State Feedback Control Method Research Articles

Extreme Homogeneous and Heterogeneous Multistability in a Novel 5D Memristor-Based Chaotic System with Hidden Attractors

This paper proposes a novel five-dimensional (5D) memristor-based chaotic system by introducing a flux-controlled memristor into a 3D chaotic system with two stable equilibrium points, and increases the dimensionality utilizing the state feedback control method. The newly proposed memristor-based chaotic system has line equilibrium points, so the corresponding attractor belongs to a hidden attractor. By using typical nonlinear analysis tools, the complicated dynamical behaviors of the new system are explored, which reveals many interesting phenomena, including extreme homogeneous and heterogeneous multistabilities, hidden transient state and state transition behavior, and offset-boosting control. Meanwhile, the unstable periodic orbits embedded in the hidden chaotic attractor were calculated by the variational method, and the corresponding pruning rules were summarized. Furthermore, the analog and DSP circuit implementation illustrates the flexibility of the proposed memristic system. Finally, the active synchronization of the memristor-based chaotic system was investigated, demonstrating the important engineering application values of the new system.

Anti-control of Hopf bifurcation for a chaotic system

Abstract The anti-control of Hopf bifurcation is a method used for bifurcation control. It can be used to realize the occurrence or delay of bifurcation at the specified position to meet the needs of engineering applications. In this study, a 4D chaotic system is studied, and a dynamic state feedback control method is proposed to realize the anti-control of Hopf bifurcation for the system. By adjusting the control parameters of the controller, the system Hopf bifurcation can be generated or delayed at the specified position to realize the anti-control of Hopf bifurcation. This control method avoids complicated calculation processes and has remarkable control effects. Through numerical simulation analysis, the correctness of this control method is verified.

Data‐driven disturbance compensation control for discrete‐time systems based on reinforcement learning

SummaryIn this article, a self‐learning disturbance compensation control method is developed, which enables the unknown discrete‐time (DT) systems to achieve performance optimization in the presence of disturbances. Different from traditional model‐based and data‐driven state feedback control methods, the developed off‐policy Q‐learning algorithm updates the state feedback controller parameters and the compensator parameters by actively interacting with the unknown environment, thus the approximately optimal tracking can be realized using only data. First, an optimal tracking problem for a linear DT system with disturbance is formulated. Then, the design for controller is achieved by solving a zero‐sum game problem, leading to an off‐policy disturbance compensation Q‐learning algorithm with only a critic structure, which uses data to update disturbance compensation controller gains, without the knowledge of system dynamics. Finally, the effectiveness of the proposed method is verified by simulations.

New results on dynamic output state feedback stabilization of some class of time-varying nonlinear Caputo derivative systems

In modern control theory applications, input–output feedback often arises and plays a crucial role in stabilizing any target control systems. However, in many practical applications, the knowledge of full information on the state of systems may not be available in general due to measurements. In order to control such types of systems, this paper uses a universal concept of real order calculus to stabilize by the method of dynamic output feedback control. Is it possible to design a dynamic output feedback stabilization for time-varying real order control systems? This work develops a new dynamic output feedback control method and proposes linear homogeneous time-varying control law to stabilize incommensurate nonlinear time-varying real order systems under the action of Caputo derivative with an addendum of ultimate random initial-time. We utilize the ideas of the comparison method and establish order-dependent asymptotic results associated with uniform Lipschitz continuous functions that provide stabilization by means of the dynamic output state feedback control method. We provide three examples that include a practical system and show the importance of some theoretical results in the demonstration to stabilize the problems by means of proposed control method.

Dynamical complexities and chaos control in a Ricker type predator-prey model with additive Allee effect

<abstract><p>This work investigates the dynamic complications of the Ricker type predator-prey model in the presence of the additive type Allee effect in the prey population. In the modeling of discrete-time models, Euler forward approximations and piecewise constant arguments are the most frequently used schemes. In Euler forward approximations, the model may undergo period-doubled orbits and invariant circle orbits, even while varying the step size. In this way, differential equations with piecewise constant arguments (Ricker-type models) are a better choice for the discretization of a continuous-time model because they do not involve any step size. First, the interaction between prey and predator in the form of the Holling-Ⅱ type is considered. The essential mathematical features are discussed in terms of local stability and the bifurcation phenomenon as well. Next, we apply the center manifold theorem and normal form theory to achieve the existence and directions of flip bifurcation and Neimark-Sacker bifurcation. Moreover, this paper demonstrates that the outbreak of chaos can stabilize in the considered model with a higher value of the Allee parameter. The existence of chaotic orbits is verified with the help of a one-parameter bifurcation diagram and the largest Lyapunov exponents, respectively. Furthermore, different control methods are applied to control the bifurcation and fluctuating phenomena, i.e., state feedback, the Ott-Grebogi-Yorke, and hybrid control methods. Finally, to ensure our analytical results, numerical simulations have been carried out using MATLAB software.</p></abstract>

Passivity-Based Output Consensus for Second-Order Nonlinear Multiagent Systems

The output consensus for a second-order nonlinear multiagent system (MAS) with mismatched input and output vectors is investigated by exploiting the output strict passivity (OSP). By resorting to the Lyapunov functional approach and the state feedback control method, an OSP criterion for the MAS is derived. Based on the OSP and the relationship between output consensus and the OSP, a sufficient condition to ensure the output consensus of the MAS is obtained. At last, a numerical simulation is given to substantiate the merits of the obtained theoretical results.

Full state feedback and feed forward control of servo smart window using MATLAB/Simulink

<p>House as a place to carry out daily activities requires healthy air. The right step to improve air circulation is to use smart window. A control system method is needed so that smart windows can automate air circulation better. Temperature sensor will determine the minimum, maximum, and opening size of the smart window in order to perform the function of opening and closing effectively. Servo motors are used as actuators in the process of opening - closing windows. In this research, the full state feedback and feed forward control method are used to determine the best control theory for servo motor control for smart window systems. The motor control system modeling in smart window is designed by applying the previously studied control theory. Mathematical modeling was carried out to obtain system equations and performance index. The equation is then applied to the MATLAB/Simulink simulation so that the stability of the system can be monitored against disturbances in the form of noise originating from the sensor or the control system itself.</p>

Principle and Control of Active Engine Mount Based on Magnetostrictive Actuator

Engine mount system affects the automobile NVH performance. Active mounts would achieve excellent vibration isolation and relative displacement control performance in a broad frequency bandwidth by outputting controlled force to the mounting system. The actuator and control method of the active mounts determine the system performance. In this paper, an active mount based on the smart material, i.e., Terfenol-D rod, is proposed, which mainly includes three parts: rubber spring, magnetostrictive actuator (MA), and hydraulic amplification mechanism (HAM). Dynamic model of the active mount is correspondingly established. A state feedback control method based on x-LMS (Least-Mean-Square) algorithm is proposed as well. Specifically, with the consideration of the unmeasurable state parameters in the active mounting system, an x-LMS state feedback controller with the system state as the reference signal is constructed by employing Sage-Husa Kalman filter to realize the state estimation of the active mounting system. Then a detailed analysis of the proposed control method is conducted, with deriving iterative formula of tap-weight vector. Sequentially, the problem of the dependence on the excitation signal in the x-LMS algorithm is addressed. The feasibility and capability of the proposed control method are verified and evaluated by simulation of a two-degree-of-freedom active mounting system.

Adaptive State Feedback Control Method Based on Recursive Least Squares

This study revealed an adaptive state feedback control method based on recursive least squares (RLS) that is introduced for a time-varying system to work with high efficiency. Firstly, a system identification block was created that gives the mathematical model of the time-varying system using the input/output data packets of the controller system. Thanks to this block, the system is constantly monitored to update the parameters of the system, which change over time. Linear quadratic regulator (LQR) is renewed according to these updated parameters, and self-adjustment of the system is provided according to the changed system parameters. The Matlab/Simulink state-space model of the variable loaded servo (VLS) system module was obtained for the simulation experiments in this study; then the system was controlled. Moreover, experiments were carried out on the servo control experimental equipment of the virtual simulation laboratories (VSIMLABS). The effectiveness of the proposed new method was observed taking the performance indexes as a reference to obtain the results of the practical application of the proposed method. Regarding the analysis of simulation and experimental results, the proposed approach minimizes the load effect and noise and the system works at high efficiency.

Dynamic analysis and circuit realization of a novel variable-wing 5D memristive hyperchaotic system with line equilibrium

By introducing flux-controlled memristor and linear feedback term into the three-dimensional (3D) chaotic system, and using the state feedback control method to increase dimension, a novel variable-wing 5D memristive hyperchaotic system has been proposed in this paper. The proposed memristive hyperchaotic system has a line equilibrium point whose position is directly determined by the control parameter. The remarkable feature of the system is that the influence of positive feedback memristor and negative feedback memristor on the system and their similarities and differences are considered. Meanwhile, by analyzing the complex dynamic behavior of the system under different control parameters and initial values, it can be found that the proposed memristive hyperchaotic system shows many interesting phenomena including hidden extreme multistability, transient chaotic transition behavior and variable-wing characteristics. Finally, the hardware electronic circuit of the memristive hyperchaotic system is designed. The hardware experimental results are highly consistent with the numerical simulation ones, which demonstrate the physical realizability of the proposed system.

Adaptive State-Feedback Stabilization for Stochastic Nonlinear Systems with Time-Varying Powers and Unknown Covariance

This paper investigates the adaptive state-feedback stabilization problem for stochastic nonlinear systems. Compared with the existing results, we consider more general and more practical systems, i.e., systems with time-varying powers and unknown covariance simultaneously. We propose a new adaptive state-feedback control method, which ensures that the closed-loop system is globally stable in probability and the states are regulated to the origin almost surely. Finally, the feasibility of the design method is verified by two examples.

Fixed-time synchronization criteria of fuzzy inertial neural networks via Lyapunov functions with indefinite derivatives and its application to image encryption

In this paper, we investigate the fixed-time synchronization for fuzzy inertial neural networks with time-varying coefficients and time delays. The fuzzy inertial neural networks are transformed into two forms of first-order differential systems, and then two kinds of different controllers of time-variable are designed. In these schemes, a series of novel criteria are proposed to ensure the fixed-time synchronization for the drive-response fuzzy inertial neural networks via state feedback control methods. Sufficient conditions of delay-dependent and delay-independent are obtained in terms of algebraic inequalities, not the matrix inequalities. Moreover, these new criteria allow the derivative of the Lyapunov function can be positive, but not negative definite as the earlier work. And the algebraic conditions become easy to be tested under the new criteria. Finally, two examples are added to illustrate effectiveness of the results we obtained. Meanwhile, a new image encryption algorithm is proposed based on the synchronization of drive-response networks, and the effectiveness of this algorithm is also demonstrated.

Guaranteed Cost Control for Interval Type-2 Fuzzy Semi-Markov Switching Systems Within a Finite-Time Interval

This article focuses on the finite-time guaranteed cost (FTGC) control problem for interval type-2 (IT2) fuzzy semi-Markov switching systems (S-MSSs) with additive disturbances. Based on the IT2 fuzzy S-MSSs and the state feedback control method, a novel IT2 mode-dependent fuzzy guaranteed cost (GC) controller is developed under the mismatched membership functions. Then, some new sufficient conditions are given to ensure that IT2 fuzzy S-MSSs are finite-time (FT) stochastically stable based on the designed IT2 mode-dependent fuzzy GC controller. Furthermore, the transition rate boundary condition is relaxed, and a new incomplete transition rate boundary model is constructed to reflect the transition rate information. For both the incomplete transition rate boundaries and the actuator fault phenomenon, the improved stability criteria are provided to stabilize the IT2 fuzzy S-MSSs within an FT interval and determine the gains of the IT2 mode-dependent fuzzy GC controller, resulting in a much greater design flexibility. Distinct from the existing results, the presented FTGC control scheme is more suitable for many practical systems because the IT2 fuzzy S-MSS model, which is more general compared with the traditional fuzzy system and S-MSSs, is considered. Finally, three illustrative examples are offered to explain the effectiveness and feasibility of the proposed FTGC control approach.

The feedback stabilization of finite-state fuzzy cognitive maps

Fuzzy cognitive maps (FCMs) are a kind of cognitive model for knowledge representation and causal inference. Meanwhile, as fuzzy dynamical systems, FCMs have also been widely applied in the control-related fields, such as mobile robots, unmanned aerial vehicles (UAVs), and industrial controls. However, the existing works mainly focused on the practical applications but lacked the necessary theoretical discussions related to the FCM-based control mechanism. As is known, stabilization is one of the fundamental issues in the control fields. Till date, rigorous research on the stabilization of FCMs is still an issue to be studied. In this article, using state feedback control method, the global stabilizations of finite-state FCMs are investigated. First, utilizing the semi-tensor product (STP) of matrices, the algebraic expression of FCM can be derived. Some theorems ensure the sufficient condition for the existence of the state feedback controller of the global stabilization. Second, the constructive design processes of state feedback controllers are discussed in detail. Third, the global stabilization is further extended into partial stabilization, where only specific concepts of FCMs can be stabilized. The corresponding theoretical analysis is implemented. Finally, the effectiveness of the proposed methods is verified by several examples.

A Novel Discrete-Time Leslie–Gower Model with the Impact of Allee Effect in Predator Population

The discrete-time system has more complex and chaotic dynamical behaviors as compared to the continuous-time system. This paper extends a discrete Leslie–Gower predator-prey system with the Allee effect in the predator’s population, whose dynamics are analyzed and explored. We have determined the equilibrium points and studied their local stability properties. We find that the system undergoes flip bifurcation and Neimark–Sacker bifurcation around the interior equilibrium point by choosing the Allee parameter as a bifurcation parameter. We discuss the stability and direction of both bifurcations with the help of the normal form theory and center manifold theorem. The flip bifurcation and Neimark–Sacker bifurcation are the most common routes to the chaotic orbit in the discrete system. Moreover, we utilize state feedback, pole placement, and hybrid control methods to control the chaos in the system. The work is complete with the numerical simulations to confirm the analytical findings.

Dynamics of discrete predator- prey system with fear effect and density dependent birth rate of the prey species

This paper analyses a discrete predator-prey system with fear effect and density dependent birth rate of the prey species. The fixed points of the system are determined and their stability is examined. The criterion for Neimark-Sacker bifurcation and flip bifurcation is developed. The chaotic orbit at an unstable fixed point can be stabilized by applying the state feedback control method. Numerically, we illustrate our analytical findings and observe the complex behaviour of the system that leads to stable state to chaotic one.

Adaptive friction compensation for a class of mechanical systems based on LuGre model

AbstractThis paper deals with the problem of friction compensation for a class of uncertain mechanical systems based on LuGre model. The objective is to develop control laws such that the position variable of the system tracks a periodic desired signal or a constant desired signal. Since the friction behavior of the system with periodic desired signals is largely different from that of the system with constant desired signals, two different adaptive control methods are presented for the two cases, respectively. For the case of periodic desired signals, an adaptive repetitive learning control method is presented, and for the case of constant desired signals, an adaptive dynamic state feedback control method is presented. Both the control laws can guarantee that all the signals in the closed loop system are bounded and the tracking errors converge to zero. Several numerical simulations are carried out to show effectiveness of the proposed control algorithms.

Master-slave synchronization of Lurie systems with time-delay based on event-triggered control

<abstract><p>This paper investigates the master-slave synchronization of Lurie systems with time delay via the event-triggered control. Different from some state feedback control methods with a fixed sampling period or impulsive control with random sampling moments, the event-triggered control means that the controller is updated only if some event-triggering conditions are satisfied. A predefined triggering condition is provided by using the Lyapunov stability theory. Moreover, this condition is proved not to be commonplace. Finally, a numerical example is given to show the correctness of the proposed method.</p></abstract>

Stabilization of Impulsive BNs With Stochastic Disturbances: An Aperiodic/Periodic Scheme

This brief investigates the stabilization problem for impulsive Boolean networks (BNs) with stochastic disturbances. Firstly, dynamic evolution of the impulsive BN is converted into an algebraic form by using the semi-tensor product method of matrices. By analyzing the reachable set, the notion of distance between each state of the network and the equilibrium is defined, based on which the algorithm is then proposed for designing the appropriate aperiodic impulsive sequences. After that, based on the state-feedback control method, some criteria are presented to stabilize the Boolean control networks with periodic impulses and stochastic disturbances. Numerical examples are also presented to show feasibility of the theoretical results established.

Chaotic motion and control of the driven-damped Double Sine-Gordon equation

<p style='text-indent:20px;'>In this paper, the chaotic motion of the driven and damped double Sine-Gordon equation is analyzed. We detect the homoclinic and heteroclinic chaos by Melnikov method. The corresponding Melnikov functions are derived. A numerical method to estimate the Melnikov integral is given and its effectiveness is illustrated through an example. Numerical simulations of homoclinic and heteroclinic chaos are precisely demonstrated through several examples. Further, we employ a state feedback control method to suppress both chaos simultaneously. Finally, numerical simulations are utilized to prove the validity of control methods.</p>