Suitable Sliding Mode Controller Research Articles

Stability and Finite-Time Synchronization Analysis for Recurrent Neural Networks with Improved Integral-Type Time-Varying Delays

This paper studies the stability criterion of integral time-varying recurrent neural networks (RNNs) with zero lower bound and finite-time synchronization based on improved sliding mode control (SMC). Firstly, a sufficient criterion for universal asymptotic stability of RNNs with integral time-varying delays is obtained by estimating a tight upper bound of augmented Lyapunov-Krasovskii functional (LKF) derivative with inequality scaling technique and mutually convex combined inequality. Secondly, in order to eliminate the time that error system state trajectory slides along sliding mode flow pattern until convergence at the origin, based on drive response and SMC theory, a suitable sliding mode controller is designed by considering that sliding mode flow pattern is equal to synchronization error. Finally, maximum allowable upper bound of delay under different delay derivatives are obtained by considering trajectory change of input function under different initial value. Synchronization trajectory of drive and response systems with mismatched parameters and activation functions under the influence of controller are studied, and synchronization time which is required for error system to reach stability is obtained. Simulation results show that the introduction of integral delay can be more comprehensive from both difference and area, so that drive system state is eventually steady at equilibrium point and synchronized with response system. Stability criterion of this paper not only has less conservative and computation complexity but also has shorter synchronization control time.

System Simulation Comparison of Sliding Mode and PID Controller for Buck Converter

In this paper, the performance of the closed loop sliding mode controller (SMC) is compared with the conventional PID controller for DC-DC buck converter. We specifically address the comparison of the two controllers from system simulations point of view by first developing the system model of the DC-to-DC buck converter circuit and designing a suitable SMC controller.Using MATLAB/SIMULINK system simulations, the performance of the SMC controlled buck converter is compared with the PID controller in terms of the overshoot, rise time and settling time of the load voltage and currents. The simulation results demonstrated the high performance of the SMC controlled buck converter in accurately tracking the reference voltage, eliminating the overshoot, improving the settling time but with slower rise time as compared with the PID controller. The transient time response of the SMC controller can be further improved by tuning the system control parameters to attain improved rise time. Such SMC based buck converter can be used for the design of a stable direct current power supply for DC loads such as DC motors used for water pumps or other applications.

Non-fragile [formula omitted] finite-time sliding mode control for stochastic Markovian jump systems with time delay

This article mainly discusses the realization of H∞ finite-time control for a class of uncertain stochastic time-delay systems with unmeasured states through sliding mode control (SMC). The purpose of this paper is to design a suitable SMC controller to suppress the influence of factors such as model switching and time delay on the system performance, so that the system state can be stabilized within a limited time interval. First, the state of the system is reconstructed through the H∞ state observer, and the SMC law based on the state observer is designed so that the state trajectory reaches the specified sliding surface (s.s.s) in a given finite time. Next, by introducing the concept of time-partitioning strategy, the finite-time boundedness (FTBs) of the reaching phase and the sliding motion phase are realized respectively. Then, according to the linear matrix inequality(LMI), the asymptotic stochastic stability of the system and sufficient conditions for sliding mode dynamics with a given interference attenuation level are derived. Finally, the numerical example and single-link robot arm model (S-lram) show the effectiveness of the method.

Parameter-dependent sliding mode control for Markovian jump systems within finite-time interval: handling randomly occurring actuator faults

In this article, the finite-time sliding mode control problem is studied for the Markovian jump systems. The uncertainties and actuator faults are randomly occurring and varying, which are simultaneously considered in the controlled systems. In order to characterise the stochastic phenomenon, two independent exponentials distributed random variables are introduced. To implement finite-time control performance, a suitable sliding mode controller is developed, which forces the trajectories of the system onto the specified sliding surface in a given finite-time (possibly short) interval. Besides, sufficient conditions are obtained to guarantee the stochastic finite-time boundedness within the entire finite-time interval, including the reaching and the sliding motion phases. Finally, simulation results demonstrate the feasibility of the proposed control strategy.

Sliding Mode Controller Design for Conic-Type Nonlinear Semi-Markovian Jumping Systems of Time-Delayed Chua’s Circuit

This paper is concerned with the sliding mode control (SMC) via finite-time stabilization (FTS) for a class of conic-type nonlinear semi-Markovian jumping systems (SMJSs). Comparing with the classical Markovian jumping systems, the transition rates of SMJSs are related to the random sojourn-time g. Based on this, a suitable SMC law for driving the state trajectories to the designed sliding surface within a finite-time interval is given. Then, the FTS over reaching phase and sliding motion phase is further proved to guarantee the FTS of the whole SMJSs. Finally, the effectiveness of the proposed method is demonstrated by a time-delayed Chua's circuit simulation.

Synchronization of time invariant uncertain delayed neural networks in finite time via improved sliding mode control

This paper explores the finite-time synchronization problem of delayed complex valued neural networks with time invariant uncertainty through improved integral sliding mode control. Firstly, the master-slave complex valued neural networks are transformed into two real valued neural networks through the method of separating the complex valued neural networks into real and imaginary parts. Also, the interval uncertainty terms of delayed complex valued neural networks are converted into the real uncertainty terms. Secondly, a new integral sliding mode surface is designed by employing the master-slave concept and the synchronization error of master-slave systems such that the error system can converge to zero in finite-time along the constructed integral sliding mode surface. Next, a suitable sliding mode control is designed by using Lyapunov stability theory such that state trajectories of the system can be driven onto the pre-set sliding mode surface in finite-time. Finally, a numerical example is presented to illustrate the effectiveness of the theoretical results.

New results on robust sliding mode control for linear time-delay systems

AbstractThis work focuses on the sliding mode control (SMC) for a family of linear systems with uncertainties and time-varying delays. First, an integral switching surface is constructed to verify the robust asymptotic stability of the considered system and the results are extended to analyse the mixed $\mathscr{H}_{\infty }\big /$Passivity performance index. Thereafter, a suitable SMC law is developed to force the system state onto the predefined switching surface in short time. By using Lyapunov stability theory, some novel results are obtained, and the required stability conditions are established in terms of linear matrix inequalities which can be solved by standard Matlab toolbox. Finally, the results are validated over a Chua’s circuit model, which describes the practical application of the developed results.

Adaptive Event-Triggered SMC for Stochastic Switching Systems With Semi-Markov Process and Application to Boost Converter Circuit Model

In this article, the sliding mode control (SMC) design is studied for a class of stochastic switching systems subject to semi-Markov process via an adaptive event-triggered mechanism. Network-induced communication constraints, semi-Markov switching parameters, and uncertain parameters are considered in a unified framework for the SMC design. Due to the constraint of measuring transducers, the system states always appear with unmeasurable characteristic. Compared with the traditional event-triggered mechanism, the adaptive event-triggered mechanism can effectively reduce the number of triggering than the static event-triggered mechanism. During the data transmission of network communication systems, network-induced delays are characterized from the event trigger to the zero-order holder. The aim of this work is to design an appropriate SMC law based on an adaptive event-triggered communication scheme such that the resulting closed-loop system could realize stochastic stability and reduce communication burden. By introducing the stochastic semi-Markov Lyapunov functional, sojourn-time-dependent sufficient conditions are established for stochastic stability. Then, a suitable SMC law is designed such that the system state can be driven onto the specified sliding surface in a finite-time region. Finally, the simulation study on boost converter circuit model (BCCM) illustrates the effectiveness of the theoretical findings.

Fixed-time sliding mode controller design for a class of nonlinear Markovian jumping systems

In this paper, a sliding mode control (SMC) strategy is applied to investigate the fixed-time stabilization (FTS) problems for nonlinear Markovian jumping systems (NMJSs) with nonlinear parts satisfying conic conditions. We aim to design a suitable SMC law to drive the system state trajectories onto the specified sliding mode surfaces (SMS) within a specified fixed-time interval. Then, by using the slack matrix approach, the sufficient conditions are derived to ensure the FTS of MJSs during the reaching phase. An appropriate Lyapunov-Krasovskii functional method is given to guarantee the FTS of the NMJSs during the slidinging motion phase. Finally, the FTS condition of the NMJSs in the whole fixed-time interval is given and proved. The effectiveness of the method is verified by a simulation result related to the Chua’s circuit.

Improved Sliding Mode Control for Finite-Time Synchronization of Nonidentical Delayed Recurrent Neural Networks.

This brief further explores the problem of finite-time synchronization of delayed recurrent neural networks with the mismatched parameters and neuron activation functions. An improved sliding mode control approach is presented for addressing the finite-time synchronization problem. First, by employing the drive-response concept and the synchronization error of drive-response systems, a novel integral sliding mode surface is constructed such that the synchronization error can converge to zero in finite time along the constructed integral sliding mode surface. Second, a suitable sliding mode controller is designed by relying on Lyapunov stability theory such that all system state trajectories can be driven onto the predefined sliding mode surface in finite time. Moreover, it is found that the presented control approach can be conveniently verified and does not need to solve any linear matrix inequality (LMI) to guarantee the finite-time synchronization of delayed recurrent neural networks. Finally, three numerical examples are exploited to demonstrate the effectiveness of the presented control approach.

Finite-Time Sliding-Mode Control of Markovian Jump Cyber-Physical Systems Against Randomly Occurring Injection Attacks

This paper addresses a finite-time sliding-mode control problem for a class of Markovian jump cyber-physical systems. It is assumed that the control input signals transmitted via a communication network are vulnerable to cyber-attacks, in which the adversaries may inject false data in a probabilistic way into the control signals. Meanwhile, there may exist randomly occurring uncertainties and peak-bounded external disturbances. A suitable sliding mode controller is designed such that state trajectories are driven onto the specified sliding surface during a given finite-time (possibly short) interval. By introducing a partitioning strategy, the stochastic finite-time boundedness over the reaching phase and the sliding motion phase is analyzed, respectively. A key feature is that a set of mode-dependent sufficiently small scalars are introduced into some coupled Lyapunov inequalities such that the feasible solutions are easily obtained for the stochastic finite-time boundedness of the closed-loop systems. Finally, the practical system about a single-link robot-arm model is given to illustrate the present method.

Finite-time Sliding Mode Control of Markovian Jump Systems Subject to Actuator Faults

This paper addresses the problem of finite-time boundedness (FTB) for a class of Markovian jump systems (MJSs) via sliding mode control (SMC) technique, in which there may happen actuator faults in all of control channels and mismatched external disturbance. By means of the available boundary information of actuator faults, a suitable sliding mode controller is designed such that state trajectories are driven to sliding surface before a specified finite (possibly short) time interval. Furthermore, a partitioning strategy is introduced to derive the sufficient conditions for ensuring the FTB of the closed-loop systems over the whole specified finite-time interval including the reaching phase and the sliding motion phase. Finally, a practical example are provided from an F-404 aircraft engine system to illustrate the proposed method.

Finite-time sliding mode control of Markovian jump systems subject to actuator nonlinearities and its application to wheeled mobile manipulator

This work is concerned with the finite-time sliding mode control for a class of Markovian jump systems subject to actuator nonlinearities, where the elements in the transition rate matrix are uncertain or even completely unknown. A suitable sliding mode controller is designed such that the finite-time stochastic boundedness of state trajectories is attained during a given finite-time interval, in which two different robust terms are introduced for the known and unknown modes to deal with the effect of uncertain transition rates. Moreover, the connections among sliding functions under Markovian jumping for SMC systems are analyzed. Finally, some simulation results with a wheeled mobile manipulator are provided.

Dynamics, circuit implementation and synchronization of a new three-dimensional fractional-order chaotic system

In this paper, a new three-dimensional autonomous fractional-order chaotic system is presented. There are four different nonlinear terms in the governed equations. By means of theoretical analysis and numerical simulation, some basic dynamical properties, such as phase diagrams, bifurcation diagram, Lyapunov exponents spectrum and chaos diagram of the new fractional-order chaotic system are investigated. Then, we completed the circuit design of the fractional-order chaotic system, and realized the analog hardware circuit. Both the hardware experiment results and circuit simulation results are agreed well with those of numerical simulation. Finally, based on the theory of sliding-mode control and the fractional stability theory, a suitable sliding mode controller is designed for the novel three-dimensional fractional-order chaotic system. Numerical simulations are provided to verify the effectiveness of the proposed synchronization scheme.

Finite-Time Stabilization via Sliding Mode Control

This technical note investigates the sliding mode control (SMC) design based on finite-time boundedness (FTB) for a class of nonlinear systems. A suitable SMC law is constructed to drive the state trajectories onto the specified sliding surface during a specified finite (possibly short ) time interval. Besides, by introducing a partitioning strategy , the corresponding FTB over reaching phase and sliding motion phase are guaranteed, respectively. And then, the sufficient conditions are derived to ensure the FTB of the closed-loop systems over the whole finite-time interval. Finally, a simulation example is given to show the effectiveness of the proposed design method.

Finite-time sliding mode control synthesis under explicit output constraint

This work deals with the input–output finite-time stabilization problem for a class of nonlinear systems by employing sliding mode control (SMC) approach. A suitable SMC law is designed to ensure that the state trajectories can be driven onto the specified sliding surface during the assigned finite-time interval. Moreover, some parameters-dependent sufficient conditions are derived such that the input–output finite-time stability (IO-FTS) during both reaching phase and sliding motion phase are attained. Simulation results are provided to illustrate the proposed approach.

Sliding mode control design for synchronization of fractional order chaotic systems and its application to a new cryptosystem

In this paper, the synchronization method of two identical fractional order chaotic systems is developed with lower order than the existing fractional order 3 by designing suitable sliding mode control. Further, a new cryptosystem is derived for an image encryption and decryption based on the synchronized lowest fractional order 2.01 chaotic systems. To validate the theoretical results, numerical simulations are presented for the proposed cryptosystem.