Finite-time Boundedness Research Articles

Finite‐Time Boundedness of Conformable Faulty Fuzzy Systems With Time Delay

This article investigates the finite‐time (FT) boundedness problem for the time delay (TD) Takagi–Sugeno fuzzy model (TSFM) with conformable derivative (CD) and in the presence of certain actuator faults. Through the reconstruction of an appropriate Lyapunov–Krasovskii functional, some sufficient conditions expressed by the linear matrix inequalities (LMIs) are given to ensure the FT boundedness of the proposed model not only during regular operation but also when encountering certain actuator faults. Finally, a numerical example and an inverted pendulum system are presented to illustrate our theoretical results.

Finite-time passivity of neutral-type complex-valued neural networks with time-varying delays.

In this work, we investigated the finite-time passivity problem of neutral-type complex-valued neural networks with time-varying delays. On the basis of the Lyapunov functional, Wirtinger-type inequality technique, and linear matrix inequalities (LMIs) approach, new sufficient conditions were derived to ensure the finite-time boundedness (FTB) and finite-time passivity (FTP) of the concerned network model. At last, two numerical examples with simulations were presented to demonstrate the validity of our criteria.

Dynamic dissipative control for fuzzy distributed parameter cyber physical system under input quantization and DoS attack.

This article explores the dissipative control for a class of nonlinear DP-CPS (distributed parameter cyber physical system) within a finite-time interval. By utilizing a Takagi-Sugeno (T-S) fuzzy model to represent the system's nonlinear aspects, the studied system is formulated as a class of fuzzy parabolic partial differential equation (PDE). In order to optimize network resources, both the system state and input signal are subjected to quantization using dynamic quantizers. Subsequently, a dynamic state control strategy is proposed, taking into account potential DoS attack. The finite-time boundedness of the fuzzy parabolic PDE is analyzed, with respect to the influence of quantization, through the construction of an appropriate Lyapunov functional. The article then presents the conditions for finite-time dissipative control design, alongside the adjustment parameters for the dynamic quantizers within the fuzzy closed-loop system. Furthermore, the decoupling of interlinked nonlinear terms in the control design conditions is achieved by using an arbitrary matrix. Finally, an example is provided and the simulation results indicate the effectiveness of the dissipative control method proposed.

Finite-Time Boundedness of Switched Time-Varying Delay Systems With Actuator Saturation: Applications in Water Pollution Control

Finite-Time Boundedness of Switched Time-Varying Delay Systems With Actuator Saturation: Applications in Water Pollution Control

Proportional-Integral Observer-Based State Estimation for Markov Memristive Neural Networks With Sensor Saturations.

This article investigates the resilient proportional-integral observer (PIO) problem for Markov switching memristive neural networks (MSMNNs) with randomly occurring sensor saturation within a finite-time interval. The Markov switching of memristive neural networks is regulated by a higher level deterministic switching signal, whose transition probabilities are piecewise time-varying and can be depicted by the average dwell-time strategy. Meanwhile, a Bernoulli stochastic process associated with an uncertain packet arriving rate is adopted to describe the randomly occurring sensor saturation. The aim is to design a resilient PIO such that the augmented dynamic has the property of stochastic finite-time boundedness while meeting the desired performance index. By applying the Lyapunov method and the average dwell-time scheme, sufficient criteria are established for MSMNNs, and a unified design method is presented for the existence of the PIO. Lastly, the attained theoretical results are validated via a numerical simulation.

Flexible Robust Control Strategy for Synchronization of Uncertain Non-Linear Systems with Control Input Non-Linearity

A robust global fuzzy sliding mode controller is designed in this paper for the synchronization of non-linear systems with control input non-linearities (CIN) and uncertainties. A consistent global fuzzy sliding mode control (GFSMC) law is developed, which guarantees the suppression of the reaching phase and the presence of the sliding phase from the initial time. Chattering phenomenon, which is characteristic of customary sliding mode control (SMC), avoided by the on-line fuzzy regulation of the sliding surface in the controller, when the system is subject to disturbances and CIN. Finite-time boundedness (FTB) properties are designed with adequate conditions, which are entrenched in terms of linear matrix inequalities (LMIs) with the help of cost and Lyapunov functions. Numerical simulations for the synchronization problem of the chaotic modified Colpitt’s system and Duffing system clearly show the good performance of the proposed control scheme. The present work provides a regular procedure to design GFSMC for a class of non-linear systems with CIN.

Active Thermal Control of IGBT Modules Based on Finite-Time Boundedness.

One of the most important causes of the failure of power electronic modules is thermal stress. Proper thermal management plays an important role in more reliable and cost-effective energy conversion. In this paper, we present an advanced active thermal control (ATC) strategy to reduce a power device's thermal stress amplitude during operation, with the aim of improving the reliability and lifetime of the conversion system. A state-space model based on a Foster-type thermal model is developed to achieve junction temperature estimation in real time. A feedback controller based on finite-time boundedness (FTB) is proposed to precisely regulate the temperature in order to reduce the thermal stress according to the temperature profile. The designed controller permits the precise control of the temperature and strongly reduces the thermal stress during fast transients in the power demand. Simulation and experimental results are provided to validate the effectiveness of the proposed method.

Finite-Time Control of Markov Jump Lur'e Systems With Singular Perturbations

This paper investigates the asynchronous controller design issue for Markov jump Lur'e systems with singular perturbations within a fixed time interval. For broader practical applications, the variation of system modes is regulated by a switched nonhomogeneous Markov process that corresponded to both lower-level nonhomogeneous stochastic jumping and higher-level deterministic switching. By resorting to the hidden nonhomogeneous-Markov model, an asynchronous control law that relies on the detected mode information is proposed. In light of the mode-dependent average dwell time strategy and mode-dependent stochastic system theory, the singularly perturbed parameter-independent conditions are attained to ensure the stochastic finite-time boundedness of the resulting systems. With respect to a linear matrix inequality optimization problem, a solution to the maximum singular perturbation parameter is obtained. Finally, the feasibility and applicability of the devised theoretical results are verified by simulation examples.

Finite-time L 1-gain output tracking control for positive linear systems

The problem of L 1 output tracking control of positive linear systems in finite time is addressed in this paper. By constructing a linear copositive Lyapunov–Krasovskii functional, some sufficient conditions are achieved to ensure that the states are finite-time bounded and the measurement outputs have L 1 − gain performance for given systems, respectively. Next, a state feedback controller is designed to ensure that the output signals of the tracking system can effectively trace the specified signals of reference model with finite-time boundedness and L 1 -gain performance. Finally, an example is given to illustrate the efficiency of the proposed method.

The finite-time boundedness and control analysis of switched nonlinear time-varying delay systems based on auxiliary matrices

This paper explores the finite-time boundedness and controller problem of switching nonlinear delay systems. The time delay is considered as time-varying delay rather than constant delay. First of all, an appropriate Lyapunov–Krasovskii functional (LKF) which contains three integral terms is selected. The upper and lower bounds of these integral terms are given by segmenting the time delay interval. Meanwhile, the auxiliary matrix method is used to separate the Lyapunov matrix from the system matrix. Moreover, a new state-dependent switching law is designed to switch between subsystems according to the change of the magnitude of the LKF. Based on the above methods, the first step is to research the finite-time bounded analysis of delayed system without control input. Then, a sufficient condition is obtained to ensure the finite-time boundedness of switched systems with control input. Further, by designing an observer-based H∞ controller, the closed-loop system with time-varying delay is bounded and has H∞ performance index ν by using the Finsler’s Lemma and Singular Value Decomposition (SVD). Simultaneously, the controller and observer gains are designed. Finally, two simulations are used to verify the effectiveness and feasibility of the proposed methods.

Design of proportional integral observer‐based resilient control for periodic piecewise time‐varying systems: The finite‐time case

AbstractThe prime intent of this study is to scrutinize the state estimation and finite‐time (FT) stabilization problems for a class of periodic piecewise time‐varying systems (PPTVSs) in the presence of external disturbances, immeasurable states and gain fluctuations by dint of resilient control. Moreover, the proportional integral observer system is built in line with the output of the PPTVSs to reconstruct the states of the PPTVSs, since the state dynamics of the system are often not measurable. Meanwhile, the output signals are quantized with the use of a logarithmic quantizer prior to being fed into the constructed observer systems. Further, the fluctuations in the controller and observer gain matrices are considered to occur in a random manner and they pursue the pattern of a Bernoulli distributed white sequence. Subsequently, by means of Lyapunov stability theory and the matrix polynomial lemma, the adequate requirements for ascertaining the FT boundedness and IO‐FT stabilization of the addressed system are procured in the context of linear matrix inequalities. Thereupon, on the premise of the established criteria, the gain matrices of the controller and observer are obtained. Ultimately, the simulation results have been showcased including the mass spring damper system to exemplify the efficacy and usefulness of the theoretical conclusions drawn.

Exponentially finite-time dissipative discrete state estimator for delayed competitive neural networks via semi-discretization approach

This article is concerned with the investigation of finite-time boundedness and exponential (Q,S,R)-dissipative performance for a class of discretized competitive neural networks (CNNs) with time-varying delays. Initially, by employing the semi-discretization technique, a discrete analog of the continuous-time CNNs is formulated, which preserves the dynamical behaviors of their continuous-time counterpart. An appropriate state estimator is developed for the discretized CNNs so that the dynamics of the associated estimation error system attain finite-time exponential (Q,S,R)-dissipative performance. Further, to obtain a tighter summation bound, two novel weighted summation inequalities are proposed, which linearize the quadratic summable terms occurring in the finite difference of the considered Lyapunov–Krasovskii functional. Finally, to refine our prediction, an illustrative example is provided that demonstrates the sustainability and merits of the proposed method.

Finite-time dissipative control for discrete-time memristive neural networks via interval matrix method

This paper addresses the problems of finite-time dissipative analysis and control for discrete-time memristive neural networks (DMNNs). With the help of interval matrix method (IMM), the challenges posed by the mismatched state-dependent parameters of DMNNs can be solved, which is different from the maximal absolute value operation-based method (MAVOM) in most existing literature. Based on a discrete-time Lyapunov-Krasovskii functional (LKF) and some inequality techniques, several sufficient conditions are established for achieving both finite-time bounded (FTB) behavior and finite-time (Q,S,R)−γ dissipative (FTD). Moreover, the control gains are obtained by solving a series of linear matrix inequalities (LMIs) and convex optimization problems. Finally, the validity of our main findings and the superiority of the control strategies are verified through numerical simulations.

Event-triggered finite-time [formula omitted] control of switched systems via composite anti-bump switching control input

This paper discusses the event-triggered composite anti-bump H∞ control problem for the networked switched systems in the finite-time stability sense. An event-triggered scheme (ETS) is constructed to reduce resource usage while maintaining desired control performance. Then, a novel switching bumpless control method based on ETS is given to resist the impact of bump transition between different modes. Sufficient criteria for finite-time boundedness of the closed-loop systems with bumpless transfer characteristics and H∞ performance are derived by resorting to a mode-dependent average dwell time (MADT), and a trigger-based bumpless transfer controller is designed. Finally, a simulation example is provided to demonstrate the efficacy and feasibility of the proposed control strategy.

Secure Filter Design of Fuzzy Switched CPSs With Mismatched Modes and Application: A Multidomain Event-Triggered Strategy

This article investigates the finite-time secure filter design of fuzzy switched cyber-physical systems equipped with a resource-constraint network that may undergo false data injection attacks (FDIAs). To strike a higher level balance between the resource consumption and filtering performance, a multidomain probabilistic event-triggered mechanism (MDPETM) is initially developed. And the mode mismatched phenomenon between the filter and the system is characterized through a delayed switching signal. Based on the MDPETM and a virtual delay partitioning approach, fuzzy mismatched secure filters are first devised whose modes could differ from the system. Then, filter-mode-dependent Lyapunov functionals are created to obtain new sufficient criteria such that the filtering error achieves finite-time boundedness with extended dissipativity subject to admissible FDIAs. The filter gains are obtained by solving a set of convex optimization problems. Finally, an application-oriented example is employed to test the effectiveness and advantages of the proposed results.

Finite‐time observer‐based fault detection with nonfragile control design for switched nonlinear networked systems with time‐delays

AbstractThe strategy of observer‐based nonfragile control and fault‐detection over finite‐time horizon has been examined for a class of uncertain switched nonlinear networked control systems (NNCSs) contingent with time varying delays inferred by the networks from sensor to controller and controller to actuator. Also, in this study, an observer‐based fault detection control has been designed for the NNCSs. By making use of fault detection control as residual generator, the conveyed fault detection problem is then transformed into attenuation problem. By employing multiple Lyapunov function and average dwell time (ADT) approach, sufficient conditions in terms of linear matrix inequalities (LMIs) ensures the finite‐time boundedness (FTB) criterion of the resulting switched NNCSs with a prescribed disturbance attenuation. Subsequently, the preferred LMIs constraints realizes the controller and observer gains. Finally, two numerical examples are proffered to showcase the efficacity of the proposed technique.

Finite‐time boundedness and control design of uncertain switched systems with time‐varying delay under new switching rules

AbstractIn this article, the finite‐time boundedness and control problem for time‐delay switched systems with uncertainties are studied. The delay is considered as time‐varying delay rather than constant delay, which is more suitable for practical engineering. First, the property of finite time boundedness for uncertain switched system without control input is researched by constructing a proper Lyapunov–Krasovskii functional (LKF) with three integral terms and the minimum LKF switching rules. Then, a state feedback controller with switching is designed. By utilizing Finsler's Lemma and singular value decomposition (SVD), sufficient conditions for finite‐time boundedness of time‐delay switched systems with control input and controller gain are presented. Additionally, a filter system is designed. The finite time boundedness and filter parameters of the closed‐loop error system are obtained by using the auxiliary matrix method. Finally, the feasibility of the proposed methods and the significance of switching rule are demonstrated through two numerical examples.

Finite-Time Fuzzy Boundary Control for 2-D Spatial Nonlinear Parabolic PDE Systems

Seldom existing studies directly focus on the control issues of two-dimensional (2-D) spatial PDE systems, although they have strong application backgrounds in production and life. Therefore, this article investigates the finite-time control problem of an 2-D spatial nonlinear parabolic PDE system via T–S fuzzy boundary control scheme. First, the overall fuzzy system model is constructed using T–S fuzzy rules to approximate the original nonlinear system. Second, based on the planar distributed measurement, boundary collocated measurement, and linear measurement methods, three novel kinds of fuzzy boundary controllers are designed. Then, by employing the variable substitution and integral inequality techniques, three criteria that ensure the finite-time boundness of the considered system are obtained. Finally, simulations of main results are provided to verify the effectiveness and practicability of the proposed measurement and control schemes.

Robust sliding mode passive control for uncertain markovian jump discrete systems with stochastic communication delays

This paper focuses on the robust sliding mode passive control (SMPC) problem for uncertain Markovian jump discrete systems under the finite time setting. For the considered model, the phenomenon of stochastic communication delays (SCDs) is depicted via some Bernoulli distributed stochastic variables, which involve inaccurate occurrence probability information. In view of initial condition, a common form of sliding surface is chosen. Further, the sliding motion equation can be given for the original system. Our aim of this paper is to propose some potential sufficient criteria for finite-time boundedness and passive requirement of the sliding motion. With the same objective, a comprehensive reaching condition is also utilized to construct the robust sliding mode passive controller such that the controlled system can be kept remain in a region of the sliding surface thereafter. Finally, an example is given to show the usefulness of our proposed scheme here.

Parameter-dependent functional observer-based finite-time adaptive memory ISMC for continuous LPV systems with unknown nonlinear functions

This paper investigates a parameter-dependent (PD) functional observer-based finite-time adaptive memory integral sliding mode controller (ISMC) scheme for continuous linear parameter varying (LPV) systems with unknown nonlinear functions. First, a novel functional observer including parameters and parameter rates is proposed, and the observer gains can be directly designed. Different from the previous studies, a memory ISMC scheme with a time-varying delay through the functional observer is used for the first time in LPV systems to improve the performance. Moreover, to fully adopt the model characteristics of LPV systems and the functional observer, an integral PD surface function that contains PD input matrices and a memory parameter is established simultaneously. And then, an adaptive compensator is deduced for eliminating the influence of unknown nonlinear functions, so that the designed memory ISMC can make closed-loop LPV systems stable within a preset finite time. Furthermore, stability criteria with less conservatism for the LPV systems are proposed by memory Lyapunov–Krasovskii functional with measurable parameters. These criteria can guarantee LPV systems are finite-time boundedness with performance (FTB-) on the sliding stage, arriving stage and entire finite-time region. Finally, a riderless bicycle is given to display the validity and superiority of the developed approach.