Markovian Jump Systems Research Articles

Adaptive Neural Event-Triggered Control of Networked Markov Jump Systems Under Hybrid Cyberattacks.

This article is concerned with the neural network (NN)-based event-triggered control problem for discrete-time networked Markov jump systems with hybrid cyberattacks and unmeasured states. The event-triggered mechanism (ETM) is used to reduce the communication load, and a Luenberger observer is introduced to estimate the unmeasured states. Two kinds of cyberattacks, denial-of-service (DoS) attacks and deception attacks, are investigated due to the vulnerability of cyberlayer. For the sake of mitigating the impact of these two types of cyberattacks on system performance, the ETM under DoS jamming attacks is discussed first, and a new estimation of such mechanism is given. Then, the NN technique is applied to approximate the injected false information. Some sufficient conditions are derived to guarantee the boundedness of the closed-loop system, and the observer and controller gains are presented by solving a set of matrix inequalities. The effectiveness of the presented control method is demonstrated by a numerical example.

Dynamic event-triggered control for discrete-time nonlinear Markov jump systems using policy iteration-based adaptive dynamic programming

This paper investigates a dynamic event-triggered optimal control problem of discrete-time (DT) nonlinear Markov jump systems (MJSs) via exploring policy iteration (PI) adaptive dynamic programming (ADP) algorithms. The performance index function (PIF) defined in each subsystem is updated by utilizing an online PI algorithm, and the corresponding control policy is derived via solving the optimal PIF. Then, we adopt neural network (NN) techniques, including an actor network and a critic network, to estimate the iterative PIF and control policy. Moreover, the designed dynamic event-triggered mechanism (DETM) is employed to avoid wasting additional resources when the estimated iterative control policy is updated. Finally, based on the Lyapunov difference method, it is proved that the system stability and the convergence of all signals can be guaranteed under the developed control scheme. A simulation example for DT nonlinear MJSs with two system modes is presented to demonstrate the feasibility of the control design scheme.

Finite-Time H∞ Control for Time-Delay Markovian Jump Systems with Partially Unknown Transition Rate via General Controllers

This paper deals with the problems of finite-time boundedness (FTB) and H∞ FTB for time-delay Markovian jump systems with a partially unknown transition rate. First of all, sufficient conditions are provided, ensuring the FTB and H∞ FTB of systems given by linear matrix inequalities (LMIs). A new type of partially delay-dependent controller (PDDC) is designed so that the resulting closed-loop systems are finite-time bounded and satisfy a given H∞ disturbance attenuation level. The PDDC contains both non-time-delay and time-delay states, though not happening at the same time, which is related to the probability distribution of the Bernoulli variable. Furthermore, the PDDC is extended to two other cases; one does not contain the Bernoulli variable, and the other experiences a disordering phenomenon. Finally, three numerical examples are used to show the effectiveness of the proposed approaches.

Stabilizing control of Markovian jump systems with sampled switching and state signals and applications

AbstractThis article addresses the stabilization problem of continuous‐time Markovian jump systems (MJSs). Because of both switching and state signals sampled, a novel system with an exponential matrix characterizing the sampling effects is developed. It is used to be an auxiliary system and plays important roles in system analysis and synthesis. Sufficient stabilization conditions are presented and fully consider the sampling rate. The applications of established methods and results are applied to networked control in the presence of denial‐of‐service (DoS). The frequency and duration of DoS attacks ensuring stability of the closed‐loop system are characterized. Meanwhile, more special situations about particular transition rate matrix, sampling logic and improved mode‐dependent controller are considered respectively. The analysis results are significant and bring an important method to study the control for MJSs with sampled switching and state signals. A numerical example is offered to verify the effectiveness and superiority of the methods proposed in this study.

Observer-Based Finite-Time Fuzzy H∞ Control for Markovian Jump Systems with Time-Delay and Multiplicative Noises

Observer-Based Finite-Time Fuzzy H∞ Control for Markovian Jump Systems with Time-Delay and Multiplicative Noises

Improved results on reachable set synthesis of Markovian jump systems with time-varying delays: General asynchronous control approaches

This paper investigates the reachable set synthesis (RSS) issue of Markovian jump systems (MJSs) with time-varying delays via various asynchronous controls. The goal is to devise appropriate asynchronous controllers to assure that the reachable set (RS) of the generated closed-loop dynamic system (CDS) is constrained in the specified region. Firstly, a hidden Markov model (HMM) is used to describe mismatch case among controller modes and system modes. Next, coupling problem of mode mismatch is solved by using an effective inequality condition, and the sufficient conditions for the existence of the asynchronous controllers by linear matrix inequalities (LMIs) are given. Based on the desired asynchronous controllers, the additional reachable set synthesis results of two related controls for the MJSs are obtained. Finally, two simulations are given to demonstrate the feasibility and superiority of the provided methods.

Asynchronous Sampled-Data Controller Design for Switched Markov Jump Systems and Its Applications

This article is dedicated to design asynchronous aperiodic sampled-data controller for a class of Markov jump systems with switching transition rate. The sampling controller corresponding switching transition rate matrix mode is not synchronized with the system corresponding switching transition rate matrix mode due to the possible switching of the transfer rate matrix in the sampling interval. With the help of T–S fuzzy models, the state-space representation of the system is turned into a fuzzy Itô stochastic switched Markov jump systems. By constructing novel Lyapunov functionals, mean square exponential stability criteria, and dissipativity criteria are presented. Furthermore, an asynchronous aperiodic sampled-data controller is designed for fuzzy Itô stochastic Markov jump systems. At last, by fuzzing the nonlinear tunnel diode circuit model and nonlinear mass-spring-damper mechanical model, the effectiveness and lower conservativeness of the proposed method are illustrated.

Asynchronous Control of Markov Jump Systems Under Aperiodic DoS Attacks

The secure asynchronous control problem of Markov jump systems (MJSs) against aperiodic discrete denial-of-service (DoS) attacks is discussed in this brief. DoS attacks cut off the communication networks, resulting in the loss of state information. The impact of DoS attacks may cause mismatched behavior between controlled plant modes and controller modes, which can be illustrated by a hidden Markov model (HMM). An asynchronous controller is utilized to overcome the mismatched phenomenon. By employing multiple Lyapunov functions and iterative methods, and analyzing the conditions on malicious DoS attacks, sufficient conditions are derived to guarantee mean square stable of MJSs under aperiodic DoS attacks. By solving a set of linear matrix inequalities (LMIs), the asynchronous controller is designed. At last, the effectiveness of the proposed theoretical method is certified by a numerical simulation.

Observer-Based Model Reference Tracking Control of the Markov Jump System with Partly Unknown Transition Rates

This paper deals with the model reference tracking control problem of linear systems based on the observer for Markov jump systems with unknown transition rates. The main contributions are as follows: Firstly, we designed a descriptor observer for a given model by the matrix transformation. Then, a tracking control law composed of a feedforward compensator and feedback control law was designed by calculating variations based on the designed observer. The feedback part can stabilize the system. The feedforward part is the complete parametric feedforward tracking compensator. The two parts can be solved separately, and a controller that can make the system stable is proposed under the condition that transition rates are partially unknown through the Lyapunov stability theory. The feedforward parametric solution is given by the generalized Sylvester equation. The algorithm and criteria are proved by several examples and compared with the existing conclusions.

Dynamic event-triggered [formula omitted] control for markov jump systems with input saturation

This paper is mainly to explore H∞ state feedback control problem for Markov jump systems (MJSs) with input saturation. To avoid the waste of network resources, a dynamic event-triggered mechanism (DETM) is proposed from system plant to controller, which produces a larger interval between two consecutive events compared with the traditional static one. On the basis of this model, sufficient criteria for stochastic stability of the controlled MJSs are derived by linear matrix inequalities (LMIs) and the controllers are designed. Then the maximum estimate of the domain of attraction (DOA) is obtained by the optimization procedure. Finally, examples show that the proposed DETM has better properties of saving resources than static event-triggered mechanism (ETM) while maintaining the same performance.

Adaptive control of T-S fuzzy systems with Markov switching parameters through observer-based sliding mode approach

This paper addresses the problem of observer-based adaptive sliding mode control (SMC) for nonlinear Markov jump systems (MJSs), using a Takagi-Sugeno (T-S) fuzzy model with the premise variables of fuzzy rules depend on system state. Firstly, an integral sliding surface is designed based on fuzzy observer system; Secondly, sufficient conditions for stochastic stability and $ H_{\infty} $ perturbation attenuate level are provided for the obtained sliding mode dynamics and error systems using linear matrix inequality techniques. Furthermore, an adaptive SMC law is combined with the observed state variables to ensure finite time reachability of the sliding surface. Lastly, the theory is validated with simulations based on a practical example.

Finite-Time Observer-Based Sliding-Mode Control for Markovian Jump Systems With Switching Chain: Average Dwell-Time Method.

In this article, the finite-time observer-based sliding-mode control (SMC) problem is considered for stochastic Markovian jump systems (MJSs) with a deterministic switching chain (DSC) subject to time-varying delay and packet losses (PLs). First, the stochastic MJSs with DSC are appropriately modeled and the PLs case is characterized by using some Bernoulli random variables. Then, a nonfragile finite-time bounded sliding-mode observer is designed. Our objective is to propose a finite-time observer-based SMC approach such that for the above addressed system, the finite-time boundedness in a certain time interval can be guaranteed by giving sufficient criteria via the stochastic analysis skills and average dwell time (ADT) method. Moreover, a new robust finite-time sliding-mode controller can be designed to ensure reachability of the common sliding surface in the estimation space. Finally, a numerical example is provided to illustrate our theoretical results.

Learning, Control, and Reduction for Markov Jump Systems

Learning, Control, and Reduction for Markov Jump Systems

Asynchronous Fault Detection Observer for 2-D Markov Jump Systems.

In this article, the problem of the asynchronous fault detection (FD) observer design is discussed for 2-D Markov jump systems (MJSs) expressed by a Roesser model. In general, the FD observer cannot work synchronously with the system, that is, the mode of the observer varies with the mode of the system in line with some conditional transitional probabilities. For dealing with this difficult point, a hidden Markov model (HMM) is employed. Then, combining the H∞ attenuation index and H_ increscent index, a multiobjective solution to the FD problem is formed. In terms of linear matrix inequality technology, sufficient conditions are gained to guarantee the existence of the asynchronous FD. Simultaneously, an asynchronous FD algorithm is generated to acquire the optimal performance indices. Finally, a numerical example concerned with the Darboux equation is demonstrated to exhibit the soundness of the developed approach.

Finite-Time Control for Discrete-Time Positive Systems Subject to Event-Triggered Scheme and Markov Jump Parameters

This brief investigates the finite-time control problem for discrete-time positive systems subject to event-triggered scheme and Markov jump parameters. Switching transition probability is used to extend the fixed transition probability, which is more suitable to describe the performance of Markov jump systems (MJSs). On the basis of the 1-norm, a developed event-triggered scheme is proposed to be associated with the sample signal and the actual signal. Furthermore, a linear Lyapunov function and an average dwell time approach are adopted to obtain sufficient conditions for guaranteeing stochastic finite-time stability of the underlying systems. Additionally, a matrix decomposition strategy is constructed to design a finite-time event-triggered control law such that the corresponding MJSs are positive and stochastically finite-time bounded. All conditions are proposed on the basis of linear programming. Finally, a local railway transportation model is provided to verify the practicability of the strategy.

Fuzzy-Based Adaptive Optimization of Unknown Discrete-Time Nonlinear Markov Jump Systems With Off-Policy Reinforcement Learning

This article explores a novel adaptive optimal control strategy for a class of sophisticated discrete-time nonlinear Markov jump systems (DTNMJSs) via Takagi–Sugeno fuzzy models and reinforcement learning (RL) techniques. First, the original nonlinear system model is represented by fuzzy approximation, while the relevant optimal control problem is equivalent to designing fuzzy controllers for linear fuzzy systems with Markov jumping parameters. Subsequently, we derive the fuzzy coupled algebraic Riccati equations for the fuzzy-based discrete-time linear Markov jump systems by using Hamiltonian–Bellman methods. Following this, an online fuzzy optimization algorithm for DTNMJSs as well as the associated equivalence proof is given. Then, a fully model-free off-policy fuzzy RL algorithm is derived with proved convergence for the DTNMJSs without using the information of system dynamics and transition probability. Finally, two simulation examples, respectively, related to the single-link robotic arm and the half-car active suspension are given to verify the effectiveness and good performance of the proposed approach.

Compensation-Based Output Feedback Control for Fuzzy Markov Jump Systems With Random Packet Losses.

This article is concerned with the problem of compensation-based output feedback control for Takagi-Sugeno fuzzy Markov jump systems subject to packet losses. The phenomenon of packet losses is assumed to randomly occur in the feedback channel, which is modeled by a Bernoulli process. Employing the single exponential smoothing method as a compensation scheme, the missing measurements are predicted to help offset the impact of packet losses on system performance. Then, an asynchronous output feedback controller is designed by the hidden Markov model. Based on the mode-dependent Lyapunov function, some novel sufficient conditions on the controller existence are derived such that the closed-loop system is stochastically stable with strict dissipativity. Besides, an algorithm for determining the optimal smoothing parameter is proposed. Finally, the validity and advantages of the design approach are manifested by some simulation results.

Asynchronous Frequency-Dependent Fault Detection for Nonlinear Markov Jump Systems Under Wireless Fading Channels.

In this article, the asynchronous fault detection (FD) strategy is investigated in frequency domain for nonlinear Markov jump systems under fading channels. In order to estimate the system dynamics and meet the fact that not all the running modes can be observed exactly, a set of asynchronous FD filters is proposed. By using statistical methods and the Lynapunov stability theory, the augmented system is shown to be stochastic stable with a prescribed l2 gain even under fading transmissions. Then, a novel lemma is developed to capture the finite frequency performance. Some solvable conditions with less conservatism are subsequently deduced by exploiting novel decoupling techniques and additional slack variables. Besides, the FD filter gains could be calculated with the aid of the derived conditions. Finally, the effectiveness of the proposed method is shown by an illustrative example.

Asynchronous Bumpless Transfer Finite-Time H∞ Control for Markovian Jump Systems With Application to Circuit System

This brief focuses on the asynchronous bumpless transfer finite-time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control problem for a class of Markovian jump systems (MJSs). The hidden Markov principle is introduced to represent the asynchronous jumping phenomenon between the MJSs and the designed bumpless transfer finite-time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> controller. The asynchronous jumping transient behavior of MJSs is described by using a bumpless transfer constraint index. First, an asynchronous bumpless transfer constraint is proposed to limit the control bumps caused by asynchronous jumping. Then, an asynchronous bumpless transfer finite-time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> controller is constructed, and sufficient conditions are given to ensure the finite-time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance for MJSs under the proposed asynchronous bumpless transfer method. Finally, an RLC circuit model is provided as an application example to show the effectiveness of the proposed control method.

Mean square exponential stabilisation for directional 2D Roesser hidden Markov model

ABSTRACT Based on the two-dimensional (2D) Roesser model, this paper focuses on the asynchronous controller design for directional 2D Markov jump systems (MJSs). Considering the more practical situation that the modes of the 2D MJSs in the horizontal and vertical directions are independent, and the system modes are asynchronous with that of the controller, the directional 2D MJSs are proposed and the asynchronous controller is designed, respectively. Based on the Lyapunov theory, a sufficient condition for the mean square exponential stability of the controlled directional 2D MJSs is given. Moreover, the partially unknown transition probabilities in systems and controllers are considered. Finally, an example is given to illustrate that the proposed method is effective.