Stochastic Finite-time Boundedness Research Articles

Finite-time asynchronous control for semi-Markov jump systems with random uncertainties and actuator faults

This article is aimed at studying the finite-time reliable asynchronous control issue for continuous semi-Markov jump systems (S-MJSs) with actuator failures and randomly occurring uncertainties (ROUs). To characterize the asynchronous phenomenon between the system mode and the controller mode, the mode detector approach via a hidden semi-Markov model (HSM) is adopted. The transition probability (TP) matrix of the HSM is nonhomogeneous, which can be provided by a polytopic structure. By resorting the mode-dependent Lyapunov function, sufficient conditions are attained to guarantee the stochastic finite-time boundedness (SFTB) and H∞ performance of the closed-loop system. Then, according to a skillful matrix inequality transforming method, the reliable asynchronous control law is constructed. Finally, a tunnel diode circuit system and a mass-spring-damper mechanical system are proposed to demonstrate the superiority, effectiveness and practicality of the developed design method.

Observer-based finite-time H∞ control for discrete-time singular Markovian jump systems with asynchronous modes

The asynchronous observer-based finite-time [Formula: see text] control problem for discrete-time singular Markovian jump systems with time-varying delays is studied, where the asynchronism of the controller and observer with respect to the original system is fully taken into consideration. By the use of finite-time analysis theory and the construction of suitable Lyapunov-Krasovskii functionals, sufficient conditions to determine the closed-loop error system is singular stochastic finite-time boundedness are given with [Formula: see text] performance level. Then, by applying linear matrix inequalities, the desired observer parameters and controller parameters can be computed. Finally, the effectiveness of our proposed method is confirmed by simulation.

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.

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.

Asynchronous Boundary Control of Markov Jump Neural Networks With Diffusion Terms.

This article concerns with the asynchronous boundary control for a class of Markov jump reaction-diffusion neural networks (MJRDNNs). In consideration of nonsynchronous behavior between the system modes and controller modes, a novel asynchronous boundary control design is proposed for MJRDNNs. Based on the designed asynchronous boundary controller, a sufficient criterion is established to ensure the stochastic finite-time boundedness for the considered MJRDNNs by constructing a Lyapunov-Krasovskii functional and utilizing Wirtinger-type inequality. Then, a sufficient condition is acquired to guarantee that MJRDNNs are stochastic finite-time bounded with performance. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design method.

Multiple interval delay-dependent finite-time control of fuzzy stochastic systems

This work is concerned with multiple interval delay-dependent stochastic finite-time boundedness as well as input-output finite-time mean square stabilization for fuzzy plants against state constraints as well as input constraints. Nonlinear dynamics, intermittent actuator faults, exogenous disturbances, model uncertainties and intermittent sensor faults appear in the multiplicative form in these systems. The switching between the faulty and healthy conditions is described via semi-Markov chain. First, a semi-Markovian fault-tolerant controller is researched. Next, the closed-loop model is gathered. The issue of robust stochastic finite-time boundedness as well as input-output finite-time mean square stabilization against H∞ performance is realized via fuzzy stochastic Lyapunov function. Meanwhile, sufficient conditions are presented with linear matrix inequalities. At last, this validity of this approach in this paper is proved by two examples.

Finite‐time stochastic dissipative output tracking control of semi‐Markov jump systems via an adaptive event‐triggered mechanism

AbstractThis work focuses on the output tracking control for a class of continuous‐time semi‐Markov jump systems (SMJSs). In the controller design, not only the finite‐time stochastic boundedness (FTSB), but also the dissipative performance over a finite‐time interval is considered. In order to save communication resources, a version of adaptive event‐triggered mechanism (AETM) is utilized. Different from the traditional static event‐triggered mechanism, the threshold coefficient in AETM is time‐varying and can be adjusted in real‐time to fit the system evolution. Moreover, the asynchronous switching between the controller modes and the plant modes is taken into account. The design objective is to synthesis an adaptive event‐triggered asynchronous state‐feedback controller such that not only the augmented closed‐loop system is FTSB with a certain level of dissipative performance, but also the communication burden can be reduced to some extent. It is the first attempt to investigate the output tracking control of SMJSs over a finite‐time interval. By constructing a plant model‐dependent Lyapunov function, a set of conditions is derived for the FTSB analysis, based on which a controller design algorithm is presented. Finally, an illustrative example is given to verify the availability of the theoretical findings.

Finite‐time dissipative control for semi‐Markovian jump systems with time‐varying delays and generally uncertain transition rates

AbstractIn this paper, we mainly address the issue of finite‐time stochastic boundedness (FTSB) and finite‐time stochastic dissipation for semi‐Markovian jump systems (SMJSs) with generally uncertain transition rates (TRs). Firstly, by resorting to linear matrix inequities (LMIs), some sufficient conditions on FTSB for SMJSs with uncertain TRs are introduced, which includes two cases. Then, dissipative control is developed and a state feedback controller is designed to ensure the FTSB of the closed‐loop system by solving a series of LMIs. Finally, two examples are used to illustrate the results.

Finite-time decentralized event-triggered feedback control for generalized neural networks with mixed interval time-varying delays and cyber-attacks

<abstract><p>This article investigates the finite-time decentralized event-triggered feedback control problem for generalized neural networks (GNNs) with mixed interval time-varying delays and cyber-attacks. A decentralized event-triggered method reduces the network transmission load and decides whether sensor measurements should be sent out. The cyber-attacks that occur at random are described employing Bernoulli distributed variables. By the Lyapunov-Krasovskii stability theory, we apply an integral inequality with an exponential function to estimate the derivative of the Lyapunov-Krasovskii functionals (LKFs). We present new sufficient conditions in the form of linear matrix inequalities. The main objective of this research is to investigate the stochastic finite-time boundedness of GNNs with mixed interval time-varying delays and cyber-attacks by providing a decentralized event-triggered method and feedback controller. Finally, a numerical example is constructed to demonstrate the effectiveness and advantages of the provided control scheme.</p></abstract>

Protocol-Based Control for Semi-Markov Jump Systems With Dynamic Quantization

This brief is devoted to protocol-based control method design for semi-Markov switching systems with dynamic quantization. Essential different from the semi-Markov process with arbitrary switchings, by proposing a novel semi-Markov process subjected to a deterministic switching signal, a generalized framework of semi-Markov switching systems is set up. With respect to the quantization range of the dynamic quantizer, an improved event-triggered protocol associated with the quantizer parameter is proposed. On account of mode-dependent Lyapunov theory, sufficient conditions are established to ensure the stochastic finite-time boundedness of the resulting system. In the end, a tunnel diode circuit model shows the practicability and effectiveness of the presented method.

A Hierarchical Structure Approach to Finite-Time Filter Design for Fuzzy Markov Switching Systems With Deception Attacks.

This work is concerned with the issue of finite-time filter design for a type of Takagi-Sugeno (T-S) fuzzy Markov switching system (MSSs) with deception attacks (DAs). In view of communication network security, the randomly occurring DAs are considered in the measurement output (MO), in which the malicious unknown but bounded signals are launched by the adversary. Notably, to characterize the fallibility of the communication links between the MO and the filter, the packet dropouts, DAs, and quantization effects are taken into account simultaneously, which signifies that the resulting system is much more applicable than the existing results. Meanwhile, to deal with the phenomenon of asynchronous switching, a hierarchical structure approach is adopted, which involves the existing nonsynchronous/synchronous strategy as special cases. By means of a fuzzy-basis-dependent Lyapunov strategy, sufficient criteria are formulated such that the resulting system is stochastic finite-time boundedness under randomly occurring DAs. Finally, a double-inverted pendulum model and a numerical example are provided to validate the feasibility of the attained method.

Protocol-based control for nonlinear systems with environment-dependent energy harvesting sensors: An average dwell-time method

In this paper, a protocol-based controller is designed for nonlinear systems with multiple sensors, which are powered by environment-dependent energy harvesting (EDEH) devices. The Round–Robin (RR) protocol is adopted to coordinate the data transmission of sensors. The protocol-based transmission can be realized only when the energy harvested by EDEH devices is sufficient. The aim of this paper is to design the protocol-based controller to ensure the stochastic finite-time boundedness with EDEH and RR protocol. Firstly, modeling the EDEH by a switching sequence with varying sojourn probabilities, assuming a finite battery capacity constraint, and associating protocol-based transmission with a given energy cost, we propose a new recursive model to depict the dynamic of energy levels for each sensor. Then, combining with the stochastic analysis method and the dynamic of energy levels, the explicit expressions of the controller for each environment with average dwell time (ADT) are obtained. Finally, an example is provided to demonstrate the effectiveness of the designed controllers.

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.

Finite-time dissipative control for discrete-time stochastic delayed systems with Markovian switching and interval parameters

The problem of finite-time dissipative control for discrete-time stochastic delayed systems (DTSDSs) with Markovian switching and interval parameters is studied in this paper. Firstly, DTSDSs are equivalently transformed into discrete-time uncertain stochastic delayed systems, whose interval parameters are described by a series of convex combinations of the endpoints information. Then, finite-time stochastic boundedness (FTSB) and finite-time stochastic exponential (Qi,Si,Ri)−α dissipative (FTSED) are analysed by constructing a discrete-time Lyapunov–Krasovskii functional. Correspondingly, several sufficient conditions are obtained in terms of Linear Matrix Inequalities (LMIs). Furthermore, the delay-feedback controllers with memory are designed such that the finite-time dissipative performance of the DTSDSs is satisfied. Finally, the proposed results are validated through a switching energy-storing electrical circuit.

Event‐based finite‐time H∞ filtering of discrete‐time singular jump network systems

AbstractThis article presents the analysis and design problems of event‐based (EB) finite‐time (FT) filtering for discrete‐time singular Markov jump network systems (SMNSs) based on separation of matrix inequality variables. According to the EB method, an SMNS model of network‐induced delay is introduced. Sufficient conditions of singular stochastic FT boundedness are then obtained for the augmented SMNS model by applying a stochastic Lyapunov functional and introducing slack matrix variables. In addition, using separation schemes for decoupling matrix inequality variables, the EBFT filter gain matrices and triggered ones are co‐designed to ensure that the augmented SMNSs are singularly stochastic FT bounded with a prescribed performance index. Finally, a practical DC test example is presented to show effectiveness of the proposed approach.

Non-fragile finite-time sliding mode control for Markovian jump systems with randomly occurring uncertainties and controller gain variations

This paper considers the sliding mode control (SMC) problem of a class of uncertain Markovian jump systems, in which there exist randomly occurring parameter uncertainties and random gain variations in the controller. By introducing two independent random variables obeying Bernoulli distribution, the random characteristics of parameter uncertainties and controller gain variations are described. A mode-dependent sliding surface is constructed, and then, the non-fragile SMC scheme is synthesized such that the specified sliding surface is reached in finite time. Furthermore, the stochastic finite-time boundedness over both the reaching and sliding stages are ensured simultaneously under some sufficient conditions. Finally, the developed non-fragile SMC approach is verified by a practical example.

A robust distributed secure interval observation approach for uncertain discrete-time positive systems under deception attacks

This paper deals with the network-based robust distributed state estimation problem of a class of discrete-time positive systems with bounded parameter perturbation and bounded disturbance. The system outputs are measured by multiple groups of sensors and transmitted to observers through communication networks suffering from deception attacks. To attain real-time monitoring and interval estimation of the system state and achieve a satisfactory estimation accuracy, a distributed secure interval observation approach is presented, where the interval observer is composed of an upper-bounding observer and a lower-bounding observer. The construction of each interval observer is based on the system positivity and the bounds of parameter perturbation, disturbance input and attack signals. Using the stochastic finite-time boundedness and l1-gain analysis method together with the linear programming technique, some sufficient conditions on analysis, design and optimization of the distributed interval observers for the uncertain positive system against deception attacks are established. The practicability and advantage of the proposed approach is checked by a numerical example, which comes from the remote monitoring of power distribution in smart grid.

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.