Showing papers on "Piecewise published in 2022"
TL;DR: In this article , the authors analyzed the proper equations of the intraparticle diffusion model and their applications, discussed the interpretation of the mass transfer steps revealed by this model, and provided the solving methods.
45 citations
TL;DR: In this article , a hybrid Nussbaum technique was proposed to handle uncertain agents with high-power dynamics where the backstepping procedure fails, with nonsmooth behaviors (switching and quantization), and with multiple unknown control directions for each agent.
Abstract: This work investigates the consensus tracking problem for high-power nonlinear multiagent systems with partially unknown control directions. The main challenge of considering such dynamics lies in the fact that their linearized dynamics contain uncontrollable modes, making the standard backstepping technique fail; also, the presence of mixed unknown control directions (some being known and some being unknown) requires a piecewise Nussbaum function that exploits the a priori knowledge of the known control directions. The piecewise Nussbaum function technique leaves some open problems, such as Can the technique handle multiagent dynamics beyond the standard backstepping procedure? and Can the technique handle more than one control direction for each agent? In this work, we propose a hybrid Nussbaum technique that can handle uncertain agents with high-power dynamics where the backstepping procedure fails, with nonsmooth behaviors (switching and quantization), and with multiple unknown control directions for each agent.
43 citations
TL;DR: In this article , an unknown input observer-based appointed-time funnel control policy is proposed for quadrotors suffering from environmental disturbances and parametric uncertainties, where a continuous piecewise function is embedded to specify the funnel envelop, such that the stringent temporal constraints can be arbitrarily prescribed by operators.
43 citations
TL;DR: In this paper , a new mathematical model to better understand the novel coronavirus (omicron variant) was constructed to study the possible occurrence of the layers(waves) of COVID-19 with the omicron variant and present their mathematical results.
34 citations
01 Sep 2022
TL;DR: In this article , the existence of Filippov solutions for a discontinuous IPFONN with piecewise Caputo derivatives was investigated and decision theorems for the existence and uniqueness of the (periodic) solution, global exponential stability, and impulsive control global stabilization were established.
Abstract: It is well known that the conventional fractional-order neural networks (FONNs) cannot generate nonconstant periodic oscillation. For this point, this article discusses a class of impulsive FONNs with piecewise Caputo derivatives (IPFONNs). By using the differential inclusion theory, the existence of the Filippov solutions for a discontinuous IPFONNs is investigated. Furthermore, some decision theorems are established for the existence and uniqueness of the (periodic) solution, global exponential stability, and impulsive control global stabilization to IPFONNs. This article achieves four key issues that were not solved in the previously existing literature: 1) the existence of at least one Filippov solution in a discontinuous IPFONN; 2) the existence and uniqueness of periodic oscillation in a nonautonomous IPFONN; 3) global exponential stability of IPFONNs; and 4) impulsive control global Mittag–Leffler stabilization for FONNs.
33 citations
TL;DR: In this article , a new intelligent event-triggering mechanism is proposed, in which the event triggering threshold is optimized by a Q-learning algorithm, and a switched system approach is proposed to deal with the aperiodic DoS attack occurring in the communication channels.
Abstract: This article addresses the dynamic positioning control problem of a nonlinear unmanned marine vehicle (UMV) system subject to network communication constraints and deny-of-service (DoS) attack, where the dynamics of UMV are described by a Takagi-Sugeno (T-S) fuzzy system (TSFS). In order to save limited communication resource, a new intelligent event-triggering mechanism is proposed, in which the event triggering threshold is optimized by a Q -learning algorithm. Then, a switched system approach is proposed to deal with the aperiodic DoS attack occurring in the communication channels. With a proper piecewise Lyapunov function, some sufficient conditions for global exponential stability (GES) of the closed-loop nonlinear UMV system are derived, and the corresponding observer and controller gains are designed via solving a set of matrix inequalities. A benchmark nonlinear UMV system is adopted as an example in simulation, and the simulation results validate the effectiveness of the proposed control method.
31 citations
TL;DR: In this article , a piecewise probabilistic harmonic power flow method is proposed to evaluate the harmonic emission level, and a decoupled approach combing the graph theory and current injection method is established to calculate the HPF with residential loads.
28 citations
TL;DR: In this article , a fuzzy adaptive design is proposed to solve the finite-time constrained tracking for hypersonic flight vehicles (HFVs) by considering actuator dynamics and asymmetric time-varying constraints.
Abstract: This article proposes a fuzzy adaptive design solving the finite-time constrained tracking for hypersonic flight vehicles (HFVs). Actuator dynamics and asymmetric time-varying constraints are considered when solving this problem. The main features of the proposed design lie in 1) introducing a novel piecewise but differentiable switching control law, with an appropriate design thought to avoid the singularity issues typical of finite-time control; 2) handling actuator magnitude, bandwidth, and rate constraints, thanks to the introduction of an auxiliary compensating system counteracting the adverse effects caused by actuator physical constraints, while guaranteeing the closed-loop stability; and 3) handling asymmetric time-varying state constraints, thanks to the introduction of tan-type barrier Lyapunov functions working for both constrained and unconstrained scenarios. Comparative simulation results illustrate the effectiveness of the proposed strategy over existing methods for HFVs in terms of convergence, smoothness, actuator performance, and constraints satisfaction.
24 citations
TL;DR: In this article , a piecewise covid-19 mathematical model with quarantine class and vaccination using SEIQR epidemic model is presented. And the stability of the model is discussed regarding the reproductive number.
Abstract: In the current manuscript, we deal with the dynamics of a piecewise covid-19 mathematical model with quarantine class and vaccination using SEIQR epidemic model. For this, we discussed the deterministic, stochastic, and fractional forms of the proposed model for different steps. It has a great impact on the infectious disease models and especially for covid-19 because in start the deterministic model played its role but with time due to uncertainty the stochastic model takes place and with long term expansion the use of fractional derivatives are required. The stability of the model is discussed regarding the reproductive number. Using the non-standard finite difference scheme for the numerical solution of the deterministic model and illustrate the obtained results graphically. Further, environmental noises are added to the model for the description of the stochastic model. Then take out the existence and uniqueness of positive solution with extinction for infection. Finally, we utilize a new technique of piecewise differential and integral operators for approximating Caputo-Fabrizio fractional derivative operator for the purpose of constructing of the fractional-order model. Then study the dynamics of the models such as positivity and boundedness of the solutions and local stability analysis. Solved numerically fractional-order model used Newton Polynomial scheme and present the results graphically.
24 citations
01 Jan 2022
TL;DR: In this paper , an adaptive attitude controller is systematically presented to ensure that the spacecraft attitude can converge into a small region around the origin within a predefined time, which can be explicitly determined in advance by assigning a simple parameter.
Abstract: This article proposes a novel adaptive nonsingular predefined-time control strategy for rigid spacecrafts with inertia uncertainties. Following the backstepping recursive design procedures, an adaptive attitude controller is systematically presented to ensure that the spacecraft attitude can converge into a small region around the origin within a predefined time, which can be explicitly determined in advance by assigning a simple parameter. Moreover, by designing quadratic functions in the controllers, the singularity can be avoided directly without using any filters or piecewise continuous functions, such that the stability analysis becomes more concise and straightforward. Simulations are conducted to show the effectiveness of the presented method.
23 citations
TL;DR: In this article , a fuzzy switching dynamic adaptive control technique is developed such that all signals of the tracking error equation are bounded, and the system state trajectory tracks the reference model state trajectory under a disturbance attenuation level as closely as possible.
Abstract: This article investigates the H∞ stochastic tracking control problem for uncertain fuzzy Markovian hybrid switching systems by using a fuzzy switching dynamic adaptive control approach. The long and the short is to construct multiple piecewise stochastic Lyapunov functions which provide an effective tool for designing hybrid switching law and fuzzy switching dynamic adaptive law. A hybrid switching law, including both stochastic switching and deterministic switching, is designed to represent more general switching scenarios, which can improve the H∞ adaptive tracking performance through offering a running time before stochastic switching for the adaptive control strategy to work well. A fuzzy switching dynamic adaptive control technique is developed such that all signals of the tracking error equation are bounded, and the system state trajectory tracks the reference model state trajectory under a disturbance attenuation level as closely as possible. Finally, an application study verifies the effectiveness of the acquired methods.
TL;DR: In this article , the authors investigated the problem of resilient secure control of cloud-aided 5-DOF active semivehicle suspension systems (SVSSs) subject to Denial of Service (DoS) attacks.
Abstract: This article investigates the problem of resilient secure control of cloud-aided 5-DOF active semivehicle suspension systems (SVSSs). A novel joint model considering both the event-triggered mechanism (ETM) and Denial of Service (DoS) attacks is established. Under such a model, during the active period of DoS attacks, periodic transmission attempt is made to ensure the control system can receive the control information at the earliest time; the ETM turns to be a conventional one when the DoS attack is in sleeping period. Meanwhile, the valid attack period is proposed to address the problem of the DoS attack ending within a sampling period, which is a challenging problem in modeling DoS attacks. Takagi–Sugeno (T–S) fuzzy model is used to characterize the uncertainties of sprung and unsprung mass of SVSSs. By converting the cloud-aided active SVSS into a fuzzy-based switched time-delay system, and using the method of piecewise Lyapunov function, sufficient conditions are derived to ensure the performances of active SVSSs subject to DoS attacks. Finally, the effectiveness of the proposed method is validated by a numerical example of active SVSSs subject to DoS attacks.
TL;DR: In this article , the authors constructed a piecewise continuous space using the reproducing kernel function (RKF) of smooth reproducing Kernel Hilbert space (RkHS) W3.
TL;DR: In this paper , a fixed-time consensus proposal by fuzzy adaptive method is proposed to solve the consensus tracking problem for multi-agent systems, and a back-stepping design procedure is presented to construct the fixed time fuzzy adaptive controller.
Abstract: This article discusses the consensus tracking issue for multiagent systems, and the purpose is to develop a fixed-time consensus proposal by fuzzy adaptive method. To this end, we first set up a more general fixed-time stability criterion. By using the proposed stability criterion, a backstepping design procedure is presented to construct the fixed-time fuzzy adaptive controller. The suggested fuzzy adaptive control protocol guarantees that 1) for each agent, its closed-loop signals keep bounded; 2) the consensus tracking error tends to a small region around origin in fixed time. In addition, the virtual control signals are constructed to be the piecewise functions to prevent the singularity of their derivatives. Curve fitting method is used such that the designed virtual control signals are derivable at the point of partition. Finally, numerical simulation further checks the validity of the suggested control strategy.
TL;DR: In this article , a kind of intermittently coupled spatiotemporal networks (ICSNs) is proposed, where the couplings among nodes are intermittent and the coupling strengths are related to both time and space.
Abstract: In biology networks, social networks, mobile robots, and many real networks, spatial factors are crucial to the evolution of networks and individual interactions are not always continuous. In this article, a kind of intermittently coupled spatiotemporal networks (ICSNs) is proposed, where the couplings among nodes are intermittent and the coupling strengths are related to both time and space. By constructing piecewise auxiliary functions and developing a direct error method, a distributed intermittent adaptive protocol and its pinning form are designed to determine the space-time dependent weights of edges to realize synchronization of ICSNs. Lastly, the theoretical analysis is supported by means of a numerical example.
TL;DR: In this paper , the authors proposed a mathematical model for the transmission dynamics of SARS-CoV-2 in a homogeneously mixing non constant population, and generalize it to a model where the parameters are given by piecewise constant functions.
TL;DR: In this article, a new physics-informed meta-learning framework for tool wear prediction under varying wear rates is presented, which employs the empirical equations' parameters to improve the interpretability of the modeling and optimization of the data-driven models.
TL;DR: In this article , a new physics-informed meta-learning framework for tool wear prediction under varying wear rates is presented, which employs the empirical equations' parameters to improve the interpretability of the modeling and optimization of the data-driven models.
TL;DR: In this paper , a novel iteration scheme based on the multigrid idea and homotopy method was developed for solving the numerical identification of the piecewise constant permeability function for a nonlinear diffusion equation within the two-phase porous media flow.
TL;DR: In this article , the Cauchy type dynamical system under piecewise equations with fractional order Caputo derivative is studied and the required results for the existence and uniqueness are developed.
Abstract: This research work is related to study the Cauchy type dynamical system under piecewise equations with fractional order Caputo derivative. Using traditional fixed point tools due to Banach and Schauder, the required results for the existence and uniqueness are developed. Since stability analysis is an important aspect of the aforesaid analysis, so we also attempt on Hyers-Ulam (HU) type stability results for the proposed system. For this purposes, we use tools of nonlinear functional analysis. Further a numerical method based on Newton polynomials of interpolation is applied to compute approximate solution for the considered system. For application and validity purpose of our main results, we give two illustrative examples.
TL;DR: In this paper , the existence of a unique solution with the aid of the fixed point theorem is guaranteed with an especial focus on higher-order systems and discretized piecewise polynomial collocation methods are used for approximating the exact solution.
Abstract: Terminal value problems for systems of fractional differential equations are studied with an especial focus on higher-order systems. Discretized piecewise polynomial collocation methods are used for approximating the exact solution. This leads to solving a system of nonlinear equations. For solving such a system an iterative method with a required tolerance is introduced and analyzed. The existence of a unique solution is guaranteed with the aid of the fixed point theorem. Order of convergence for the given numerical method is obtained. Numerical experiments are given to support theoretical results.
TL;DR: In this article , a switched observer-based event-triggered adaptive fuzzy funnel control approach is proposed by exploiting the average dwell time method and backstepping to estimate unmeasurable system states, a switched fuzzy observer and switched update laws for individual subsystems are designed.
Abstract: This article addresses the event-triggered output-feedback funnel tracking control problem for a class of switched nonlinear systems. A novel switched-observer-based event-triggered adaptive fuzzy funnel control approach for solving the problem is proposed by exploiting the average dwell time method and backstepping. To estimate unmeasurable system states, a switched fuzzy observer and switched update laws for individual subsystems are designed. Compared with the existing funnel controllers designed in the framework of continuous-time feedback control, the proposed approach constructs event-triggered funnel controllers of subsystems and a switching event-triggered mechanism (ETM), which greatly alleviates the unnecessary waste of communication and computation resources, and, without any known limitation on maximum asynchronous time, handles the issue of asynchronous switching between the candidate controllers of subsystems and subsystems. Also, a strictly positive lower bound on interevent time is ensured by introducing a piecewise constant variable into the ETM, which overcomes the difficulty of switched measurement error being discontinuous. It is guaranteed that the tracking error evolves within a prespecified performance funnel. Finally, two examples including a mass-spring-damper system are presented for illustrating the validity of the developed approach.
TL;DR: It is proved that the proposed schemes, which combine a linearly stabilized splitting scheme, are unconditionally energy-stable and satisfy the mass conservation.
TL;DR: In this paper , a piecewise linear oscillator with a play was used to investigate the dynamics of a non-smooth system, and the Incremental Harmonic Balance Method and the method of Harmonic balance with alternating frequency and time were used to compute the period one orbits, including those exhibiting grazing and large impacts.
TL;DR: In this paper , a quantized control capable of appointed-time performances for quadrotor attitude tracking is investigated, where a continuous and piecewise behavior boundary is devised using error transformation to enforce attitude convergence to preassigned transient and steady zones in an appointed time.
Abstract: In this article, a quantized control capable of appointed-time performances for quadrotor attitude tracking is investigated. A continuous and piecewise behavior boundary, rather than an exponential decaying function employed in traditional prescribed performance control, is devised using error transformation to enforce attitude convergence to preassigned transient and steady zones in an appointed time. To circumvent the inertia moment uncertainties and external perturbations, an extended state observer with only one parameter to be tuned is introduced to precisely estimate the total disturbances acting on the angular rate subsystem. Additionally, a hysteretic quantizer capable of converting continuous control behaviors to finite discrete scalars is established in a controller to actuator channel to reduce the transmission burden and amount of sampling data. With a novel quantization decomposition, an attitude quantized controller is integrated in terms of guaranteed tracking. The prominent feature is that a prescribed appointed-time attitude response can be preserved with a decreased demand of communication bandwidth, despite uncertainties. Theoretical analysis shows that all error signals are ultimately uniformly bounded. Eventually, the superiority of explored control strategy is demonstrated through experimental results.
TL;DR: In this article , the effectiveness of vaccination in the current outbreak of COVID-19 by modeling a three-compartments model is investigated, which includes susceptible, infected, and vaccinated classes.
Abstract: This manuscript is devoted to investigating the effectiveness of vaccination in the current outbreak of COVID-19 by modeling a three-compartments model. The proposed model includes susceptible, infected, and vaccinated classes (we abbreviate as SIV). In this regard, some graphical presentations are provided under the said noise terms. Furthermore, the model is treated under piecewise equations of nonsingular kernel-type derivative of ABC. We derive some fundamental results about the feasibility and positivity of the solution in the sense of nonsingular-type derivative by using Laplace transform. Also, we compute the strengthen number by the matrix method. Moreover, we simulate the model by using a powerful numerical algorithm by taking some real data for initial values of vaccinated and infected classes. We investigate the proposed model under stochastic noise by using stochastic differential equations (SDEs). [ FROM AUTHOR]
TL;DR: Considering the strain-dependant characteristic of coatings, a unified nonlinear modelling approach is presented for investigating the nonlinear vibration characteristics of a coupling hard-coated ring disc-cylindric shell structure as discussed by the authors .
TL;DR: In this paper , the leader-following consensus issue for continuous-time multiagent systems with semi-Markov jump parameters is systematically addressed, where a hybrid event-triggered strategy associated with an improved threshold function is employed for economizing the network bandwidth resources.
Abstract: This article aims to systematically address the leader-following consensus issue for continuous-time multiagent systems with semi-Markov jump parameters. A more universal random process, semi-Markov process, is utilized to model the variations of parameters which may result from the complexity of environment. The innovative hybrid event-triggered strategy associated with an improved threshold function is employed for economizing the network bandwidth resources. It presents an exponential decay term in the threshold function for decreasing the transmission frequency of superfluous data packets, ulteriorly reducing triggering times. The dominating core concentrates on the design of a controller interrelated with the hybrid event-triggered condition, which can be implemented to ensure the leader-following consensus of the considered systems. On the strength of time-dependent and piecewise Lyapunov–Krasovskii functional, several criteria, which are capable of ensuring the leader-following consensus of the multiagent systems, are derived. Ultimately, two suitable numerical examples and a meaningful practical one are utilized to demonstrate the validity and potential of the derived results.
TL;DR: Considering the strain-dependent characteristic of coatings, a unified nonlinear modeling approach is presented for investigating the nonlinear vibration characteristics of a coupling hard-coated ring disc-cylindric shell structure.
TL;DR: In this paper , a discrete-time asynchronous integral sliding surface is constructed, which yields matched-nonlinearity-free slidingmode dynamics (SMDs), and a sufficient condition is established for ensuring the stochastic stability of SMD with extended dissipation.
Abstract: This article analyzes the problem of the sliding-mode control (SMC) design for discrete-time piecewise nonhomogeneous Markov jump nonlinear systems (MJNSs) subject to an external disturbance with time-varying transition probabilities (TPs). A discrete-time asynchronous integral sliding surface is constructed, which yields matched-nonlinearity-free sliding-mode dynamics (SMDs). Then, by using the mode-dependent Lyapunov function technique, a sufficient condition is established for ensuring the stochastic stability of SMD with extended dissipation. The solution to designing controller gains is obtained. Moreover, an SMC law and an adaptive law are, respectively, derived for driving the system trajectories to move into a predetermined sliding-mode region with specified precision. Finally, the feasibility and effectiveness of the new design are verified and demonstrated by a simulation example.