Markovian Jump Systems Research Articles

Antidisturbance Control for Hidden Markovian Jump Systems: Asynchronous Disturbance Observer Approach

This paper investigates the anti-disturbance control issue for a class of Markovian jump systems (MJSs) with matched/mismatched disturbances by using disturbance observer approach. A key feature here is that the external disturbance is considered to be generated by a Markovian jump exogenous dynamics, in which the disturbance mode may not be synchronized with the system mode. Meanwhile, it is supposed that both system and disturbance modes can just be estimated via a hidden Markov mode detector. To overcome the possible obstacle in handling dual hidden Markov modes, a mapping technique for continuous-time Markov chain is provided firstly. Then, a novel asynchronous disturbance observer is developed to estimate the external disturbance by utilizing the detected mode. Based upon the estimated disturbance, asynchronous anti-disturbance controllers are investigated for matched and mismatched disturbance cases, respectively. By employing a decoupling technique with the idea of completing the square, sufficient conditions are established for guaranteeing the stability in probability of the resultant closed-loop systems. Finally, two numerical examples are provided to verify the effectiveness of the proposed asynchronous anti-disturbance control approaches under inaccessible system and disturbance modes.

Asynchronous Event-Triggered Output-Feedback Control of Singular Markov Jump Systems.

This study focused on the asynchronous event-triggered output-feedback controller design problem for discrete-time singular Markov jump systems (MJSs). A hidden Markov model (HMM) was employed to estimate the system mode, which cannot always be ideally detected in practice. Because the full state is also difficult to obtain in practical scenarios, an output-feedback control scheme was used. In addition, an HMM-based event-triggered mechanism was also employed in the design of the controller to reduce the communication burden of the networked system. Sufficient conditions for the stochastic admissibility of a closed-loop singular MJS with a prescribed H∞ performance index were established using the Lyapunov functional technique. Finally, design procedures for an asynchronous event-triggered controller were summarized as a linear-matrix-inequality-based optimization algorithm. Two examples were considered to verify the effectiveness of the asynchronous event-triggered output-feedback controller design method.

Asynchronous H∞ Control for Continuous-Time Hidden Markov Jump Systems With Actuator Saturation.

In this article, we address the asynchronous H∞ control problem of a class of hidden Markov jump systems (HMJSs) subject to actuator saturation in the continuous-time domain. A bunch of convex hulls is utilized to represent the saturated nonlinearity. Considering that there is an asynchronous mode mismatch between the system and the controller, we establish a hidden Markov model (HMM) to simulate the situation. By means of the Lyapunov theory, sufficient conditions are presented to ensure that the resultant closed-loop HMJS is stochastically mean square stable within the domain of attraction with a prescribed H∞ performance index. Furthermore, the state feedback gain matrix and the estimation of the domain of attraction are given by solving an optimization problem, which is constructed via linear matrix inequality (LMI) techniques. Finally, the reliability and validity of the derived results are examined by a numerical example.

Asynchronous Dissipative Control of Discrete-Time Fuzzy Markov Jump Systems With Dynamic State and Input Quantization

A numerically tractable two-step approach based on backtrack and optimization searches is proposed for asynchronous quantized dissipative control of discrete-time fuzzy Markov jump systems (DFMJSs) under the networked control framework. The asynchrony of modes between the plant and controller is described by a hidden Markov model. Both dynamic state and input quantization are considered. The dynamic zooming factors of the quantizers are designed as piecewise functions with respect to their arguments to avoid division by zero. A fuzzy asynchronous quantized controller is devised to make sure that the closed-loop system is stochastically stable and strictly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\mathcal {Q},\mathcal {S},\mathcal {R})$</tex-math></inline-formula> - dissipative via using a quadratic Lyapunov function and equivalent matrix transformations. Then, the iterative two-step approach is used to determine the optimal dissipativity level and the corresponding control gain and quantization parameters. Analysis and control synthesis for DFMJSs without quantization are also presented, covering some previous results as special cases. Finally, a single-link robot arm system and another numerical example are utilized to validate the present asynchronous dissipative control approaches for the quantization and non-quantization cases, respectively.

$$\mathcal {H}_{\infty }$$ Control of Time-Delayed Markov Jump Systems Subject to Mismatched Modes and Interval Conditional Probabilities

$$\mathcal {H}_{\infty }$$ Control of Time-Delayed Markov Jump Systems Subject to Mismatched Modes and Interval Conditional Probabilities

A design of fuzzy sliding mode control for Markovian jumping system with different input matrices

In this paper, by means of sliding mode control (SMC), the problem resulted by local input matrices is investigated for fuzzy markovian jumping system. The stability of the considered fuzzy Markovian system with multiple sub-input matrices can be fulfilled using the method in this paper. First, the state equation of the considered system is transformed according to the input matrices. Second, according to the state equation, sliding mode surface is constructed. This surface contains several sub-surfaces. It can deal with this kind of fuzzy Markovian system with multiple sub-input matrices and uncertainties. And another characteristic is that there is not the process of reaching the sliding mode surface; It can settle the problem resulted by Markovian jumping and sliding mode method together. Third, by use of the Cramer's rule, a criterion is provided to judge the existence of sliding mode dynamics equation. A controller containing several sub-controllers components is designed. And these sub-controllers should keep the considered system on the several sub-surfaces and not leave it. At last, simulations are provided to illustrate the validity of the method in this paper.

Event-Triggered SMC for Networked Markov Jumping Systems With Channel Fading and Applications: Genetic Algorithm.

The event-triggered sliding-mode control (SMC) for discrete-time networked Markov jumping systems (MJSs) with channel fading is investigated by means of a genetic algorithm. In order to reduce resource consumption in the transmission process, an event-triggered protocol is adopted for networked MJSs. A key feature is that the signal transmission is inevitably affected by fading phenomenon due to delay, random noise, and amplitude attenuation in a networked environment. With the aid of a common sliding surface, an event-triggered SMC law is designed by adjusting the system network mode. Under the framework of stochastic Lyapunov stability, sufficient conditions are constructed to ensure the mean-square stability of the closed-loop networked MJSs, and the sliding region is reached around the specified sliding surface. Moreover, based on the iteration optimizing accessibility of objective function, an effective SMC approach under genetic algorithm is proposed to minimize the convergence region around the sliding surface. Finally, the effectiveness of the proposed method is proved by the F-404 aircraft model.

Finite-Region Dissipative Control for 2-D Fuzzy Jump Systems Under Hidden Mode Detection

In this work, we consider the problem of finite-region asynchronous dissipative control and pay more attention to the transient behavior of a class of two-dimensional fuzzy Markov jump systems (MJSs). First, the considered plant is modeled based on a well-known Fornasini–Marchesini equation. The asynchronization phenomenon between the system modes and controller modes is characterized by a hidden Markov model. Then, by a fuzzy-basis-dependent and mode-dependent Lyapunov function, sufficient conditions are established, which can make the overall closed-loop fuzzy dynamic MJSs be finite-region bounded with a strictly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(T, S, R)$</tex-math> </inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta$</tex-math> </inline-formula> -dissipative performance. Finally, a numerical example concerning the Darboux equation is employed to validate the effectiveness and performance of the presented control scheme.

Asynchronous Sliding Mode Control for Nonlinear Markov Jumping Systems With PDT-Switched Transition Probabilities

This paper studies the asynchronous sliding mode control for nonlinear Markov jump systems (NMJSs), whose transition probabilities is piecewise-constant and subjected to the persistent dwell-time (PDT) switching rule. By resorting to the interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy set theory, the nonlinearity and uncertainty features of the investigated systems are modeled. Taking the uncertain membership functions (MFs) of IT2 T-S fuzzy systems into consideration, the non-parallel distributed compensation strategy is employed for designing the MFs of the controller such that them do not need to be obtained in time. Furthermore, in view of the difficulty of accurately acquiring the mode of NMJSs with complex transition probabilities, the hidden Markov model is employed to provide a detected mode for constructing the sliding mode law. Afterwards, a novel fuzzy sliding surface is proposed, and an asynchronous IT2-fuzzy-model-based sliding mode control law is designed for forcing the closed-loop systems to move on the predefined sliding surface. Thereafter, a novel two-mode-dependent Lyapunov-like function is conceived for the studied systems, where modes of NMJSs and transition probabilities are permitted to change simultaneously. Through applying an improved technique to handle the parametric matrix inequalities, some less-conservative sufficient conditions in the form of linear matrix inequality are obtained for ensuring the stochastic exponentially asymptotical stability of the sliding mode with <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. Finally, a mass-spring mechanical system is presented to substantiate the validity of the proposed main results.

Adaptive event-triggered output tracking control for Markovian jump systems: A robust [formula omitted] MPC approach

This work focuses on the output tracking control for discrete-time Markov jump systems (MJSs) via a model predictive control (MPC) approach. Not only the mean-square stability (MSS), but also the H2 performance and H∞ performance is considered in the MPC controller design. To save communication resources, a version of adaptive event-triggered mechanism (AETM) is utilized. Different from the traditional static event-triggered mechanism, its threshold coefficient 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 MPC controller such that not only the augmented closed-loop system is MSS with a certain level of H2/H∞ performance, but also the communication burden can be reduced to some extent. It is the first attempt to investigate the output tracking control of MJSs via an MPC approach. By constructing a plant model-dependent Lyapunov function, a set of conditions is derived to determine a desired MPC controller. In addition, two MPC related issues, namely recursive feasibility and closed-loop MSS, are also studied. At last, an illustrative example is given to verify the availability of the theoretical findings.

Adaptive neural network control for Markov jumping systems against deception attacks

This paper proposes an innovative approach for mitigating the effects of deception attacks in Markov jumping systems by developing an adaptive neural network control strategy. To address the challenge of dual-mode monitoring mechanisms, two independent Markov chains are used to describe the state changes of the system and the intermittent actuator. By employing a mapping technique, these individual chains are amalgamated into a unified joint Markov chain. Additionally, to effectively approximate the unbounded false signals injected by deception attacks, an adaptive neural network technique is skillfully built. A mode monitoring scheme is implemented to design an asynchronous control law that links the mode information between the joint Markov chain and controller with fewer modes. The paper derives sufficient criteria for the mean-square bounded stability of the resulting system based on Lyapunov theories. Finally, a numerical experiment is conducted to demonstrate the effectiveness of the proposed method.

Co-Design of Adaptive Event-Triggered Mechanism and Asynchronous H∞ Control for 2-D Markov Jump Systems via Genetic Algorithm.

This article concerns the co-design scheme of the adaptive event-triggered mechanism (AETM) and asynchronous H∞ control for two-dimensional (2-D) Markov jump systems. First, we introduce a hidden Markov model with the observation that the asynchronous phenomenon is inevitable between the plant mode and the controller mode. Besides, for economizing the communication times, an innovative 2-D AETM is constructed, which can dynamically regulate the event-triggered thresholds to strive for better system performance. Then, by utilizing the 2-D Lyapunov stability theory, nonlinear matrix inequalities are built to ensure the asymptotic mean-square stability with an H∞ performance for the closed-loop 2-D system. To avoid introducing any conservatism when handling the above nonlinear matrix inequalities, a binary-based genetic algorithm (BGA) is exploited to treat some variables as known, such that derive some directly solvable linear matrix inequalities. Finally, a simulation example is provided to verify the effectiveness of the proposed 2-D AETM-based asynchronous controller strategy with a BGA.

Asynchronous Event-Triggered-Based Control for Stochastic Networked Markovian Jump Systems With FDI Attacks

In this article, a new asynchronous event-triggered-based output-feedback control method is proposed for a special type of networked Markovian jump systems susceptible to network delays and attacks. A novel controller is designed to make allowances for four cases that are common in practical situations: 1) a network delay; 2) false data injection (FDI) attacks; 3) asynchrony between system modes and controller modes; and 4) an event-triggered scheme. First, to avoid traditional assumptions about system delays, a novel Lyapunov function is proposed, based on which a new stability theory is formulated to guarantee exponential stability. Second, an FDI attack is represented as a stochastic process, which can be dealt with properly by the designed controller. Third, a new delay-based event-triggered scheme is brought into the controller design to reduce the network bandwidth consumption and save the network transmission resources. Then, an asynchronous controller is engineered with the aid of a hidden-Markov model, which can extend the application scope of the proposed method. Note that we put the above four factors into one framework, which implies a co-design of an anti-attack controller and an event-triggered scheme is developed. Finally, an operational amplifier circuit is simulated to verify the feasibility and superiority of the designed controller.

Event-Triggered Quantized Stabilization of Markov Jump Systems under Deception Attacks

This paper focuses on the event-triggered quantized control for Markov jump systems with deception attacks. First, we design an event-triggered scheme relying on dwell time and end instants of attacks. It can limit the number of switches within the triggered intervals and the lower bound of triggered instants. Second, the quantization rules and the increasing/decreasing rate of Lyapunov function are obtained for different cases. Next, combined with the increasing/decreasing rate, the lower bound of triggered instants, and the probability of switches occurring, the upper bound of Lyapunov function at the triggered instants is provided. On this basis, sufficient conditions ensuring the exponential convergence in the mean sense of the closed-loop system are given. Finally, atwo-tank system is provided to verify the effectiveness of the proposed stability analysis framework for Markov jump systems.

Co-Design of Adaptive Event Generator and Asynchronous Fault Detection Filter for Markov Jump Systems via Genetic Algorithm.

This article investigates the co-design problem of adaptive event-triggered schemes (AETSs) and asynchronous fault detection filter (AFDF) for nonhomogeneous higher-level Markov jump systems, involving the hidden Markov model (HMM), higher-level Markov chain (MC), and conic-type nonlinearities. The transformation of the system transition probability can be reflected by the designed higher-level MC. An HMM with another conditional transition probability is applied to detect higher-level Markov processes and make the system be more practical. In order to balance the utilization of network resources and system performance, a novel AETS is proposed and used in the construction of the AFDF. By the Lyapunov theory, sufficient conditions are given to ensure the existences of the AETS and AFDF. It is not only an appropriate tradeoff between the utilization of network resources and system performance, but also reduces the conservatism. Finally, a numerical example is given to detect the faults effectively by the co-designed AFDF.

Asynchronous Output Regulation Control for Continuous-Time Markovian Jump Systems with Colored-Noise

Asynchronous Output Regulation Control for Continuous-Time Markovian Jump Systems with Colored-Noise

Dynamic output feedback model predictive control for asynchronous Markovian jump systems under try‐once‐discard protocol

AbstractThis paper is concerned with the dynamic output feedback robust model predictive control (RMPC) problem for a class of discrete‐time asynchronous Markovian jump systems (MJSs) subject to polytopic parameter uncertainties and hard constraints on states and inputs. A hidden Markov model is employed to describe the asynchronous phenomenon between the detected modes and the system modes. For the purpose of improving the network utilization as well as reducing the transmission burden and avoiding data collisions, the try‐once‐discard (TOD) protocol is deployed in the shared communication network between sensor nodes and the controller node. Considering the difficulty of obtaining the system state in the practice, the dynamic output‐feedback control in the framework of RMPC is adopted, and the worst‐case optimization problem over the infinite moving horizon is formulated for the performance analysis and control synthesis. By means of the Lyapunov‐like function approach, free weighting matrices and inequality techniques such as the ‐procedure are introduced to deal with the non‐convexity caused by couplings between decisive variables and the negative influence resulting from the data orchestration is mitigated. Based on the delicate establishments, a certain upper bound of the objective function is employed to construct an auxiliary optimization problem with solvability to find the desired controllers, and sufficient conditions are obtained to guarantee that the MJSs under the proposed RMPC‐based controllers are mean‐square stable. Finally, an illustrative example is used to demonstrate the validity of the proposed methods.

Predictive control of linear discrete-time Markovian jump systems by learning recurrent patterns

Incorporating pattern-learning for prediction (PLP) in many discrete-time or discrete-event systems allows for computation-efficient controller design by memorizing patterns to schedule control policies based on their future occurrences. In this paper, we demonstrate the effect of PLP by designing a controller architecture for a class of linear Markovian jump systems (MJSs) where the aforementioned “patterns” correspond to finite-length sequences of modes. In our analysis of recurrent patterns, we use martingale theory to derive closed-form solutions to quantities pertaining to the occurrence of patterns: (1) the expected minimum occurrence time of any pattern from some predefined collection, (2) the probability of a pattern being the first to occur among the collection. To make our method applicable to real-world dynamics, we make two extensions to common assumptions in prior pattern-occurrence literature. First, the distribution of the mode process is unknown, and second, the true realization of the mode process is not observable. As demonstration, we consider fault-tolerant control of a dynamic topology-switching network, and empirically compare PLP to two controllers without PLP: a baseline based on the novel System Level Synthesis (SLS) approach and a topology-robust extension of the SLS baseline. We show that PLP is able to reject disturbances just as effectively as the topology-robust controller at reduced computation time and control effort. We discuss several important tradeoffs, such as the size of the pattern collection and the system scale versus the accuracy of the mode predictions, which show how different PLP implementations affect stabilization and runtime performance.

Reliable fuzzy control of uncertain nonlinear networked systems under actuator faults

This study investigates a reliable fuzzy static-output feedback control (SOFC) scheme for uncertain Takagi–Sugeno fuzzy model (TSFM)-based nonlinear systems under the networked induced delays, information package losses and actuator faults, simultaneously. For this purpose, firstly, a comprehensive model for the actuator fault is suggested to enhance the performance of the actuator in the networked control systems (NCSs). More precisely, the suggested model contains an additive stochastic perturbation term in the actuator to further realize the control scheme. Besides, the Markov chain (MC) is employed to model the networked induced arbitrary delays and the information package losses. Hence, the corresponding closed-loop system lies in the Markovian jump systems (MJS). Then, based on the Lyapunov theory, the stochastic robust stability of the obtained system is studied and necessary conditions are extracted in new offline linear matrix inequalities (LMIs). Since the accurate value of the transition probabilities (TP) of the MC is not definite and even the identification is difficult, in view of practical applications in our control strategy, partly unknown TPs are assumed. Finally, to validate the superiorities of the suggested control approach, a truck-trailer system is adopted and simulated. The simulation results confirm the superiorities of the suggested control approach.

The Multiple Model Poisson Multi-Bernoulli Mixture Filter for Extended Target Tracking

In an intelligent transportation system (ITS), the single motion model is not enough to meet the needs of simulation systems (or practical applications) and guarantee good tracking performance for multiple maneuvering extended target tracking (ETT). This paper presents multiple models Poisson multi-Bernoulli mixture (MM-PMBM) filter for extended target tracking to address this problem. To make multiple models transform in an accurate manner, the jump Markov system (JMS) is timely introduced in filtering recursion. After that, the model probability of target is recursively updated and used to estimate the target position. In addition, we derive the closed-form solution to the proposed filter based on the Gamma Gaussian inverse-Wishart (GGIW) implementation. The approach to handling the merging problem of GGIW components via Kullback-Leibler divergence (KLD) minimization is also presented, resulting in better utilization of available components. Simulation results demonstrate that the proposed filter has superior performance in comparison to several state-of-the-art multi-target filters.