Impulsive Systems Research Articles

Asymptotic solutions of differential equations with singular impulses

The paper considers impulsive systems with singularities. The main novelty is that beside the singularity of the differential equation, the impulsive equation is a singular one. The method of boundary functions is applied to obtain the main result. Examples with simulations confirming the theoretical results are given.

Controllability and Stability of Non-instantaneous Impulsive Stochastic Multiple Delays System

Controllability and Stability of Non-instantaneous Impulsive Stochastic Multiple Delays System

A note on existence results for noninstantaneous impulsive integrodifferential systems

A note on existence results for noninstantaneous impulsive integrodifferential systems

Almost sure exponential stability and stochastic stabilization of impulsive stochastic differential delay equations

In this paper, we mainly study the almost sure exponential stability of impulsive stochastic differential delay equations (ISDDEs) with bounded variable delays. The main technique is to compare ISDDEs with corresponding impulsive stochastic differential equations (ISDEs) without delay, to obtain the upper bound τ∗ of delays that ISDDEs can maintain stability by accurate calculation. The results show that if the corresponding ISDEs are almost surely exponentially stable, then the ISDDEs are also almost surely exponentially stable as long as these delays are less than τ∗. In addition, the stability theory established in this paper can be applied to noise stabilization based on sampled-data observations of a class of unstable impulsive systems. Taking impulsive Lurie systems (ILSs) as an example, we discuss the design of noise stabilization strategies.

Stability analysis for nonautonomous impulsive hybrid stochastic delay systems

In this paper, the problems on the existence and uniqueness, and the input-to-state stability for the global solution of nonlinear nonautonomous impulsive stochastic delay systems with Markovian switching are considered. The existence and uniqueness for the global solution of such systems is studied by using the Lyapunov function, the theory of stochastic analysis, and the function of the impulsive density. In order to overcome the difficulty stemming from the simultaneous presence of the indefinite derivative for the Lyapunov function, the bounded external disturbances, and a nonnegative and bounded time-varying delay, one impulsive generalized Halanay inequality of integral version is established. The input-to-state stability, the integral input-to-state stability, the stochastic input-to-state stability and the eλt(λ>0)-weighted input-to-state stability for the global solution of nonlinear nonautonomous impulsive stochastic delay systems with Markovian switching are investigated, respectively. One example is provided to illustrate the effectiveness of the theoretical results obtained.

Bumpless transfer control for switched impulsive positive systems with [formula omitted]-gain performance

This paper investigates the problem of bumpless transfer control for switched impulsive positive systems with L1-gain performance. For switched impulsive positive systems, the control bump is brought from both switching behavior and impulsive effects. First, the concept of bumpless transfer performance is proposed by imposing magnitude constraints on the control signal to measure the level of bumpless transfer in the switched impulsive positive system. Then, based on a new class of multiple piecewise-continuous copositive Lyapunov function, a tighter mode-dependent average dwell time switching signal bound and bumpless transfer controller are designed to realize positive property, bumpless transfer and L1-gain performance of the closed-loop systems. Finally, the feasibility and superiority of the proposed control strategy are illustrated by simulations.

Improving the insulin therapy for diabetic patients using optimal impulsive disturbance rejection: Continuous time approach

The paper proposes a new model-based optimization approach to improve the clinical efficiency of compensatory insulin bolus treatment in diabetic patients, aiming to mitigate the consequences of diabetes. The most important contribution of this paper is a novel methodology for determining the optimal parameters of insulin treatment, namely the size and timing of insulin boluses, to effectively compensate for carbohydrate intake. This concept can be seen as the so-called optimal model-based bolus calculator. The presented theoretical framework deals with the problem of optimal disturbance rejection in impulsive systems by minimizing an integral quadratic cost function. The methodology considers a personalized empirical transfer function model with static gains and time constants as the only parameters assumed to be known, making the bolus calculator more straightforward to implement in clinical practice. Contrary to other techniques, the proposed methodology considers impulsive insulin administration in the form of boluses, which is more feasible than continuous infusion. In contrast to the conventional bolus calculator, the proposed algorithm allows for maximizing therapy performance by optimizing the relative time of insulin bolus administration with respect to carbohydrate intake. Another feature to highlight is that the solution of the optimization problem can be obtained analytically, hence no numerical iterative solvers are required. Additionally, the continuous-time domain approach allows for a much finer adjustments of the insulin administration timing compared to discrete-time models. The proposed approach was validated in an in-silico study, which demonstrated the importance of systematically determined insulin–carbohydrate ratio and the relative delay between disturbance and its compensation. The results showed that the proposed optimal bolus calculator outperforms the traditional suboptimal formula.

Event-Triggered Impulsive Control for Input-to-State Stabilization of Nonlinear Time-Delay Systems.

This article investigates the event-triggered impulsive control (ETIC) problem for a class of nonlinear time-delay systems subject to exogenous disturbances. An original event-triggered mechanism (ETM) which utilizes the information of system state and external input is constructed based on Lyapunov function approach. To achieve the input-to-state stability (ISS) of the considered system, some sufficient conditions are presented, in which the underlying relationship among ETM, exogenous input, and impulse action is established. Furthermore, the possible Zeno behavior induced by the proposed ETM is excluded simultaneously. As an application, the design criterion of ETM and impulse gain is put forward for a class of impulsive control systems with delay according to the feasibility of some linear matrix inequalities (LMIs). Finally, two examples with numerical simulations are provided to confirm the effectiveness of the developed theoretical results, where the synchronization issue of delayed Chua's circuit is considered.

Quasi‐synchronization for complex networks under deception attacks via saturated impulsive control

AbstractThis paper addresses the issue of saturated impulsive control for a class of dynamical networks with hybrid delays and unknown bounded disturbances that are susceptible to deception attacks. Achieving local exponential quasi‐synchronization is the objective. Physical networks are often restricted by saturation, making them more vulnerable to cyberattacks that can disrupt network performance. Unlike previous studies on saturated impulsive control, this paper fully considers the effect of deception attacks on saturated impulse by proposing a new constraint of set inclusion. Criteria for the local quasi‐synchronization problem are established using the Lyapunov method and the comparison principle of impulsive systems. Our results demonstrate that the error bounds for quasi‐synchronization are closely linked to the impulsive interval, time‐delay, intensity of external disturbances, and deception attacks. Finally, numerical simulations are conducted to validate the effectiveness of our proposed approach.

Impulsive Effects and Complexity Dynamics in the Anti-Predator Model with IPM Strategies

When confronted with the imminent threat of predation, the prey instinctively employ strategies to avoid being consumed. These anti-predator tactics involve individuals acting collectively to intimidate predators and reduce potential harm during an attack. In the present work, we propose a state-dependent feedback control predator-prey model that incorporates a nonmonotonic functional response, taking into account the anti-predator behavior observed in pest-natural enemy ecosystems within the agricultural context. The qualitative analysis of this model is presented utilizing the principles of impulsive semi-dynamical systems. Firstly, the stability conditions of the equilibria are derived by employing pertinent properties of planar systems. The precise domain of the impulsive set and phase set is determined by considering the phase portrait of the system. Secondly, a Poincaré map is constructed by utilizing the sequence of impulsive points within the phase set. The stability of the order-1 periodic solution at the boundary is subsequently analyzed by an analog of the Poincaré criterion. Additionally, this article presents various threshold conditions that determine both the existence and stability of an order-1 periodic solution. Furthermore, it investigates the existence of order-k (k≥2) periodic solutions. Finally, the article explores the complex dynamics of the model, encompassing multiple bifurcation phenomena and chaos, through computational simulations.

Model-based MIN/MAX override control of centrifugal compressor systems

We propose an application-oriented nonlinear control approach for centrifugal compressors, tailored to meet requirements of industrial applications such as variable process demands and adherence to operational constraints, for instance surge avoidance. Our compressor model modifies an approach of Gravdahl and Egeland by including key features of an industrial setting. In particular, it takes into account the joint action of adjustable positions of the guide vane and the blow-off valve, while compensating variable disturbances introduced by the process valve. Moreover, the modified model is also valid for higher differential pressures across the compressor. By integrating the nonlinear output regulation framework with MIN/MAX-override control, we enable trajectory tracking within specified state constraints. Additionally, we analyze the switching scheme and give a proof of practical stability of the closed-loop MIMO system using the corresponding switched and impulsive error system. The effectiveness of the override control is demonstrated by typical scenarios in process control such as discharge pressure control, anti-surge control, and maximum discharge pressure limitation.

Exponential stability of fractional‐order uncertain systems with asynchronous switching and impulses

AbstractDifferent from the Mittag–Leffler stability or asymptotic stability, the exponential stability issue, which provides faster and explicit convergence rate, is studied in this paper for fractional‐order uncertain systems with asynchronous switching and impulses, where the impulsive functions rely on not only switching modes but also impulsive time. Instead of using the inequality , by utilizing the theory of fractional‐order differential equations, the methods of Lyapunov function and mathematical induction, some novel and less‐conservative stability criteria are developed, respectively, for the case of switched stable subsystems or switched unstable subsystems. The obtained results build a tradeoff between impulsive function, impulsive interval, average dwell time and fractional order. In addition, our results with are also novel in contrast with the ones of integer‐order switched impulsive systems. Finally, five numerical examples are given to show the effectiveness of theoretical results.

Reinforcement learning for optimal control of linear impulsive systems with periodic impulses

This paper focuses on the finite- and infinite-horizon optimal control problems of linear impulsive systems with periodic impulses under the quadratic performance index. Necessary and sufficient conditions for the optimal impulsive system are derived in terms of hybrid Riccati equations by utilizing the variational method and the collocation method combined with a time-varying Lyapunov function. Different from the existing model-based impulsive control schemes, three reinforcement learning (RL)-based algorithms are proposed to solve the optimal impulsive controller and hybrid controller for the impulsive system without the exact knowledge of the system dynamics. The asymptotical stability of the impulsive control system and the convergence of the RL-based algorithms are proved rigorously. Finally, a numerical simulation illustrates the effectiveness of the proposed control methods.

Iterative learning based convergence analysis for nonlinear impulsive differential inclusion systems with randomly varying trial lengths

SummaryThis paper studies the finite‐time tracking problem for nonlinear impulsive differential inclusion systems with randomly varying trial lengths. First, we convert the set‐valued mapping in the differential inclusion systems to single‐valued mapping by a Steiner‐type selector. For the tracking problem of random discontinuous output trajectories, this paper defines a piecewise continuous variable by zero‐order holder to correct the tracking error of segmented continuity. Then, we introduce the average operator with forgetting factor to design three novel learning schemes, and establish convergence results by using the mathematical analysis tools such as impulsive Gronwall inequality and ‐norm. Finally, a numerical example verifies the validity of the theoretical results, and we compare the tracking performance of the output trajectories for different forgetting factors.

Ground state solutions for the fractional impulsive differential system with ψ‐Caputo fractional derivative and ψ–Riemann–Liouville fractional integral

This article examines a new family of (p,q)‐Laplacian type nonlinear fractional impulsive differential coupled equations involving both the ‐Caputo fractional derivative and –Riemann–Liouville fractional integral. With the help of Nehari manifold in critical point theory and fractional calculus properties, we obtain the existence of at least one nontrivial ground state solution for the coupled system with some natural and easily verifiable superlinear conditions on the nonlinearity.

New results on synchronization control of memristor-based quaternion-valued fuzzy neural networks with delayed impulses

A model of memristor-based quaternion-valued fuzzy neural networks (MQVFNNs) with delayed impulses and time-varying delays is established, and the synchronization issue is investigated in this paper. Firstly, to avoid non-commutativity, the MQVFNNs are decomposed into real-valued delayed impulsive neural networks. Secondly, a novel lemma for delayed impulsive system is introduced based on Halanay differential inequality. Then, by employing the theory of differential inclusion and the proposed lemma, some sufficient conditions are deduced to guarantee the global exponential synchronization of memristive quaternion-valued fuzzy neural networks under a simple delayed nonlinear control scheme. Finally, a numerical simulation is given to demonstrate the effectiveness of our theoretical results.

Piecewise conformable fractional impulsive differential system with delay: existence, uniqueness and Ulam stability

Piecewise conformable fractional impulsive differential system with delay: existence, uniqueness and Ulam stability

Default mode network aberrance in subjects of alcohol and opioid use disorders during working memory task: An exploratory EEG microstates study.

Aberrance in switching from default mode network (DMN) to fronto-parietal network (FPN) is proposed to underlie working memory deficits in subjects with substance use disorders, which can be studied using neuro-imaging techniques during cognitive tasks. The current study used EEG to investigate pre-stimulus microstates during the performance of Sternberg's working memory task in subjects with substance use disorders. 128-channel EEG was acquired and processed in ten age and gender-matched subjects, each with alcohol use disorder, opioid use disorder, and controls while they performed Sternberg's task. Behavioral parameters, pre-stimulus EEG microstate, and underlying sources were analyzed and compared between subjects with substance use disorders and controls. Both alcohol and opioid use disorder subjects had significantly lower accuracy (P < 0.01), while reaction times were significantly higher only in subjects of alcohol use disorder compared to controls (P < 0.01) and opioid use disorder (P < 0.01), reflecting working memory deficits of varying degrees in subjects with substance use disorders. Pre-stimulus EEG microstate revealed four topographic Maps 1-4: subjects of alcohol and opioid use disorder showing significantly lower mean duration of Map 3 (visual processing) and Map 2 (saliency and DMN switching), respectively, compared to controls (P < 0.05). Reduced mean durations in Map 3 and 2 in subjects of alcohol and opioid use disorder can underlie their poorer performance in Sternberg's task. Furthermore, cortical sources revealed higher activity in both groups of substance use disorders in the parahippocampal gyrus- a hub of DMN; superior and middle temporal gyri associated with impulsivity; and insula that maintains balance between executive reflective system and impulsive system. EEG microstates can be used to envisage neural underpinnings implicated for working memory deficits in subjects of alcohol and opioid use disorders, reflected by aberrant switching between neural networks and information processing mechanisms.

Finite-time stability for impulsive stochastic nonlinear system with uncertain parameter

This paper considered the finite-time mean square stability for impulsive stochastic nonlinear system(ISNS) with uncertain parameter. By selecting the modal dependent Lyapunov functional, using average impulsive interval approach and combining Linear Matrix Inequality (LMI) method, the correlation stability criterion of ISNS was obtained. A gain matrix of the feedback controller is obtained on the basis of this sufficient condition. Finally, the LMI toolbox in Matlab was used for data simulation, and the relevant state trajectory demonstrates the availability of the proposed theory.

ADP-Based Event-Triggered Constrained Optimal Control on Spatiotemporal Process: Application to Temperature Field in Roller Kiln.

The precise control of the spatiotemporal process in a roller kiln is crucial in the production of Ni-Co-Mn layered cathode material of lithium-ion batteries. Since the product is extremely sensitive to temperature distribution, temperature field control is of great significance. In this article, an event-triggered optimal control (ETOC) method with input constraints for the temperature field is proposed, which takes up an important position in reducing the communication and computation costs. A nonquadratic cost function is adopted to describe the system performance with input constraints. First, we present the problem description of the temperature field event-triggered control, where this field is described by a partial differential equation (PDE). Then, the event-triggered condition is designed according to the information of system states and control inputs. On this basis, a framework of the event-triggered adaptive dynamic programming (ETADP) method that is based on the model reduction technology is proposed for the PDE system. A critic network is used to approach the optimal performance index by a neural network (NN) together with that an actor network is used to optimize the control strategy. Furthermore, an upper bound of the performance index and a lower bound of interexecution times, as well as the stabilities of the impulsive dynamic system and the closed-loop PDE system, are also proved. Simulation verification demonstrates the effectiveness of the proposed method.