Sliding Motion Phase Research Articles

Sliding mode-based finite-time consensus tracking control for multi-agent systems under actuator attacks

Since it is inevitable for multi-agent systems (MASs) to encounter external malicious attack in the complex network environment, this paper studies the finite-time consensus tracking (FTCT) problem of MASs with unknown follower's states via sliding mode control (SMC) in the presence of actuator attacks. First, the states of each follower can be approximated by the designed appropriate observers. Then, the FTCT problem of MASs in two stages (i.e., reaching phase and sliding motion phase) of sliding mode dynamic is discussed by introducing partitioning strategy. Besides, the lower bound for the reaching phase is analyzed to ensure the feasibility of the designed SMC. The optimization problem is then formulated and is efficiently solved by the genetic algorithm (GA). Note that the attacks considered in this paper are false data injection attacks (FDIAs). Finally, simulation results are presented to illustrate the effectiveness and applicability of the proposed control method.

Finite-Time sliding mode control for singularly perturbed PDE systems

This article proposes a sliding mode control strategy for hyperbolic PDE systems under the requirement of finite-time boundedness. First, the singular perturbation theory is introduced to model multi-time scales phenomena, and a quantized measurement method is employed to save the communication resources in network. In addition, by considering the effect of the singular perturbation phenomenon in PDE systems, a sliding surface dependent on spatial position and singular perturbation parameter is constructed, then a sliding mode control law is developed to drive state trajectories to the designed sliding surface in finite time. Moreover, a partitioning strategy is introduced to ensure that the system is finite-time bounded in the reaching phase and the sliding motion phase, respectively. Finally, some sufficient conditions are given to ensure that the system is finite-time bounded in both reaching phase and sliding motion phase, and a simulation example of the chemical tubular reactor demonstrates the effectiveness of the proposed method.

Finite-time stochastic boundedness for Markovian jumping systems via the sliding mode control

The finite-time stochastic boundedness (FTSB) via the sliding mode control (SMC) approach is analyzed for Markovian jumping systems (MJSs) with time-delays. First, an integral switching surface is constructed. And to make sure the reachability of the sliding mode surface in a finite-time, an SMC law is designed. In addition, the delay-dependent criteria for FTSB are obtained over the reaching phase and the sliding motion phase. Furthermore, in line with linear matrix inequalities (LMIs), sufficient conditions are provided to guarantee the FTSB of systems over the whole finite-time interval. Lastly, an example is given to indicate the validity of the proposed approach.

Input–Output Finite-Time Sliding-Mode Control for T–S Fuzzy Systems With Application

This article addresses the issue of input-output finite-time stability (IO-FTS) for nonlinear systems by employing sliding-mode control (SMC) methodology. Many practical systems subject to complex factors, such as the single-link robot arm model (SLRAM), can be characterized as nonlinear systems. Our attention is focused on designing a fuzzy-model-based finite-time SMC law to attenuate the influences of uncertainty, nonlinear term, and external disturbance during the finite-time region. First, a novel integral sliding-mode surface is proposed based on the Takagi-Sugeno fuzzy rule. Then, by using the key point of Lyapunov function theory, an appropriate fuzzy SMC law is designed to make sure that the signal variables can arrive at a domain within the assigned fixed-time level. Moreover, some new IO-FTS criteria are constructed for the resulting sliding dynamics over the whole finite-time level, including reaching phase and sliding motion phase. Via the SLRAM, we demonstrate the effectiveness of the proposed SMC approach.

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.

Finite-Time Fuzzy Sliding Mode Control for Nonlinear Descriptor Systems

This article addresses the finite-time boundedness (FTB) problem for nonlinear descriptor systems. Firstly, the nonlinear descriptor system is represented by the Takagi-Sugeno (T-S) model, where fuzzy representation is assumed to be appearing not only in both the state and input matrices but also in the derivative matrix. By using a descriptor redundancy approach, the fuzzy representation in the derivative matrix is reformulated into a linear one. Then, we introduce a fuzzy sliding mode control (FSMC) law, which ensures the finite-time boundedness (FTB) of closed-loop fuzzy control systems over the reaching phase and sliding motion phase. Moreover, by further employing the descriptor redundancy representation, the sufficient condition for designing FSMC law, which ensures the FTB of the closed-loop control systems over the entire finite-time interval, is derived in terms of linear matrix inequalities (LMIs). Finally, a simulation study with control of a photovoltaic (PV) nonlinear system is given to show the effectiveness of the proposed method.

Sliding Mode Control for Markov Jump Systems With Delays via Asynchronous Approach

In this paper, the problem of sliding mode control (SMC) is considered for a class of nonlinear continuous-time Markov jump systems (MJSs) with uncertainties and time delay. A novel integral-type switching sliding surface function is designed, where the controller gain may jump asynchronously with original MJSs. Then, an SMC law is constructed to force system trajectories onto the specified switching sliding surface in a finite time. The stochastic stability and dissipative performance of sliding mode dynamics are analyzed and the delay-dependent sufficient condition for the existence of the desired switching surface is developed. Moreover, we also extend SMC to investigate the finite-time stability problem during both reaching phase and sliding motion phase in the stochastic setting. Finally, simulation results are given to illustrate the effectiveness of the proposed design techniques.

Robust finite-time sliding mode control for discrete-time singular system with time-varying delays

This paper explores the finite-time bounded issue for discrete-time singular time-varying delay system via sliding mode control method. A suitable discrete-time sliding mode control law is constructed to drive the state trajectories onto the specified sliding surface in a given finite time interval. Meanwhile, sufficient conditions for finite-time bounded to the closed-loop delayed system are provided in both reaching phase and sliding motion phase. In addition, the finite-time sliding mode controller gain matrix can be solved by using the linear matrix inequalities approach. Finally, three numerical examples are illustrated to demonstrate the superiority and practicability of presented results.

Non-fragile [formula omitted] SMC for Markovian jump systems in a finite-time

This paper mainly discusses H∞ finite-time realization for a class of uncertain Markovian jump systems (MJSs) with unmeasurable state via sliding mode control (SMC) method. A key question is how to design an appropriate SMC approach in a finite-time to reduce the effects of model switching and external interference on the overall performance of the system under consideration. First, by designing an appropriate finite-time SMC law based on a non-fragile observer, the state trajectory can reach a specified sliding surface (SSS) within given finite-time interval. Then, by means of time-partitioning strategy, finite-time boundedness (FTBs) criteria including the reaching phase and the sliding motion phase are proposed for uncertain MJSs with H∞ performance. Second, by solving the corresponding linear matrix inequalities (LMIs), the controller gain and the observer gain are obtained. Finally, a single-link robot arm model (S-LRAM) is given to prove the effectiveness of the proposed method.

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.

Finite-time boundedness of uncertain Hamiltonian systems via sliding mode control approach

This paper seeks to address the problem of finite-time stabilization for a class of uncertain Hamiltonian systems via sliding mode control approach. A novel sliding function in connection with the state and energy function of the considered system is constructed, and then, a suitable controller is designed to drive the state trajectories onto the specified sliding surface before the given finite-time. Moreover, the finite-time boundedness of the closed-loop system over both reaching phase and sliding motion phase are analyzed and the corresponding conditions are obtained. Furthermore, two optimization problems are formed to enhance the performance of finite-time boundedness, which will be solved via genetic optimization algorithm. Finally, a simulation example is provided to illustrate the proposed control strategy.

Robust Observer-Based Finite Time Sliding Mode Control for One-Sided Lipschitz Systems With Uncertainties

Abstract This paper investigates the problem of observer-based finite time sliding mode control (SMC) for a class of one-sided Lipschitz (OSL) systems with uncertainties. The parameter uncertainties are assumed to be time-varying norm-bounded appearing not only in both the state and output matrices but also in the nonlinear function. For a time interval [0,T], we divide it into two parts: one part is the reaching phase within [0,T*] and another part is the sliding motion phase within [T*,T]. First, the reachability of the sliding mode surface with T*≤T is proved. Next, several conditions are proposed which ensure robust finite time boundedness (FTB) of the corresponding closed-loop systems in the interval [0,T*] and [T*,T], respectively. Then, the sufficient conditions, which guarantee robust finite time boundedness of the closed-loop system in whole time interval [0,T], are given in terms of linear matrix inequalities (LMIs), and further the robust observer and controller can be designed in an LMI frame. A convex optimization problem subject to LMIs is formulated to optimize the desired performance indices of interest to us. Finally, a practical example is given to demonstrate the effectiveness of the proposed methods.

Finite-time stochastic boundedness of Markovian jump systems: A sliding-mode-based hybrid design method

This work investigates the problem of finite-time stochastic boundedness for a class of Markovian jump systems by synthesizing the sliding mode control and the transition rate matrix. First, a sufficient condition on the transition rate matrix is derived to guarantee the finite-time stochastic boundedness of the unforced Markovian jump systems. Moreover, a hybrid design scheme integrating the transition rate matrix with the sliding mode controller is synthesized such that the closed-loop systems are ensured to be finite-time stochastically bounded over both reaching phase and sliding motion phase. Finally, two examples are exploited to illustrate the proposed method.

Finite-time Boundedness of T-S Fuzzy Systems Subject to Injection Attacks: A Sliding Mode Control Method

This paper studies the sliding mode control for T-S fuzzy systems in the framework of finite-time boundedness. It is assumed that the control signals are transmitted via vulnerable channels, where injection attacks might happen. A fuzzy sliding mode controller is firstly synthesized to guarantee the finite-time reachability of the prescribed sliding surface and attenuate the effect of the injection attacks. By introducing a partitioning strategy, the finite-time boundedness over both the reaching phase and the sliding motion phase are analyzed. Furthermore, sufficient criteria are derived such that the closed-loop system is finite-time bounded over the whole specified finite-time interval despite of the injection attacks. An optimal algorithm is further provided for searching ideal control gains with fewer energy demands. Finally, a simulation example verifies the proposed sliding mode control approach.

Finite-Time Observer-Based Sliding Mode Control for Quantized Semi-Markov Switching Systems With Application

This article investigates the problem of sliding mode control (SMC) for semi-Markov switching systems (S-MSSs) with quantized measurement in finite-time level. The transition between different subsystems obeys a stochastic semi-Markov process related to nonexponential distribution. Additionally, due to the sensor information constraints, the state vectors are not always measurable in practice. Moreover, compared with existing results in literature, the output quantization is first considered for finite-time SMC problem via a logarithmic quantizer. Our attention is to design an appropriate finite-time SMC law to attenuate the influences of parametrical uncertainty and external disturbance onto the overall performance of the system under consideration. First, by the key points of stochastic semi-Markov Lyapunov function and observer design theory, a desired SMC law is constructed to guarantee that the system trajectories can arrive at the specified sliding surface (SSS) within an assigned finite-time level. Then, ST-dependent sufficient conditions are established to ensure the required finite-time boundedness performance including both reaching phase and sliding motion phase. Finally, the applicability of the proposed results is demonstrated by a single-link robot arm model.

Finite-time asynchronous sliding mode control for Markovian jump systems

In this research article, the finite-time asynchronous sliding mode control (SMC) scheme for Markovian jump systems (MJSs) subject to sensor and actuator faulty signals, is investigated based on the average dwell time approach. Firstly, an asynchronous stochastic hybrid model is proposed in the light of the existing non-synchronization phenomenon of unmeasurable state and indirect access to jump information of original systems. The average dwell time technique, which has the ability to compensate the effects of arbitrary switching by generating a sequence of signals to regulate/choose an appropriate feedback Markov switching signal among the Markov chains, is developed during the reaching phase and sliding motion phase of the sliding mode dynamics. Secondly, based on the asynchronous stochastic hybrid model, a mode-dependent sliding mode surface function is designed. Moreover, the SMC law is synthesized such that the system state trajectories can be driven onto the specified sliding surface in a prescribed limited time. Thirdly, the finite-time analysis method combining with a mode-dependent Lyapunov function, which can reduce drastically the design conservatism, is adopted to guarantee the finite-time boundedness of the sliding mode dynamics both in the reaching phase and sliding motion phase. Fourthly, sufficient conditions are interpreted for the solutions of asynchronous controller gain matrices and an algorithm is provided to assist computing the SMC gain as an auxiliary tool. Finally, a numerical example is given to illustrate the effectiveness of the proposed new design techniques.

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.

Takagi–Sugeno Model-Based Sliding Mode Observer Design for Finite-Time Synthesis of Semi-Markovian Jump Systems

This paper is concerned with finite-time sliding mode control (SMC) of continuous-time semi-Markovian jump systems with immeasurable premise variables via fuzzy approach. First, an integral sliding surface is constructed based on fuzzy observer. Second, an observer-based SMC law is synthesized to guarantee finite-time reachability of the predefined sliding surface before the prescribed time. Third, through finite-time boundedness analysis, the required boundedness performance is conducted at the reaching phase first and then the sliding motion phase, respectively. Furthermore, sufficient conditions in terms of linear matrix inequalities (LMIs) are established to guarantee the required boundedness performance of the overall closed-loop controlled system during the two phases with generally uncertain transition rates (TRs) simultaneously. Finally, a practical example is given to show the validity of the established method numerically.

Finite-time sliding mode control of switched systems with one-sided Lipschitz nonlinearity

This work investigates the problem of input–output finite-time stability (IO-FTS) for one-sided Lipschitz switched systems by sliding mode control (SMC) approach. A key issue is how to ensure the IO-FTS of the switched systems during the whole finite-time interval under the unknown one-sided Lipschitz nonlinearity. To this end, a sliding mode law is constructed to ensure the state trajectories can be driven onto the sliding surface during the assigned finite time interval. By means of partitioning strategy and the multiple Lyapunov function (MLF) approach, the corresponding IO-FTS over reaching phase and sliding motion phase are guaranteed, respectively. And then, some sufficient conditions are derived by utilizing the one-sided Lipschitz and quadratically inner-bounded conditions. Finally, an illustrative example is given to illustrate the proposed method.

Input–output finite-time stabilisation of Markovian jump systems with incomplete transition rates: a sliding mode method

ABSTRACTIn this paper, the input–output finite-time stabilisation (IO-FTS) problem for a class of Markovian jump systems is investigated, in which some elements in the transition rate matrix are partially known and an explicit output constraint condition is required, i.e. the system output (weighted) norm does not exceed an assigned threshold β. An extended definition of IO-FTS is firstly given to reduce the conservativeness arising from zero initial condition . A parameter-dependent sliding mode control strategy is proposed to eliminate the effect of partially known transition rates such that state trajectories are driven to the specified sliding surface during a given finite (possibly short) time interval. Besides, the sufficient conditions are derived to ensure the IO-FTS of the closed-loop systems over the finite-time interval including the reaching phase and the sliding motion phase. Finally, a simulation example illustrates the validity of the proposed method.