Delayed Feedback Control Method Research Articles

Impact of extended warranty service on product pricing in online direct retailers' competitive market

In this paper, we consider a model composed of the three largest online direct retailers to investigate the impact of extended warranty service on product pricing. A single-period static game model and a dynamic game model with two delays are built. We discuss the optimal game strategies and dynamic evolution game behaviors of retailers and analyze the effects of warranty period and price adjustment speed on system stability. The result shows that the optimal extended warranty price, green degree, and extended warranty period lead to the biggest profits for the retailer. From the perspective of maximum profit, retailers should give priority to extending the warranty period, followed by extending the warranty price and extending the green degree of warranty. For the sake of system stability and player performance, retailers should take recent historical data as a reference, and a relatively slow price adjustment speed is needed. To better maintain the stability of the system, the delay feedback control method is adopted which can successfully control the instability of the system.

A Portable Soft Exosuit to Assist Stair Climbing with Hip Flexion

Soft exosuits are an emerging class of robots that have been shown to significantly reduce the metabolic cost of daily human movement. However, most soft exosuits are currently being studied for walking and running, and relatively minor research has been carried out on exosuits for stair climbing. Numerous exoskeletons used for stair climbing have a more rigid structure and are heavier, which may result in a greater force required by the wearer to overcome the weight from the exoskeleton when ascending stairs, which can result in metabolic costs. As a result, a reduction in rigid structures can reduce the weight of the exoskeleton and further reduce metabolic costs during stair climbing. In this paper, a waist-wearable soft exosuit was designed that assists hip flexion to aid stair climbing in older adults, in order to demonstrate the importance of choosing to assist hip flexion during stair climbing. An admittance delayed feedback control method was also proposed to use the angular information measured by the IMUs to enable the exosuit to adapt to different staircases. Metabolic experiments have shown that people who use soft exosuits have an average decrease of 6.9% in metabolism when they climb stairs than those who do not. The muscle fatigue experiments demonstrated a reduction in muscle fatigue of approximately 9.35%, 38.75% and 9.65% for the rectus femoris, lateral femoris and gastrocnemius muscles, respectively, when compared to cases without the soft exosuit. The results show that assisted hip flexion during stair climbing is a reasonable approach to effectively reduce metabolic consumption and muscle fatigue.

Complexity and chaos control of dynamic evolution in energy vehicle production decisions

This study aims to build a dynamic evolutionary game model for production decisions related to new energy vehicles and traditional fuel vehicles under a dual credit policy. The equilibrium point is calculated, and its stability is evaluated. Meanwhile, the dynamic evolution process of the system is simulated numerically, and the results reveal the complexity of the evolution process. Finally, the delay feedback control method is used to suppress the chaos of the model. Results show that in the production competition of duopoly automobile enterprises, automobile enterprises react too quickly to the market, thus resulting in system imbalance and chaos. At the same time, new energy vehicles are more sensitive to the market than traditional fuel vehicles. An excessively large output adjustment speed is not conducive to the smooth transformation of the automobile market. In addition, the delay feedback control method can effectively suppress the chaos in the system. The larger the delay feedback parameter, the faster the system returns to a steady state. This result suggests that policymakers should reflexively use this approach in practice.

Dynamic Game of the Dual-Channel Supply Chain Under a Carbon Subsidy Policy

This study investigates the dynamic game behaviors of dual-channel supply chains involving an oligopoly manufacturer selling low-carbon products to online and offline retailers. The price game models under government subsidy are discussed under three scenarios: (1) simultaneous decision, (2) manufacturer dominates the market, and (3) retailer dominates the market. The equilibrium strategies are compared under the government subsidy policy. Using numerical simulation, complex characteristics of the dual-channel supply chain under the carbon subsidy policy are investigated. The complexity of wholesale price and sales commission of each channel are analyzed by bifurcation, largest Lyapunov exponent and basin of attraction diagrams. Furthermore, parameter adjustment and delayed feedback control methods are proven to be effective approaches to chaos control.

Implications on managing inventory systems for products with stock-dependent demand and nonlinear holding cost via the adaptive EOQ policy

Motivated by the incomplete information of inventory managers and the ease-of-implementation feature of the adaptive EOQ (AEOQ) policy, this paper investigates whether this policy is effective in managing inventory systems for products with stock-dependent demand and nonlinear holding cost when some underlying parameters are unknown. The effectiveness of the AEOQ policy is studied from both stability and profitability perspectives. Stability analysis shows that the iterative procedure may not be convergent. However, incorporating the exponential smoothing or weighted moving average methods into the AEOQ policy could benefit the stability of this policy. Moreover, the delay feedback control method could be used to stabilize this iterative procedure when fluctuations occur. Profitability analysis firstly introduces three objective functions and shows how the relative difference in each objective function between equilibrium and optimal order quantities is affected by key parameters. Then, by defining the AEOQ policy as an effective solution if the equilibrium order quantity could balance these objectives, this paper provides the conditions under which the AEOQ policy is effective. Finally, methods are developed for inventory managers to judge this effectiveness in terms of profitability. Results highlight the feasibility of this policy and provide some practical insights for retailers to use this policy properly.

Time delay feedback control for milling chatter suppression by reducing the regenerative effect

Chatter often occurs in the milling process and results in poor surface quality, which limits machining efficiency. In order to suppress milling chatter, a time delay feedback control method is proposed and achieved in milling chatter suppression. The controller is designed by solving a Lyapunov function containing time delay and performed in the active control system. Different from traditional real time feedback control methods, this method suppresses milling chatter by reducing the regenerative effect with higher energy efficiency. Simulated andexperimental results indicate the critical depth of milling improves nearly four times with the proposed controller. In addition, the energy cost in the time delay feedback controller is about one-fifth of that in the real time feedback controller. The small actuating force requirement makes active chatter suppression possible in practical manufacture.

Complexity analysis and control of game behavior of subjects in green building materials supply chain considering technology subsidies

The national priority of carbon neutrality and decarbonization goals drive the transformation and upgrading of China’s construction industry. The production of green building materials is one of the key ways to decrease carbon emission. To better promote the green development of the construction industry and the realization of the decarbonization goals, a supply-chain system under technology subsidies, inclusive of a general contractor, two green building material manufacturers, is investigated. The Stackelberg model of green building material supply chain is constructed to explore how the green technology innovation of supply chain main body is affected by the technology subsidy. Meanwhile, the backward induction method is utilized to analyze the technology innovation decision-making behavior of green building material players of supply chain under a dynamic game. MATLAB software is used to simulate the stability and dynamic changes of the system in the long-term game. The results show that the decision-making stability of green building material supply chain is beneficial to the stability of supply chain system. The technology subsidy standard with reasonable policy promotes the degree of green building materials to achieve the maximum. However, once the adjustment coefficient of decision-making variables of the main body of the supply chain is large, the supply chain system will fall into chaos and disorder through bifurcation. The delayed feedback control method thus needs to be applied to control chaos, to ensure the sustainable and healthy development of the supply chain of green building materials. This study expands the application scenario of complex system theory in construction supply chain. It also provides theoretical guides for the government to formulate policies to encourage the promotion of green building materials.

Investigation of complex dynamics and chaos control of the duopoly supply chain under the mixed carbon policy

Against the background of the mixed carbon policy (carbon tax‑carbon trading) implemented in China, the authors analyze the complexity of a series of competition decisions between supply chains through constructing Cournot(Duopoly)game model between supply chains. The dynamics of the proposed game model and the time evolution of the supply chains are described by a nonlinear discrete dynamical system. The equilibrium point of the discrete dynamical system is obtained and its local stability is discussed. The stability of the equilibrium point is further discussed by numerical simulation, which is affected by the speed of adjusting parameters and some other cost parameters. Finally, we apply the delayed feedback control method to suppress and overcome the chaos of the discrete dynamical system. It can effectively promote the discrete dynamical system to return to the stable behavior. It is hoped that the current research can provide a theoretical basis for the competitive decision-making of supply chain node enterprises.

Dynamic analysis of a dual-channel closed-loop supply chain with fairness concerns under carbon tax regulation.

In this work, we study a dual-channel closed-loop supply chain (CLSC) where the manufacturer sells the new products via one fair caring retailer in the traditional channel and distributes the remanufactured products through her own direct channel in the presence of the carbon tax regulation. After solving the single-period Stackelberg game model by backward induction and analyzing the impacts of key parameters on the optimal pricing strategies and the performance of channel members, a multi-period dynamic Stackelberg game model with heterogeneous players is further established. The local stability of the Nash equilibrium point and complexity properties of the model are investigated by numerical simulation. The results reveal that (1) the retailer's fairness concern degree is negatively related to the optimal wholesale price as well as positively related to the optimal retail price of the new product. A high level of consumer discount perception for the remanufactured product is conducive to the manufacturer obtaining more profits while it is detrimental to the retailer. (2) The excessive value of the price adjustment speed, carbon tax rate or retailer's fairness concern degree has a strong destabilization effect on the system's stability. (3) The manufacturer suffers profit loss while the retailer's utility levels are elevated when the system falls into periodic cycles and chaotic motions. (4) The delay feedback control method can eliminate the chaos effectively in the dual-channel CLSC system.

Global dissipativity and adaptive synchronization for fractional‐order time‐delayed genetic regulatory networks

AbstractThis manuscript examines global dissipativity and synchronization criteria for time‐delayed fractional‐order gene regulatory networks (FGRNs). The Lyapunov stability theory is used to examine a class of FGRNs with delay arguments that are inspired by the integer‐order delayed gene regulatory network model. Some sufficient criteria are established using the fractional‐order comparison principle and stability theorem for fractional‐order time‐delayed systems to ensure the global dissipativity solution of FGRNs with both feedback regulation and translation time delays. Furthermore, for FGRNs, the global asymptotic synchronization condition is accomplished by constructing an adaptive delayed feedback control method for the master–slave system. Finally, two numerical examples are provided to demonstrate the applicability and superiority of the conclusions obtained.

Unpredictable oscillations of SICNNs with delay

We rigorously prove that unpredictable oscillations take place in the dynamics of shunting inhibitory cellular neural networks (SICNNs) with delay when rectangular input currents generated by an unpredictable sequence are utilized. The existence, uniqueness, and exponential stability of such oscillations are discussed. The contraction mapping principle is applied to achieve the theoretical results. Numerical simulations supporting the presence of unpredictable oscillations are provided, and the transfer of unpredictable behavior between SICNNs under unidirectional coupling is demonstrated. It is also shown by means of the delayed feedback control method that the obtained unpredictable behavior is controllable. Moreover, an application to secure communication is discussed.

Complex Dynamics of Mixed Triopoly Game with Quantity and Price Competition

This article investigates the dynamics of a mixed triopoly game in which a state-owned public firm competes against two private firms. In this game, the public firm and private firms are considered to be boundedly rational and naive, respectively. Based on both quantity and price competition, the game’s equilibrium points are calculated, and then the local stability of boundary points and the Nash equilibrium points is analyzed. Numerical simulations are presented to display the dynamic behaviors including bifurcation diagrams, maximal Lyapunov exponent, and sensitive dependence on initial conditions. The chaotic behavior of the two models has been stabilized on the Nash equilibrium point by using the delay feedback control method. The thresholds under price and quantity competition are also compared.

Stability and Bifurcation Analysis of a Discrete Singular Bioeconomic System

The main concern of this paper is to discuss stability and bifurcation analysis for a class of discrete predator-prey interaction with Holling type II functional response and harvesting effort. Firstly, we establish a discrete singular bioeconomic system, which is based on the discretization of a system of differential algebraic equations. It is shown that the discretized system exhibits much richer dynamical behaviors than its corresponding continuous counterpart. Our investigation reveals that, in the discretized system, two types of bifurcations (i.e., period-doubling and Neimark–Sacker bifurcations) can be studied; however, the dynamics of the continuous model includes only Hopf bifurcation. Moreover, the state delayed feedback control method is implemented for controlling the chaotic behavior of the bioeconomic model. Numerical simulations are presented to illustrate the theoretical analysis. The maximal Lyapunov exponents (MLE) are computed numerically to ensure further dynamical behaviors and complexity of the model.

Enlarging the stable domain of controlled high-period oscillations with transient extended delayed feedback control

A transient extended delayed feedback control method was developed by modifying the original extended delayed feedback control method with a transient control technique to enlarge the stable domain of the controlled high-period oscillations. The control force is applied to the system only when the system is in the controlling region, which is different from the static control force of the original extended delayed feedback control. The specific control performance of the transient extended delayed feedback control was analyzed through case studies. The relationships between the stable domain of the controlled high-period oscillations and the controlling regions were obtained by calculating the largest magnitude of the Floquet multipliers. It is shown that the stable domain changes in a non-smooth manner with the variation of the controlling region. In particular, the transient extended delayed feedback control can stabilize high-period unstable oscillations in a much larger stable domain than that of the original extended delayed feedback control when the controlling region is properly chosen.

Bifurcation control of a minimal model of marine plankton interaction with multiple delays

Plankton blooms and its control is an intriguing problem in ecology. To investigate the oscillatory nature of blooms, a two-dimensional model for plankton species is considered where one species is toxic phytoplankton and other is zooplankton. The delays required for the maturation time of zooplankton, the time for phytoplankton digestion and the time for phytoplankton cells to mature and release toxic substances are incorporated and the delayed model is analyzed for stability and bifurcation phenomena. It proves that periodic plankton blooms can occur when the delay (the sum of the above three delays) changes and crosses some threshold values. The phenomena described by this mechanism can be controlled through the toxin release rates of phytoplankton. Then, a delay feedback controller with the coefficient depending on delay is introduced to system. It concludes that the onset of the bifurcation can be delayed as negative feedback gain (the decay rate) decreases (increases). Some numerical examples are given to verify the effectiveness of the delay feedback control method and the existence of crossing curve. These results show that the oscillatory nature of blooms can be controlled by human behaviors.

A chaos control method of single-phase H-bridge photovoltaic inverter

There are complex nonlinear behaviors such as bifurcation and chaos in a single-phase H-bridge photovoltaic inverter under proportional integral control, which will increase the harmonic content of the output current greatly and reduce the stability of system operation and reliability of power supply. There are the problems suffering the complicated modeling and difficulty in determining the control coefficients in existing chaos control methods. The exponential delay feedback control is a further development of the delay feedback control, which has the advantages of requiring no precise mathematical model of the system and simple implementation. However, our research shows that when the exponential delay feedback control is directly applied to the system, the feedback intensity cannot be controlled, which will bring too big a disturbance to the system. Based on it, an improved exponential delayed feedback control method is proposed in this paper. Firstly, a feedback signal is formed by the difference between the output current of the system and its own delay, then the feedback signal is used to obtain the control signal through an exponential link, a subtraction link and an proportion link, and the control signal is applied to the controlled system in the form of a feedback. At the same time, the discrete mapping model of the system is established and its Jacobian matrix expression is determined. Finally, the limiting conditions of the feedback control coefficient of the control signal are derived based on the stability criterion, and the control is applied to the system. In order to verify the control effect of this method, a lot of simulation experiments are conducted. The results show that the problems that the exponential delay feedback cannot control the feedback strength and causes excessive disturbance to the system will be effectively solved by this method. When the bifurcation parameters vary greatly, the chaos behaviors in the system will be suppressed effectively, the stable operating domain of the system will be expanded greatly and the harmonic content of the output current will be reduced.

Genetic algorithm (GA)–based delay feedback control of chaotic behavior in the voltage mode controlled direct current (DC) drive system

Abstract In this paper, the chaotic behavior and chaos control in a voltage mode controlled DC drive system are investigated. The dynamical behavior of the system changing from the fundamental state to chaotic regime is obtained by the variation of some parameters. Two kinds of delay feedback controllers are designed to induce and control chaos in the voltage-mode DC drive system that exhibits chaotic behavior under certain conditions. The proposed control scheme is able to suppress chaos on the voltage mode controlled DC drive system operating in continuous conduction mode. With variation of controller parameters, the transition of dynamical behavior in the system has been demonstrated from different possible states to regular state, which may be named as period-1 operation. Unlike the traditional delay feedback control method, not only the feedback gain parameter K but also the delay parameter τ is used as variable parameters of the controller. Moreover, the genetic algorithm is used to simultaneously optimize both the feedback gain parameter K and delay parameter τ to improve the effectiveness of the controller. Numerical results show that the proposed method can control unstable periodic orbits and suppress chaos in the system, and also, optimized controller parameters provide fast response for transition from chaotic operation to normal operation.

Complexity analysis of a decision-making game concerning governments and heterogeneous agricultural enterprises with bounded rationality

Abstract Government subsidy intensity, nitrogen emission reductions, and pricing decisions in a Bertrand agricultural products supply chain system were investigated. This paper presents the results of a decision-making competition game model involving governments and heterogeneous agricultural enterprises based on bounded rationality. The impact of government on the emission reduction behavior of agricultural enterprises was evaluated. The study revealed that the speed of price adjustment and subsidy intensity may alter the system stability and lead to chaos, with the price adjustment speed having a more sensitive influence on the system than the subsidy intensity adjustment speed. In addition, certain parameters (pe and r0) affected the system stability, decision variables, and the profits made by government and agricultural enterprises. When the parameters became harmful to enterprises and governments, the system fell into chaos and the stable region increased in the direction of the subsidy intensity adjustment speed. Finally, the chaos in the agricultural supply chain was successfully controlled by the delayed feedback control method.

Analysis of Complex Dynamics in Different Bargaining Systems

This paper focuses on the bargaining behavior of supply chain members and studies the stability of the bargaining system. There are two forms of bargaining in the process of negotiation. One is separate bargaining, and the other is that the automobile manufacturers form an alliance and bargain with the supplier collectively. We explore the influence of bargaining power and adjustment speed on the stability of the dynamic system and find that both of the factors need to be small to maintain the stability of the supply chain. After comparing the two forms of bargaining in terms of profits and stable regions, we find that the collective bargaining is a pattern with the existence of risk and benefit simultaneously. In order to control chaos in collective bargaining to lower the risk, we adopt the delay feedback control method. With the introduction of the control factor, the system tends to be stable finally.

Complexity Analysis of a 3-Player Game with Bounded Rationality Participating in Nitrogen Emission Reduction

In this paper, a decision-making competition game model concerning governments, agricultural enterprises, and the public, all of which participate in the reduction of nitrogen emissions in the watersheds, is established based on bounded rationality. First, the stability conditions of the equilibrium points in the system are discussed, and the stable region of the Nash equilibrium is determined. Then, the bifurcation diagram, maximal Lyapunov exponent, strange attractor, and sensitive dependence on the initial conditions are shown through numerical simulations. The research shows that the adjustment speed of three players’ decisions may alter the stability of the Nash equilibrium point and lead to chaos in the system. Among these decisions, a government’s decision has the largest effect on the system. In addition, we find that some parameters will affect the stability of the system; when the parameters become beneficial for enterprises to reduce nitrogen emissions, the increase in the parameters can help control the chaotic market. Finally, the delay feedback control method is used to successfully control the chaos in the system and stabilize it at the Nash equilibrium point. The research of this paper is of great significance to the environmental governance decisions and nitrogen reduction management.