. Model reference control can reduce pilot-induced oscillation tendencies caused by either of these factors. This paper presents the methods used to train the model reference controller, including conditions for system stability under model reference control. It then showcases results from a pair of simulation experiments applying the control design to compensate for rate limiting and aeroelasticity, respectively. Results demonstrate that the model reference control scheme reduces pilot-induced oscillation tendencies and improves closed-loop tracking performance.

Complex Dynamics and PID Control Strategies for a Fractional Three-Population Model

In recent decades, there have been many studies on Hopf bifurcation and population stability with time delay. However, the stability and Hopf bifurcation of fractional-order population systems with time delay are lower. In this paper, we discuss the dynamic behavior of a fractional-order three-population model with pregnancy delay using Laplace transform of fractional differential equations, stability and bifurcation theory, and MATLAB software. The specific conditions of local asymptotic stability and Hopf bifurcation for fractional-order time-delay systems are determined. A fractional-order proportional–integral–derivative (PID) controller is applied to the three-population food chain system for the first time. The convergent speed and vibration amplitude of the system can be changed by PID control. For example, after fixing the values of the integral control gain ki and the differential control gain kd, the amplitude of the system decreases and the convergence speed changes as the proportional control gain kp decreases. The effectiveness of the PID control strategy in complex ecosystem is proved. The numerical simulation results are in good agreement with the theoretical analysis. The research in this paper has potential application values concerning the management of complex population systems. The bifurcation theory of fractional-order time-delay systems is also enriched.

Multi-agent behavior strategies of WEEE recycling considering public participation under environmental regulation: A perspective of dual governance

To explore the dual management mechanism within the waste electrical and electronic equipment (WEEE) processing industry under environmental regulation, in this article we examine the role of public participation in supervision and incorporate degree variables into the strategic selections of national and local governments. Following this, we design a tripartite evolutionary game model, comprising the national government, local government, and recycler. We analyze the system stability strategies and conditions, and investigate the impact of pertinent factors on the behavior strategies of each subject. The findings reveal that adjusting the intensity of actions by both the national and local governments can significantly impact the time required for system stability, with changes in the regulatory intensity of the national government proving more effective. Active public participation emerges as a critical means to prompt proactive environmental measures by the local government and recycler. Intriguingly, increased public participation may drive the national government to opt for stricter regulatory strategies. Regarding the allocation ratio of special governance funds, an optimal value exists, and the local government can choose different ratios based on distinct objectives. In conclusion, to augment effective WEEE recycling management under environmental regulation, we make several recommendations. These include adjusting the allocation ratio of special governance funds and optimizing the penalty mechanism.

H∞ control for interval type-2 fuzzy singularly perturbed systems with multi-node round-robin protocol and packet dropouts

The H∞ control of the interval type-2 (IT2) fuzzy singularly perturbed systems (SPSs) with packet losses is studied in this paper. To alleviate data collision, a multi-node round-robin protocol (RRP) is adopted to decide the communication sequences between the sensors and controller. With the help of multi-node RRP, only partial sensor nodes have the priority to access the network channels at each instant. Meanwhile, a Bernoulli packet dropout model is used to further analyze the occurrence of packet dropouts during data transmission. This article's main research results and contributions consist of two parts: (1) Firstly, by combining multi-node RRP, Bernoulli packet loss model and mismatched membership functions, an IT2 fuzzy controller dependent on scheduling state information is designed, under which the control performance of the system can be effectively enhanced. (2) Secondly, by establishing a new Lyapunov functional related to singular perturbation parameter, the system stability conditions can be obtained and ill-conditioned issue is alleviated. Eventually, the feasibility of developed method is validated by the Van der Pol circuit system example.

An active queue management method for multiple bottleneck networks based on distributed average tracking

The active queue management (AQM) is a key technology for the information infrastructure and the Internet. The AQM for multiple bottleneck networks is especially challenging than that for single-bottleneck networks because the stability analysis of multiple bottleneck networks is more complex. In this paper, the active queue management problem for multiple bottleneck networks is considered. A novel random early detection algorithm is designed based on distributed average tracking technology, which is used to estimate the global queue length and improve the network's performance. Sufficient conditions for global asymptotic stability of the closed-loop active queue management system are presented, and some simulation results with NS-2 are given. Compared with the RED algorithm, simulation results show that the presented algorithm has smaller oscillations at routers, which highlights its effectiveness.

Gain and Phase: Decentralized Stability Conditions for Power Electronics-Dominated Power Systems

Gain and Phase: Decentralized Stability Conditions for Power Electronics-Dominated Power Systems

Parameter-Estimation-Based Gain-Scheduling Control of Weight on Bit in Drilling Process With Uncertain Penetration Resistance Coefficient.

It is inevitable to encounter through different formations in the drilling process for deep exploration, and the penetration resistance coefficient (PRC) is an uncertain parameter related to lithology. In this article, a parameter-estimation-based gain-scheduling controller is developed to eliminate undesired system performance deterioration due to the uncertain parameter. First, a drill-string axial finite element model with the uncertain PRC is established, and a control-oriented low-order model is derived via mode selection. A gain-scheduling controller is computed based on the quadratic stability condition of the closed-loop system, which can cope with the system's parameter uncertainty using variable low-frequency gain. An adaptive observer is designed to estimate the unmeasurable scheduling variable. Field data from a geothermal drilling well is obtained to validate our model. According to this drilling well scenario, both numerical and experimental results illustrate the effectiveness of our method. The explicit relationship between the controller gain and the uncertain parameter is presented. It is found that the performance of the closed-loop system is more sensitive to the controller gain when drilling in soft formations, requiring more attention in such scenarios.

Robust Control for Multiplayer Nonzero‐Sum Differential Games With Switching Topology and Input Delay

ABSTRACTThis article investigates a multiplayer nonzero‐sum differential game (MNDG) with switching topology and input delay. The Hamilton–Jacobi–Isaacs (HJI) equation is used to derive the optimal control strategies. To solve the issue of switching topology, the control strategies are decoupled with the communication topology. Then, the stability of the system can be achieved regardless of changes in communication topology with the designed control strategies. This does not require a restriction on the dwell time, making the system stability conditions more relaxed. The Lyapunov–Krasovskii functional (LKF) is constructed to prove the stability of the system in the presence of time‐varying input delay. To cope with the real‐world situation, the input delay is considered to be disturbed by a time‐varying perturbation in this article. With these treatments, the system is more in line with real‐world applications. Simulation examples are given to validate the efficiency of the presented methods.

Design of active disturbance rejection controller for the system with unknown model using Laguerre functions

This paper concentrates on the design problem of linear active disturbance rejection control (LADRC) for uncertain systems, whose order and parameters are unknown. In general, LADRC has diversified structural forms due to different order and parameters selection. To clarify the prerequisites for constructing the LADRC strategy, a Laguerre-based LADRC (LLADRC) method is proposed, which provides controller design guidance for systems with unknown models by capturing the impulse response. Then, intensive attention is focused on establishing internal stability conditions of the feedback system and parameter tuning rules of the prescribed controller. To gain a better understanding, the internal correlation between LLADRC and standard LADRC of the same order is analyzed. It is shown that observer and controller gains of the standard LADRC can be tuned via a workable LLADRC to achieve better control performance. Finally, a numerical example and an application design of DC motor speed control are studied, both of which demonstrate the feasibility and validity of the proposed method.

Adaptive fault-tolerant control of uncertain systems with unknown actuator failures and input delay

Unknown failures and time delays of actuators which may degrade system performance seem inevitable in practical systems. However, the available results to compensate for unknown failures of time delay actuators based on adaptive approaches are very limited. In this paper, we address such a problem by considering controlling a class of second-order systems with unknown actuator failures and input delays. Firstly, the controlled system is transformed into a triangular structure model. Meanwhile, the input time delay is transformed into dynamics of the output signal. Then, an adaptive controller is developed using backstepping. Not only can the uncertainties due to actuator failure be compensated, but the unknown input delay has also been effectively restrained under the proposed control scheme. The upper bound condition of strength scalar [Formula: see text] is proposed. It is a sufficient condition for system stability. When the strength scalar satisfies this condition, the design parameters exist and the system is stable under the controlling of the proposed controller. Finally, the effectiveness of the proposed control scheme is verified through simulation results, including numerical simulation and actual system simulation. Through the comparative simulation, it can be seen that the control scheme proposed in this paper has faster convergence speed.

Distributed Adaptive Formation Control for Fractional-Order Multi-Agent Systems with Actuator Failures and Switching Topologies

In this paper, a class of distributed adaptive formation control problems are investigated for second-order nonlinear fractional-order multi-agent systems with actuator failures and switching topologies. To address these challenges, two adaptive coupling gains based on agents’ position and velocity are incorporated into the control protocol. Using the Lyapunov method along with graph theory and matrix analysis, sufficient conditions for system stability are derived in the presence of actuator failures and switching topologies. The effectiveness of the proposed control protocol is demonstrated through numerical simulations, which show its capability to maintain stable formation control under these challenging conditions.

Finite-time formation trajectory tracking control for unmanned underwater vehicles with time delays and Markov-switch topology

ABSTRACT The formation trajectory tracking control strategy of unmanned underwater vehicles is proposed for communication time delay and communication topology random switching. The methods ensure that formation systems are finite-time bounded under discrete time. Firstly, based on the consistency theory and the exact feedback linearised dynamics model of unmanned underwater vehicle, a control strategy is proposed for discrete formation system with communication time delay. Secondly, a cooperative control method is designed for communication problems of Markovian switching topology and time delay. Then, definition of finite-time bounded and linear matrix inequality technique are applied to sufficient conditions of system stability for the above problem. Finally, the formation motion of discrete unmanned underwater vehicle system in three-dimensional space is simulated, fully demonstrating the feasibility of the method.

Stabilization of nonhomogenous semi-Markov jump linear systems with synchronous switching delays via aperiodically intermittent control

A type of nonhomogenous semi-Markov jump linear systems with synchronous switching delays is considered in the present paper. Owing to the existence of time-varying delays and nonhomogenous semi-Markov switching process, the selection of Lyapunov functional and the transformation of some time-varying parameters become more complicated in comparison with many existing works. To overcome these difficulties, a sort of Lyapunov–Krasovskii functional related to switching delays is introduced. Simultaneously, the technique of convex combination is applied to tackle a variety of time-varying terms including transition probabilities (TPs), probability distribution function and probability density function (PDF). Then, a time-invariant stability criterion superior to many relevant works in conservativeness is obtained to ensure mean-square exponential stability (MES). Based on this result, time-invariant conditions for mean square exponential stability of the controlled system are also attained by the continuous feedback control. Subsequently, to stand on the point of cost reduction, an aperiodically intermittent control (AIC) is adopted in such a system and a stability criterion is attained as well under more relaxed restrictions on relative parameters. Finally, a numerical example is provided to verify the effectiveness and correctness of the results.

Robust [formula omitted] control for LFC of discrete T–S fuzzy MAPS with DFIG and time-varying delays

The H∞ LFC control problem for a class of nonlinear power systems with time-varying delays is under study. Considering uncertainties arising from nonlinear issues such as the generation rate constraint (GRC) and governor dead band (GDB), as well as the high variability of renewable energy sources like wind power, the model is transformed into a discrete-time Takagi–Sugeno (T–S) fuzzy model with parameter uncertainty. By constructing a Lyapunov–Krasovskii functional, and employing difference inequalities and generalized cross-convex matrix inequalities, sufficient conditions for the asymptotic stability of power systems are provided. Based on the obtained conditions, a controller is designed to ensure the asymptotic stability of Multi-Area Power Systems (MAPS), with the performance index being H∞. Finally, simulation results demonstrate the correctness and effectiveness of the theorem.

Observer-based quantized control for networked interconnected PDE systems with actuator failures

This paper proposes an observer-based quantized controller for parabolic partial differential equation systems interconnected by a nonlinear coupling protocol. First, a Markov jump model is introduced to describe various randomly occurring actuator failures, and an observer-based pointwise controller is designed under the averaged measurement scheme. Furthermore, taking into account the limitation of network communication resources, a quantization method is adopted to relieve bandwidth pressure. In addition, stability conditions of the closed-loop system with ℋ∞ disturbance attenuation performance are derived by utilizing appropriate Lyapunov functional and inequality techniques. Ultimately, the proposed method is applied to the Fisher equation to verify its feasibility and effectiveness.