Stochastic Finite-time Boundedness Research Articles

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.

Finite-time asynchronous sliding mode control for Markov jump systems with actuator saturation

This paper deals with the finite-time asynchronous sliding mode control for Markov jump systems subject to actuator saturation. The hidden Markov model is adopted to describe the modal information exchange between the system and the designed controller. A sufficient condition is established by employing the Lyapunov stability theorem, which guarantees the stochastic finite-time boundedness of sliding mode. In order to mitigate the effects of actuator saturation and chattering, an adaptive sliding mode controller is designed based on the auxiliary saturation compensation system. Subsequently, the reachability of sliding mode motion is analysed. The controller gain matrix is obtained by solving the minimization problem. Finally, a simulation example is used to demonstrate that the proposed control method can effectively restrain the disturbance and compensate saturation.

Dwell-time-based energy scheduling and distributed control for large-scale nonlinear systems under Round-Robin protocol

In this paper, a distributed control problem is investigated for large-scale nonlinear systems under Round-Robin (RR) protocol and the energy constraint. The large-scale system is composed of several interconnected nonlinear subsystems that are equipped with independent sensors. RR protocol is adapted to coordinate the data transmission of each sensor from the viewpoint of fairness. Moreover, an energy scheduling scheme is employed in response to the energy constraint by distributing high energy or low energy to sensors. The transmissions (between sensors and controllers) with high energy can be accurate. Correspondingly, the accessed data may be lost with a certain probability when sensors use low energy. This paper aims to design the scheduling scheme and distributed controllers jointly such that the stochastic finite-time boundedness (FTB) can be guaranteed for large-scale nonlinear systems with limited energy and communication protocols over a finite horizon. In light of the energy allocations and the induced packet dropout, novel distributed controllers are established for large-scale systems. Furthermore, the explicit expressions of the controller for each subsystem and the energy scheduling scheme with average dwell time (ADT) are derived by using recursive design methods combined with stochastic analysis. Finally, two simulation examples are given to demonstrate the effectiveness of the designed scheme and controllers.

Finite-time decentralized event-triggering non-fragile control for fuzzy neural networks with cyber-attack and energy constraints

In this study, we concerned with non-fragile control problem for T-S fuzzy neural networks (TSFNNs) within finite-time domain under decentralized event-triggered scheme, limited network-bandwidth and cyber-attack. Precisely, the event-triggered mechanism and energy constraints are introduced to mitigate the network traffic and to protect the network resources. To be specific, an event-triggered mechanism relieves the network transmission burden and the sensors which decide the measurement transmissions in accordance with event-triggered scheme. The main intention of this work is to design a decentralized event-triggered scheme and non-fragile controller for ensuring the stochastic finite-time boundedness for the desired TSFNNs with optimal mixed H∞ and passivity performance index within the prescribed time interval. In accordance with Lyapunov–Krasovskii stability theory, an adequate condition in the frame of linear matrix inequalities is established to signify the stochastic stability of the resulting closed-loop TSFNNs. Moreover, the projected gain matrix is characterized by the obtained linear matrix inequalities. At long last, a numerical example is framed to substantiate the effectiveness and superiority of the proposed control strategy.

Event-based Finite-time Boundedness of Discrete-time Network Systems

This paper deals with the event-based finite-time H∞ control problem of discrete-time network control systems with norm bounded input disturbances and nonlinear stochastic functions. A network-induced delay stochastic model is first constructed by event-triggered approach. Utilizing stochastic analysis and event-triggered schemes, conditions on stochastic finite-time (FT) boundedness and stochastic H∞ FT boundedness are then derived for the network model. Subsequently, an event-based finite-time controller and an event-triggered matrix are co-designed to ensure that the stochastic model is stochastically FT bounded or stochastically H∞ FT bounded by utilizing matrix decomposition scheme. All derived criteria can be solved in terms of convex optimal method, and numerical examples demonstrate the validity of obtained results as well.

Finite-time H_{infty } bounded control of networked control systems with mixed delays and stochastic nonlinearities

In this study, we investigate the stochastic finite-time H_{infty } bounded control problem for a class of networked control systems (NCSs) subject to mixed delays, stochastic nonlinearities, and randomly missing measurement. The mixed delays consist of discrete time-varying and distributed delays. The stochastic nonlinearities satisfy statistical means. The missing measurement is modeled by a Bernoulli-distributed random variable. By applying stochastic analysis method we present sufficient conditions guaranteeing the stochastic finite-time boundedness of a closed-loop system with desired H_{infty } performance level within a finite time interval. Moreover, dynamic output feedback controller can be obtained in terms of a set of matrix inequalities, which can be easily solved by using the cone complementarity linearization method (CCLM). Finally, we provide two numerical examples to illustrate the validity of the proposed design technique.

A hidden mode observation approach to finite-time SOFC of Markovian switching systems with quantization

This paper investigates the finite-time static output feedback control of Markovian switching systems, where quantization effects are taken into consideration from plant to controller and controller to actuator, simultaneously. The resulting system is more general, where asynchronous control, quantization, actuator failure, and external disturbance are covered. Furthermore, a descriptor representation method is employed to eliminate both the coupling term and the quantization effects. Owing to a hidden mode observation approach, sufficient conditions are achieved to guarantee the finite-time stochastic boundedness of the resulting system, and the finite-time output feedback controller is designed. Finally, a vehicle’s throttle actuator is exploited to confirm the feasibility of the proposed method.

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.

Observer‐based finite‐time asynchronous control for a class of hidden Markov jumping systems with conic‐type non‐linearities

An observer-based finite-time asynchronous control law is designed for a class of hidden Markov jumping systems with non-linearities and external disturbances. The non-linearities satisfy the conic-type constraint condition that lies in a known hypersphere with an uncertain centre. The non-synchronisation phenomenon between the system modes and observer/controller modes is modelled by a hidden Markov model. By means of the proper stochastic Lyapunov–Krasovskii functional method, a sufficient condition is obtained to guarantee the stochastic finite-time boundedness of the corresponding argument error dynamic systems with a satisfied disturbance rejection level. Finally, the feasibility and validity of the main results is illustrated through a pratical example related to the DC motor.

Finite-time sliding mode control for networked singular Markovian jump systems with packet losses: A delay-fractioning scheme

The paper is concerned with the finite-time sliding mode control (SMC) problem for a class of discrete networked singular Markovian jump systems (SMJSs) subject to packet losses (PLs) via the delay-fractioning approach. A random variable obeying the Bernoulli distribution is used to depict the phenomenon of PLs, which is frequently encountered in the practical engineering especially during the networked transmission. A key issue to be discussed is how to guarantee both the singular stochastic finite-time boundedness (SSFTB) of the resultant sliding mode dynamic systems and the reachability of the pre-selected sliding surface. Accordingly, a sufficient condition is obtained to ensure the SSFTB of sliding motion based on delay-fractioning method and linear matrix inequality technique. Furthermore, a new SMC mechanism is proposed to compensate the influence induced by LPs and ensure the reachability condition of pre-selected sliding surface simultaneously. Finally, the effectiveness of the proposed SMC approach is tested by a simulation example.

Reliable non-fragile memory state feedback controller design for fuzzy Markov jump systems

This paper concentrates on solving the finite-time bounded control problem for a family of discrete-time Takagi–Sugeno fuzzy Markov jump systems with a memory state feedback controller. In the proposed controller design, the non-fragile control protocol is considered to overcome the effect of gain perturbations and a more practical actuator fault model is employed to tolerate the time-varying faults. With the aid of a mode-dependent Lyapunov–Krasovskii functional and the Abel lemma-based finite sum inequality, sufficient conditions ensuring the stochastic finite-time boundedness for the closed-loop system are derived in the framework of matrix inequalities. Under which, a desired extended passivity performance index is guaranteed for the system under consideration. The proposed memory state feedback controller gains are computed by solving the derived matrix inequalities. Further, the feasibility and virtue of obtained theoretical findings are illustrated through two practical models, namely, single link robot arm system and Hénon system.

Distributed finite‐time control for Markovian jump systems interconnected over undirected graphs with time‐varying delay

This study considers the problems of stochastic finite-time stability analysis and distributed finite-time control for Markovian jump systems interconnected over undirected graphs with time-varying delay. First, the concepts of the well-posedness, stochastic finite-time boundedness and contractiveness for the class of systems are introduced, and the control problem formulation is presented. Then, a sufficient condition on the well-posedness, stochastic finite-time boundedness and contractiveness for the resulting closed-loop systems is proposed by a set of non-linear matrix inequalities in some given finite-time interval. For decoupling this non-linearity, a sufficient condition on the existence of a mode-dependent distributed dynamic output feedback controller is established in terms of linear matrix inequalities with some fixed parameter. Moreover, the obtained controller, which not only inherits the structure of the plant but also has the same jumping process as the plant, can guarantee that the closed-loop system is stochastic finite-time bounded and contractive in some given finite-time interval. Furthermore, an algorithm is presented to obtain the parameters of such controllers. Finally, a numerical simulation is presented to show the validity of the proposed method.

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 H∞ Control of Stochastic Singular Systems with Partly Known Transition Rates via an Optimization Algorithm

This paper is concerned with the problem of finite-time H∞ control for stochastic singular systems with partly known transition rates (TRs). The transition of system parameters follows a finite-state Markov process. Firstly, based on stochastic functional method and linear matrix inequalities (LMIs) technique, sufficient conditions are proposed to ensure finite-time stochastic boundedness (FTSB) and finite-time H∞ stochastic boundedness (FTH∞SB) of considered stochastic singular system. Secondly, by designing a state feedback controller, strict LMI conditions are obtained to guarantee the closed-loop system with partly known TRs to be FTSB and FTH∞SB. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed methods.

Observer-based finite-time H∞ control for uncertain discrete-time nonhomogeneous Markov jump systems

The problem of observer-based finite-time H∞ control for discrete-time Markov jump systems with time-varying transition probabilities and uncertainties is studied in this paper, in which time-varying transition probabilities are modelled as convex polyhedron, and the parameter uncertainty satisfies norm-bounded. First of all, a Luenberger observer is designed to measure the system state. Then, observer-based controller is constructed to ensure the stochastic finite-time boundedness of the resulting closed-loop system with an H∞ performance. Furthermore, sufficient conditions are derived in light of linear matrix inequalities. In the end, the flexibility and applicability of the developed methods are demonstrated by two illustrative examples.

Asynchronous Finite-Time Filtering of Markov Jump Nonlinear Systems and Its Applications

In this paper, the problem of asynchronous finite-time filtering issue is addressed for a class of Markov jump nonlinear systems with incomplete transition rate. The so-called asynchronization means that the filter’s modes do not synchronize with the system’s modes. Both the stochastic finite-time boundedness (FTBs) problem and the stochastic input–output finite-time stability (IO-FTSy) problem are involved. By resorting to the mode-dependent Lyapunov function approach and the matrix inequality techniques, some interesting results are derived to verify the properties of the stochastic FTBs and the stochastic IO-FTSy of the asynchronous filtering error system. The asynchronous filter parameters can be reduced to the solvability of some convex optimization problems. Finally, a single-link robot arm and a tunnel diode circuit are applied to elucidate the proposed algorithms.

Finite-time boundedness of Markovain jump nonlinear systems with incomplete information

ABSTRACT This paper deals with the finite-time H ∞ bounded control problem of a class of uncertain Markovian jump nonlinear systems with partially unknown transition probabilities and norm-bounded disturbances. The purpose of the paper is to derive a stochastic finite-time controller such that the resulting nominal or uncertain stochastic nonlinear model is stochastically finite-time H ∞ bounded by applying stochastic analysis techniques and free connection weighting matrix approach. We also provide stochastic finite-time stability and stochastic finite-time boundedness criteria of the class of nominal or uncertain stochastic nonlinear dynamics. Moreover, the derived criteria can be simplified into linear matrix inequalities (LMIs), which could be solved by employing Matlab LMI toolbox. Finally, the effectiveness of proposed approaches is demonstrated by a practical example.

A Parameter-Dependent Sliding Mode Approach for Finite-Time Bounded Control of Uncertain Stochastic Systems With Randomly Varying Actuator Faults and Its Application to a Parallel Active Suspension System

This paper addresses the mean-square finite-time bounded control problem for uncertain stochastic systems via a sliding mode approach. The stochastic phenomena of randomly occurring uncertainties and randomly varying actuator faults modeled by two independent exponential distributions are addressed effectively. A key issue for the system under the consideration is how to ensure, for any prescribed finite (possibly short ) working time interval, the stochastic finite-time boundedness (SFTB) of the resultant closed-loop systems and the reachability of the specified sliding surface in mean-square sense. To this end, a parameter-dependent sliding mode control (SMC) law is designed to force ( with probability one ) the state trajectories into a domain around the specified sliding surface during the given finite-time interval. The upper bound of the sliding domain associated with the design parameters is obtained explicitly. The sufficient conditions are established, respectively, for guaranteeing the SFTB of the SMC systems over both reaching phase and sliding motion phase . Finally, the proposed finite-time SMC approach is illustrated via a parallel active suspension system.

Finite-Time $H_{\infty}$ State Estimation for Discrete Time-Delayed Genetic Regulatory Networks Under Stochastic Communication Protocols

This paper investigates the problem of finite-time $H_{\infty }$ state estimation for discrete time-delayed genetic regulatory networks under stochastic communication protocols (SCPs). The network measurements are transmitted from two groups of sensors to a remote state estimator via two independent communication channels of limited bandwidths, and two SCPs are utilized to orchestrate the transmission orders of sensor nodes with aim to avoid data collisions. The estimation error dynamics is modeled by a Markovian switching system with two switching signals. By constructing a transmission-order-dependent Lyapunov–Krasovskii functional and utilizing an up-to-date discrete Wirtinger-based inequality together with the reciprocally convex approach, sufficient conditions are established to guarantee the stochastic finite-time boundedness for the estimation error dynamics with a prescribed $H_{\infty }$ disturbance attenuation level. The parameters of the state estimator are designed by solving a convex optimization problem which minimizes the disturbance attenuation level subject to several inequality constraints. The repressilator model is utilized to illustrate the effectiveness of the design procedure of the proposed state estimator.

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.