Impulsive Controller Design Research Articles

Fractional impulsive controller design of fractional-order fuzzy systems with average dwell-time strategy and its application to wind energy systems

In this study, the issue of adaptive impulsive control of a permanent magnet synchronous generator (PMSG)-based wind energy system (WES) with an average dwell-time strategy is investigated using a Takagi–Sugeno (T-S) fuzzy model described by fractional-order differential equations. A T-S fuzzy model is employed to describe the nonlinear fractional-order PMSG (FOPMSG) model, an average dwell time, an average impulsive condition, a Lyapunov function, and a less conservative algebraic inequality criterion that guarantees stabilization for the considered nonlinear system. First, the mathematical model of the FOPMSG in the n−m reference frame is transformed into a dimensionless chaotic system through affine transformation and time scale transformation. Then, the stabilization problem of the nonlinear chaotic FOPMSG model is considered to validate the proposed sufficient conditions, leading to the derivation of a new stability criterion for the FOPMSG model, instead of addressing the general problem to validate the proposed result. Subsequently, the desired control gains can be obtained to ensure the stabilization of the addressed closed-loop system. By combining adaptive and impulsive control, the model under consideration can be stabilized for any target dynamics. Finally, we demonstrate the efficiency and feasibility of the suggested approach through numerical simulations and comparative results.

Event-triggered impulsive tracking control for uncertain strict-feedback nonlinear systems via the neural-network-based backstepping technique

This paper studies the problem of event-triggered impulsive tracking control (ETITC) for uncertain strict-feedback nonlinear systems (USFNSs). In contrast to existing impulsive control schemes, this paper incorporates the neural-network (NN)-based backstepping technique into impulsive control design, such that stronger nonlinearities and uncertainties are allowed to be included in the concerned systems. The proposed state-feedback ETITC scheme guarantees that all the signals of the closed-loop system are bounded and the tracking error ultimately converges to an adjustable bounded region, while also avoiding the Zeno behavior. In addition, by constructing a NN-based observer, this paper further develops an output-feedback ETITC scheme to extend its investigation to the scenario where full states are not available for impulsive control design. Finally, an illustrative example involving a chemical reactor system is presented to demonstrate the effectiveness of our control schemes.

Observer-based impulsive consensus control of nonlinear multi-agent systems under denial-of-service attacks

This paper is concerned with the distributed impulsive consensus problem for nonlinear multi-agent systems (MASs) subject to denial-of-service (DoS) attacks, where the information of agent states is not fully available in the impulsive control design. To reconstruct the states of MASs and guarantee secure average consensus, a novel observer-based impulsive secure control protocol is put forward, and some sufficient conditions are derived by means of linear matrix inequality (LMI) technique and Lyapunov method. It should be pointed out that both the proposed state observer and control protocol adjust the state value abruptly at some discrete instants in an impulsive manner. Moreover, the considered asynchronous DoS attack model can allow jam each channel independently, under which the decay rates of different attack modes are estimated. Finally, two simulation examples, including a practical control system, verify the effectiveness of the proposed consensus algorithm.

Robust H∞$$ {H}_{\infty } $$ continuous‐discrete hybrid impulsive dynamic output feedback control for delays descriptor Markovian jump systems with multidimensional impulsive operator

AbstractThis study focuses on the robust continuous‐discrete hybrid impulsive dynamic output feedback (DOF) control issue for time delays descriptor Markovian jump systems (TDDMJSs) with multidimensional impulsive operator. By applying an improved impulse‐time‐dependent Lyapunov–Krasovskii (L‐K) functional, the novel stochastic admissibilization conditions are formulated as linear matrix inequalities. A desired hybrid impulsive DOF controller is achieved, which includes a continuous DOF controller and a discrete impulsive DOF controller. The stochastic admissibilization of the closed‐loop TDDMJSs can be satisfied by virtue of the desired hybrid impulsive DOF controller. In the end, the validity of the proposed hybrid impulsive DOF controller design method is demonstrated by two examples, including an oil catalytic cracking process.

Quasi-Synchronization of Timescale-Type Delayed Neural Networks With Parameter Mismatches via Impulsive Control

Most synchronization criteria are scale-free on time evolution, whose main research objects are discrete-time/continuous-time systems. Unlike these theoretical results, in order to develop impulsive control schemes for discrete-time and continuous-time neural networks (NNs) in a unified framework. This article investigates impulsive control design of timescale-type NNs (TNNs) with parameter mismatches and time-varying delays (TVDs). First, several timescale impulsive differential inequalities are demonstrated by the timescale theory, which offer new inequality techniques for the investigation of timescale-type impulsive systems. Next, some criteria are proved for discrete-time NNs and TNNs by utilizing impulsive control theory, timescale inequality techniques, and the average impulsive interval method. Unlike the published works, this article gives some impulsive control schemes to ensure quasi-synchronization (QS) even if there exist TVDs in TNNs. In the end, four simulation examples are offered to demonstrate the validness of the obtained theoretical results.

Impulsive control strategies of mRNA and protein dynamics on fractional-order genetic regulatory networks with actuator saturation and its oscillations in repressilator model

In genetic regulatory networks (GRNs), the control strategies of messenger RNA (mRNA) and protein play a key role in regulatory mechanisms of gene expression, especially in translation and transcription. However, the influence of impulsive control strategies on oscillatory gene expression is not well understood. In this article, by considering the impulsive control strategies of mRNA and protein, a novel fractional-order genetic regulatory networks with actuator saturation is proposed. By applying polytopic representation technique, the actuator saturation term is first considered into the design of impulsive controller, and less conservative linear matrix inequalities (LMIs) criteria that guarantee finite-time Mittag-Leffler stabilization problem for fractional-order genetic regulatory networks are given. The derived sufficient conditions can easily be verified by designing impulsive control gains and solving simple LMIs. Finally, to investigate the effectiveness and applicability of the control strategies, an interesting simulation example as a synthetic oscillatory network of transcriptional regulators in Escherichia coli is illustrated.

Nonlinear Impulsive Control Design for Biologically Grounded NSM Tumor Growth Model Using Exact Linearized Mapping

This paper investigates the problem of personalized chemotherapy scheduling using a system-modeling approach based on a nonlinear impulsive control technique. In particular, this work deals with the so-called Norton-Simon-Massagué (NSM) model, a minimal biologically grounded model for controlled tumor growth, which has been accepted in clinical oncology for breast cancer treatment. In this paper, we continue this line of research, to advance the concept of closed-loop control a step further towards widespread clinical use. In the present work, the problem of chemotherapy drug scheduling is approached using an impulsive control strategy combined with a state-space observer. The technical challenges of the nonlinearity of the controlled system and the impulsive nature of control input are handled via the utilization of a novel mapping that transforms the control problem into a “simplified” linear discrete-time control problem. Theoretical guarantees regarding the sign and invertibility of the proposed transformation are demonstrated. Then, an observer-based state feedback controller is proposed for chemotherapy drug scheduling as a proof-of-concept control strategy. Simulation results showing the performance of the designed closed-loop controlled chemotherapy schedules in reducing and eradicating tumor volume are provided using model's parameters derived using real tumor data and Doxirubicin drug.

Event-Triggered Impulsive Controller Design for Synchronization of Delayed Chaotic Neural Networks and Its Fractal Reconstruction: An Application to Image Encryption

This paper examines synchronization of delayed chaotic neural networks with impulsive control, event-triggered impulsive control, and event-triggered delayed impulsive control. Lyapunov-based event-triggered mechanism is constructed to derive few sufficient conditions in terms of Linear Matrix Inequalities (LMIs). The feedback and event-triggered gain matrices are evaluated with the help of numerical packages. The fractal interpolation functions are employed to reconstruct the chaotic sequence of the neural networks since the chaotic attractor has self-similar properties and coincides with the fractal functions. In this study, a linear fractal interpolation is used to reconstruct both the master-slave chaotic attractor and the encrypted chaotic attractor, with optimized scaling factors.Finally, an application of the image encryption algorithm is given in terms of RSA public-key cryptosystems, permutation, and finite field diffusion for the chaotic sequence generated by fractal interpolation functions.

Dynamic analysis of delayed neural networks: Event-triggered impulsive Halanay inequality approach

This paper proposes a generalized impulsive Halanay inequality from the impulsive control standpoints, where the impulse action is event-triggered. Namely, the control task is executed when an external event generated by the state-dependent event-triggered mechanism (ETM) is activated, rather than at a fixed time. It is shown that under the proposed event-triggered impulsive control (ETIC) strategy, the solution of the underlying inequality is guaranteed to converge to zero asymptotically. Moreover, the key point is the introduction of monitoring value to ensure a positive minimum inter-execution time, which exactly assists ETIC with reducing the pressure of information transmission. Then, the generalized impulsive Halanay inequality with appropriate ETIC scheme is utilized to the analysis of delayed neural networks (DNNs). In particular, some synchronization and asymptotic stability criteria of DNNs are derived, where the design of impulsive controller is based on ETIC strategy. At last, some numerical examples are provided to illustrate the validity of the obtained results.

Event-triggered impulsive control design for synchronization of inertial neural networks with time delays

This paper investigates the synchronization problem of inertial neural networks (INNs) with time delays by virtue of event-triggered (E-T) impulsive control, in which a Lyapunov function based E-T mechanism is used to determine impulsive instants. The synchronization analysis of INNs through E-T impulsive control technique unlike time-triggered impulsive control, which would be activated when certain well-designed conditions exist, E-T impulsive control is only allowed when certain well-defined events occur. Besides that, control input is only required at triggered instants and also no control input is required for two triggered instants in a sequence. Considering the E-T mechanism, the synchronization analysis of the INNs is discussed by reduced and non-reduced order approaches and constructing the suitable Lyapunov functionals. Finally, two simulation results are provided to illustrate the efficacy of the theoretical results.

A Chaotic Quadratic Oscillator with Only Squared Terms: Multistability, Impulsive Control, and Circuit Design

Here, a chaotic quadratic oscillator with only squared terms is proposed, which shows various dynamics. The oscillator has eight equilibrium points, and none of them is stable. Various bifurcation diagrams of the oscillator are investigated, and its Lyapunov exponents (LEs) are discussed. The multistability of the oscillator is discussed by plotting bifurcation diagrams with various initiation methods. The basin of attraction of the oscillator is discussed in two planes. Impulsive control is applied to the oscillator to control its chaotic dynamics. Additionally, the circuit is implemented to reveal its feasibility.

Exponential stability of nonlinear state-dependent delayed impulsive systems with applications

The exponential stability problem for impulsive systems subject to double state-dependent delays is studied in this paper, where state-dependent delay (SDD) is involved in both continuous dynamics and discrete dynamics and the boundedness of it with respect to states is prior unknown. According to impulsive control theory, we present some Lyapunov-based sufficient conditions for the exponential stability of the concerned system. It is shown that the stabilizing effect of SDD impulses on an unstable SDD system changes the stability and achieves desired performance. In addition, the destabilizing effect of SDD impulses is also fully considered and the corresponding sufficient conditions are derived, which reveals the fact that a stable SDD system can maintain its performance when it is subject to SDD impulsive disturbance. As an application, the proposed result can be employed to the stability analysis of impulsive genetic regulatory networks (GRNs) with SDD and the corresponding sufficient conditions are proposed in terms of the model transformation technique and the linear matrix inequalities (LMIs) technique. In order to demonstrate the effectiveness and applicability of the derived results, we give two examples including impulsive GRNs with SDD and the impulsive controller design for the nonlinear system with SDD.

Impulsive Synchronization of Unbounded Delayed Inertial Neural Networks With Actuator Saturation and Sampled-Data Control and its Application to Image Encryption.

The article considers the impulsive synchronization for inertial neural networks with unbounded delay and actuator saturation via sampled-data control. Based on an impulsive differential inequality, the difficulties caused by unbounded delay and impulsive effect may be effectively avoid. By applying polytopic representation technique, the actuator saturation term is first considered into the design of impulsive controller, and less conservative linear matrix inequality (LMI) criteria that guarantee asymptotical synchronization for the considered model via hybrid control are given. As special cases, the asymptotical synchronization of the considered model via sampled-data control and saturating impulsive control are also studied, respectively. Numerical simulations are presented to claim the effectiveness of theoretical analysis. A new image encryption algorithm is proposed to utilize the synchronization theory of hybrid control. The validity of image encryption algorithm can be obtained by experiments.

Impulsive sampled-data controller design for synchronization of delayed T–S fuzzy Hindmarsh–Rose neuron model

In this paper, the authors investigate the synchronization criteria of fuzzy impulsive sampled data control for Hindmarsh–Rose (H–R) neuronal system with time-delay. For the stability analysis, Lyapunov–Krasovskii functionals (LKF) are employed to deduce the conditions that guarantee the asymptotical stability of the proposed T–S fuzzy H–R neuron system. By utilizing free-matrix based inequality, some sufficient conditions are derived and expressed in terms of linear matrix inequalities. The obtained sufficient conditions can be checked easily by standard available software packages in MATLAB. Finally, some numerical simulations are given to validate the effectiveness of the proposed conditions.

Finite-Time Lyapunov Functions and Impulsive Control Design

In this paper, we introduce finite-time Lyapunov functions for impulsive systems. The relaxed sufficient conditions for asymptotic stability of an equilibrium of an impulsive system are given via finite-time Lyapunov functions. A converse finite-time Lyapunov theorem for controlling the impulsive system is proposed. Three examples are presented to show how to analyze the stability of an equilibrium of the considered impulsive system via finite-time Lyapunov functions. Furthermore, according to the results, we design an impulsive controller for a chaotic system modified from the Lorenz system.

Impulsive control design for output tracking of probabilistic Boolean control networks

This study investigates the impulsive control for the output tracking of probabilistic Boolean control networks (PBCNs) by the algebraic state-space representation method. Firstly, a novel system with augmented control is established by regarding the impulsive time as a special kind of control, which is equivalent to the considered impulsive PBCN (IPBCN). Secondly, based on the largest control invariant subset, a necessary and sufficient condition is proposed to design impulsive control for the output tracking problem of IPBCNs. Moreover, a constructive method is put forward to design the state feedback controller and state-dependent impulsive time sequence. Finally, an example is given to demonstrate the effectiveness of the obtained results.

Impulsive Stabilization of Nonlinear Time-Delay System With Input Saturation via Delay-Dependent Polytopic Approach

The impulsive stabilization of nonlinear time-delay system with input saturation via delay-dependent polytopic approach is studied in this article. Different from polytopic representation technique, delay-dependent polytopic technique is able to estimate a larger domain of attraction. Based on this approach, the actuator saturation term is first introduced into the design of impulsive controller, which is expressed as a convex combination of the product of delay-dependent state vectors and auxiliary matrices. By applying delay-dependent polytopic technique and delay-dependent Lyapunov–Krasovskii functional (LKF) approach, a new series of less conservative linear matrix inequality (LMI) criteria are obtained to ensure the stability of the established model. Finally, two examples are presented to claim the effectiveness of theoretical analysis results.

Concurrent design of controller and passive elements for robots with impulsive actuation systems

There are some biological evidences showing that the actuation system in legged animals is impulsive; it is not continuous. As opposed to continuous control/actuation, the control actions occur in specific intervals, and from the instant of one actuation until the start of the next one, passive elements guarantee the stability of the robotic system and govern its natural dynamics. In this paper, we present an analytical method for concurrent design of impulsive controller and passive elements (compliance and damper) for robotic systems; e.g., manipulators and legged-robots. To optimize the force profiles of passive elements, three different cost functions are presented which optimize the natural dynamics and energy consumption of the robot. The presented method can be applied to both cyclic and non-cyclic (explosive) tasks so as to attain energy efficient and bio-inspired motions. The method is applied to three biological models: a simulated human arm for throwing an object, a swing leg for drawing an oval, and a 3D quadruped robot for performing walking gait. Our findings in the simulation studies are in line with the hypothesis of impulsive actuation in nature and show the applicability of our method in robotics.

Impulsive controller design for exponential synchronization of delayed stochastic memristor-based recurrent neural networks

In this paper, impulsive synchronization of stochastic memristor-based recurrent neural networks with time delay is studied. One can find that the memristive connection weights have a certain relationship with the stability of the system. Based on the drive-response concept, the stochastic differential inclusions theory and the Lyapunov functional method with the impulsive delay differential inequality technique was established to guarantee the impulsive synchronization of memristor-based recurrent neural networks with stochastic effects. The obtained sufficient conditions can be checked easily by Linear Matrix Inequalities (LMI) Control Toolbox in MATLAB. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.

Analysis of Stability of Hopfield Neural Networks and Design of Impulsive Controller

Based on the proper Lyapunov functions and the Riccati liner inequality, the Robust H-stability of Hopfield neural networks with impulsive effects is studied and some sufficient conditions for robust H-stability are established, the impulsive stabilization criteria can be verified by the impulsive controller, simulation validate the main results.