Class Of Discrete-time Stochastic Systems Research Articles

Active Diagnosis of Incipient Actuator Faults for Stochastic Systems

In this paper, the active diagnosis problem of incipient actuator faults is investigated for a class of discrete-time stochastic systems. The input is exclusively designed for diagnosis purposes to optimally discriminate among multiple mode hypotheses that correspond to the multiple incipient actuator fault scenarios. Due to infeasibility in evaluating the misdiagnosis probability in the closed form, its new upper bound is derived as an alternative. It is proven that this upper bound is a tighter bound on the misdiagnosis probability for incipient actuator faults, compared with the widely used Bhattacharyya upper bound. For computation complexity reduction and diagnosis performance improvement purposes, a novel input design criterion is constructed for active fault diagnosis (AFD) based on the derived upper bound, under which the input design problem can be solved to global optimality. By injecting the optimal input, to fully utilize the diagnostically relevant information in the output data so as to draw a reliable diagnosis conclusion, the resulting measurement output sequence is exploited to make the AFD decision on the basis of the minimum misdiagnosis probability rule. Finally, experimental results on a four-tank system illustrate the effectiveness and superiority of the proposed AFD approach.

Active Fault Diagnosis for Stochastic Systems Within Bayesian Minimum Risk Decision Framework

In this paper, the active fault diagnosis (AFD) problem is investigated for a class of discrete-time stochastic systems. We consider multiple fault modes of the system, and the different types of misdiagnoses of these faults lead to different losses. A novel AFD framework is developed based on the Bayesian minimum risk decision framework. The misdiagnosis risk is derived to characterize the total losses caused by the misdiagnoses of all considered faults. The input is specifically designed to improve diagnosis performance by minimizing the risk of misdiagnosis. Since it is intractable to express the misdiagnosis risk in the closed form, we deduce an upper bound on it to establish a novel input design criterion based on the Bhattacharyya distance. The optimal input signal can be obtained for AFD via concave quadratic programming. For diagnosis performance enhancement and computation simplification purposes, we propose two new semi-online implementation manners of the input design for stochastic systems with and without multi-fault modes switching respectively. Given the optimal input signal and the proposed implementation manner, faults are diagnosed based on the minimum misdiagnosis risk decision principle. The effectiveness and superiority of the proposed AFD method are demonstrated by simulation results on a four-tank system.

Full Information H2 Control of Borel-Measurable Markov Jump Systems with Multiplicative Noises

This paper addresses an H2 optimal control problem for a class of discrete-time stochastic systems with Markov jump parameter and multiplicative noises. The involved Markov jump parameter is a uniform ergodic Markov chain taking values in a Borel-measurable set. In the presence of exogenous white noise disturbance, Gramian characterization is derived for the H2 norm, which quantifies the stationary variance of output response for the considered systems. Moreover, under the condition that full information of the system state is accessible to measurement, an H2 dynamic optimal control problem is shown to be solved by a zero-order stabilizing feedback controller, which can be represented in terms of the stabilizing solution to a set of coupled stochastic algebraic Riccati equations. Finally, an iterative algorithm is provided to get the approximate solution of the obtained Riccati equations, and a numerical example illustrates the effectiveness of the proposed algorithm.

A mean field absorbing control model for interacting objects systems

We study a class of discrete-time stochastic systems composed of a large number of N interacting objects, which are classified in a finite number of classes. The behavior of the objects is controlled by a central decision-maker as follows. At each stage, once the configuration of the system is observed, the controller takes a decision; then a cost is incurred and there is a positive probability the process stops, otherwise the objects move randomly among the classes according to a transition probability. That is, with positive probability, the system is absorbed by a configuration that represents the death of the system, and there it will remain without incurring cost. Due to the large number of objects, the control problem is studied according to the mean field theory. Thus, instead of analyzing a single object, we focus on the proportions of objects occupying each class, and then we study the limit as N goes to infinity.

Control of Discrete-Time Stochastic Systems With Packet Loss by Event-Triggered Approach

Event-triggered schemes are characterized in less communication traffic while maintaining the resulting controlled plant's desired stability and performance criteria. In the presence of packet dropouts, this paper is concerned with the modeling and control problems for a class of discrete-time stochastic systems with event-triggered schemes. Two different mathematical analysis methods are proposed to model the packet loss when an event-triggered scheme is subject to packet loss. First, a stochastic distributed sequence satisfying the Bernoulli process is utilized to model the triggered packets transmitted in the communication networks. Considering the difference between time-triggered and event-triggered schemes, an equivalent model with a random sequence not satisfying a Bernoulli distribution process is also analyzed, which is not the same as some existing results in the literature. Then, the mean-square exponential stability of resulting augmented system is guaranteed and the prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance level is achieved by solving resulting discrete P-problem. Two examples with simulations are provided to validate the analytical results and demonstrate the effectiveness of the proposed co-design techniques.

A Two-Phase Distributed Filtering Algorithm for Networked Uncertain Systems with Fading Measurements under Deception Attacks.

In this paper, the distributed filtering problem is addressed for a class of discrete-time stochastic systems over a sensor network with a given topology, susceptible to suffering deception attacks, launched by potential adversaries, which can randomly succeed or not with a known success probability, which is not necessarily the same for the different sensors. The system model integrates some random imperfections and features that are frequently found in real networked environments, namely: (1) fading measurements; (2) multiplicative noises in both the state and measurement equations; and (3) sensor additive noises cross-correlated with each other and with the process noise. According to the network communication scheme, besides its own local measurements, each sensor receives the measured outputs from its adjacent nodes. Based on such measurements, a recursive algorithm is designed to obtain the least-squares linear filter of the state. Thereafter, each sensor receives the filtering estimators previously obtained by its adjacent nodes, and these estimators are all fused to obtain the desired distributed filter as the minimum mean squared error matrix-weighted linear combination of them. The theoretical results are illustrated by a simulation example, where the efficiency of the developed distributed estimation strategy is discussed in terms of the error variances.

Nonlinear disturbance observer-based control for a class of discrete-time stochastic systems with multiple heterogenous disturbances

In this paper, the nonlinear disturbance observer-based control (NDOBC) scheme is proposed for a class of discrete-time stochastic systems with multiple heterogenous disturbances, which include the non-harmonic disturbance and a sequence of random vectors. A nonlinear disturbance observer (NDO) is designed to estimate the non-harmonic disturbance, then the NDOBC scheme is proposed by combining DOBC with [Formula: see text] control, such that the composite system can achieves asymptotically mean-square bounded and asymptotically mean-square stable in different conditions. Finally, simulation results show the effectiveness of the proposed method.

Receding Horizon Control-Based Stabilization of Discrete-Time Stochastic Systems With State Delay

The stabilization of receding horizon control (RHC) for a class of discrete-time stochastic systems with multiple state delay is concerned. Firstly, a cost function with the type of conditional expectation is designed. Secondly, the sufficient RHC stabilization condition has been obtained in terms of a linear matrix inequalities (LMI). And under some appropriate assumptions, it is shown that the stochastic system with state delay can be stabilized in the mean square sense if the terminal weighting matrices satisfy the given inequalities. Lastly, the explicit stabilizing controller is derived by solving a finite horizon optimal control problem. Numerical examples show that the proposed RHC can effectively stabilize stochastic systems with state delay.

Event-based finite horizon state estimation for stochastic systems with network-induced phenomena

This paper investigates a finite horizon state estimation problem for a class of discrete-time stochastic systems with random transmission delays and out-of-order packets of data. Employing an event-driven signal-choosing scheme of logic zero-order-holder (LZOH), a system model is established synthetically in a unified form considering the network-induced phenomena, to drop out-of-order packets and improve system performance. By virtue of the established system model, a novel minimum error covariance matrix for the augmented state-space is obtained from the estimated variance constraint. With the aid of a finite horizon, the upper boundary of estimation error covariance is introduced during the information transmission from sensor to estimator, and the appropriate filter parameters are probed. To improve the estimation performance and alleviate the computation burden, an estimation-based compensation approach for random transmission delays is proposed using the received valid signals. Finally, the effectiveness and applicability of the proposed state estimation method are illustrated by a numerical simulation.

Event-triggered resilient filtering with measurement quantization and random sensor failures: Monotonicity and convergence

This paper is concerned with the remote state estimation problem for a class of discrete-time stochastic systems. An event-triggered scheme is exploited to regulate the sensor-to-estimator communication in order to preserve limited network resources. A situation is considered where the sensors are susceptible to possible failures and the signals are quantized before entering the network. Furthermore, the resilience issue for the filter design is taken into account in order to accommodate the possible gain variations in the course of filter implementation. In the simultaneous presence of measurement quantizations, sensor failures and gain variations, an event-triggered filter is designed to minimize certain upper bound of the covariance of the estimation error in terms of the solution to Riccati-like difference equations. Further analysis demonstrates the monotonicity of the minimized upper bound with respect to the value of thresholds. Subsequently, a sufficient condition is also established for the convergence of the steady-state filter. A numerical example is presented to verify the effectiveness of the proposed filtering algorithm.

A new approach to distributed fusion filtering for networked systems with random parameter matrices and correlated noises

This paper is concerned with the distributed filtering problem for a class of discrete-time stochastic systems over a sensor network with a given topology. The system presents the following main features: (i) random parameter matrices in both the state and observation equations are considered; and (ii) the process and measurement noises are one-step autocorrelated and two-step cross-correlated. The state estimation is performed in two stages. At the first stage, through an innovation approach, intermediate distributed least-squares linear filtering estimators are obtained at each sensor node by processing available output measurements not only from the sensor itself but also from its neighboring sensors according to the network topology. At the second stage, noting that at each sampling time not only the measurement but also an intermediate estimator is available at each sensor, attention is focused on the design of distributed filtering estimators as the least-squares matrix-weighted linear combination of the intermediate estimators within its neighborhood. The accuracy of both intermediate and distributed estimators, which is measured by the error covariance matrices, is examined by a numerical simulation example where a four-sensor network is considered. The example illustrates the applicability of the proposed results to a linear networked system with state-dependent multiplicative noise and different network-induced stochastic uncertainties in the measurements; more specifically, sensor gain degradation, missing measurements and multiplicative observation noises are considered as particular cases of the proposed observation model.

Simultaneous Event-Triggered Fault Detection and Estimation for Stochastic Systems Subject to Deception Attacks.

In this paper, a synthesized design of fault-detection filter and fault estimator is considered for a class of discrete-time stochastic systems in the framework of event-triggered transmission scheme subject to unknown disturbances and deception attacks. A random variable obeying the Bernoulli distribution is employed to characterize the phenomena of the randomly occurring deception attacks. To achieve a fault-detection residual is only sensitive to faults while robust to disturbances, a coordinate transformation approach is exploited. This approach can transform the considered system into two subsystems and the unknown disturbances are removed from one of the subsystems. The gain of fault-detection filter is derived by minimizing an upper bound of filter error covariance. Meanwhile, system faults can be reconstructed by the remote fault estimator. An recursive approach is developed to obtain fault estimator gains as well as guarantee the fault estimator performance. Furthermore, the corresponding event-triggered sensor data transmission scheme is also presented for improving working-life of the wireless sensor node when measurement information are aperiodically transmitted. Finally, a scaled version of an industrial system consisting of local PC, remote estimator and wireless sensor node is used to experimentally evaluate the proposed theoretical results. In particular, a novel fault-alarming strategy is proposed so that the real-time capacity of fault-detection is guaranteed when the event condition is triggered.

Robust H∞ control for delayed systems with randomly varying nonlinearities under uncertain occurrence probability via sliding mode method

ABSTRACTIn this paper, we address the problem of robust sliding mode control (SMC) for a class of discrete-time stochastic systems with parameter uncertainties, time-varying delay and randomly varying nonlinearities (RVNs) under uncertain occurrence probability. Here, the norm-bounded parameter uncertainties are considered. The time-varying delay is bounded with known upper and lower bounds. In addition, the RVNs are depicted by using a Bernoulli distributed stochastic variable with uncertain occurrence probability. The aim of the paper is to provide an SMC method such that, for all parameter uncertainties, time-varying delay and RVNs, the robust asymptotic stability with a prescribed disturbance attenuation level is guaranteed for the sliding mode dynamics by providing a new sufficient condition. Moreover, the reachability analysis is carried out simultaneously, i.e. the states of the closed-loop system are driven onto a neighborhood of pre-designed sliding surface by synthesizing a robust sliding mode controller. Finally, the usefulness of the aforementioned control technique is verified by a numerical example.

Fault Detection for Complex Systems with Channel Fadings, Randomly Occurring Multiple Delays and Infinitely Distributed Delays

This paper is concerned with the fault detection (FD) problem for a class of discrete-time stochastic systems with channel fadings, randomly occurring multiple communication delays, and infinitely distributed delays. All of the three phenomena have the characteristics of randomly occurring and three sequences of stochastic variables which are mutually independent but obey the Bernoulli distribution are employed to describe them. The aim of this paper is to design an FD filter such that the FD dynamics is exponentially stable in the mean square and, at the same time, the error between the residual signal and the fault signal is made as small as possible. Intensive analysis is utilized to derive the sufficient conditions for the designed FD filter, which guarantees the exponential stability and the prescribed H∞ performance. FD filter parameters are obtained by solving a convex optimization problem. An illustrative example is provided to demonstrate the effectiveness of the FD design scheme.

‐constrained incentive Stackelberg games for discrete‐time stochastic systems with multiple followers

The authors discuss an incentive Stackelberg game with one leader and multiple non-cooperative followers, for a class of discrete-time stochastic systems with an external disturbance. In this game, the leader achieves a team-optimal solution by attenuating the external disturbance under their H ∞ constraint, whereas the followers adopt Nash equilibrium strategies according to the leader's incentive Stackelberg strategy set (declared in advance) while considering the worst-case disturbance. Using our proposed method, we demonstrate that the incentive Stackelberg strategy set can be found by solving a set of matrix-valued equations. Techniques are presented for both the finite- and infinite-horizon cases. In addition, through an academic and a practical numerical examples, we verify the efficacy of the proposed method in providing the incentive Stackelberg strategy set.

Elegant anti-disturbance control for discrete-time stochastic systems with nonlinearity and multiple disturbances

ABSTRACTAn elegant anti-disturbance control (EADC) strategy for a class of discrete-time stochastic systems with both nonlinearity and multiple disturbances, which include the disturbance with partially known information and a sequence of random vectors, is proposed in this paper. A stochastic disturbance observer is constructed to estimate the disturbance with partially known information, based on which, an EADC scheme is proposed by combining pole placement and linear matrix inequality methods. It is proved that the two different disturbances can be rejected and attenuated, and the corresponding desired performances can be guaranteed for discrete-time stochastic systems with known and unknown nonlinear dynamics, respectively. Simulation examples are given to demonstrate the effectiveness of the proposed schemes compared with some existing results.

Exponential Stability for Discrete-Time Infinite Markov Jump Systems

This technical note addresses a class of discrete-time stochastic systems with infinite Markov jump parameter. First of all, spectral criterion and Lyapunov type criteria are presented for the exponential stability of considered systems. Further, under the condition of strong detectability, a Barbashin-Krasovskii stability theorem is shown in terms of a generalized Lyapunov equation with a positive semi-definite term. As an application of the proposed Lyapunov stability criterion, a sufficient condition of $\ell_{2}$ input-state stability is derived for the infinite Markov jump systems disturbed by finite-energy random disturbance.

Event‐based security control for discrete‐time stochastic systems

This study is concerned with the event-based security control problem for a class of discrete-time stochastic systems with multiplicative noises subject to both randomly occurring denial-of-service (DoS) attacks and randomly occurring deception attacks. An event-triggered mechanism is adopted with hope to reduce the communication burden, where the measurement signal is transmitted only when a certain triggering condition is violated. A novel attack model is proposed to reflect the randomly occurring behaviours of the DoS attacks as well as the deception attacks within a unified framework via two sets of Bernoulli distributed white sequences with known conditional probabilities. A new concept of mean-square security domain is put forward to quantify the security degree. The authors aim to design an output feedback controller such that the closed-loop system achieves the desired security. By using the stochastic analysis techniques, some sufficient conditions are established to guarantee the desired security requirement and the control gain is obtained by solving some linear matrix inequalities with non-linear constraints. A simulation example is utilised to illustrate the usefulness of the proposed controller design scheme.

Linear Quadratic Regulation and Stabilization of Discrete-Time Systems With Delay and Multiplicative Noise

This paper is concerned with the long-standing problems of linear quadratic regulation (LQR) control and stabilization for a class of discrete-time stochastic systems involving multiplicative noises and input delay. These fundamental problems have attracted resurgent interests due to development of networked control systems. An explicit analytical expression is given for the optimal LQR controller. More specifically, the optimal LQR controller is shown to be a linear function of the conditional expectation of the state, with the feedback gain based on a Riccati-ZXL difference equation. It is also shown that the system is stabilizable in the mean-square sense if and only if an algebraic Riccati-ZXL equation has a particular solution. These results are based on a new technical tool, which establishes a non-homogeneous relationship between the state and the costate of this class of systems, and the introduction of a new Lyapunov function for the finite-horizon optimal control design.

Asymptotic stability in probability and stabilization for a class of discrete-time stochastic systems

Summary This paper investigates asymptotic stability in probability and stabilization designs of discrete-time stochastic systems with state-dependent noise perturbations. Our work begins with a lemma on a special discrete-time stochastic system for which almost all of its sample paths starting from a nonzero initial value will never reach the origin subsequently. This motivates us to deal with the asymptotic stability in probability of discrete-time stochastic systems. A stochastic Lyapunov theorem on asymptotic stability in probability is proved by means of the convergence theorem of supermartingale. An example is given to show the difference between asymptotic stability in probability and almost surely asymptotic stability. Based on the stochastic Lyapunov theorem, the problem of asymptotic stabilization for discrete-time stochastic control systems is considered. Some sufficient conditions are proposed and applied for constructing asymptotically stable feedback controllers. Copyright © 2014 John Wiley & Sons, Ltd.