Jump Markov Nonlinear Systems Research Articles

Finite-Time $$H_\infty $$ Control for Time-Delayed Markovian Jump Nonlinear Systems with Parameter Uncertainties and Generally Uncertain Transition Rates

Finite-Time $$H_\infty $$ Control for Time-Delayed Markovian Jump Nonlinear Systems with Parameter Uncertainties and Generally Uncertain Transition Rates

Security dissipative control for interval type‐2 fuzzy hidden Markovian jump systems under event‐triggered scheme

AbstractThis article presents a new design approach for resilient fault‐tolerant event‐triggered (ET) based security control of Markovian jump nonlinear systems (MJNSs) in the presence of nonperiodic denial‐of‐service (DoS) attacks. The approach is developed based on interval type‐2 (IT‐2) fuzzy models of the plant. The state error produced by data packet loss is turned into a parameter in the proposed ET condition during nonperiodic DoS attacks. The uncertain triggering variable is considered in the resilient fault‐tolerant ET condition for the MJNSs. In contrast to the usual strategy, the fault‐tolerant ET strategy is designed to send the required data packets to the controller during nonperiodic DoS attacks, which significantly contributes to the minimization of performance loss. Dissipative, passive, and ‐control schemes are all covered in a unifying framework by using a generalized performance index. Plant and controller modes are considered under mismatched membership functions to regulate asynchronous phenomena. Sufficient conditions depending on the membership functions that guarantee the stability of the closed‐loop system are derived. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed approach.

Designing asynchronous resilient sampled data controller for nonlinear Markov jump systems via hidden Markov model and quantum genetic algorithm

The article delves into the problem of stochastic stability analysis for nonlinear Markov jump systems (MJSs) with fuzzy asynchronous resilient sampled-data controllers (SDCs) using hidden Markov model (HMM) and quantum genetic algorithms (QGAs). A novel framework using QGA has been developed to obtain the control gain matrices by solving the linear matrix inequality (LMI). A new criterion is proposed to guarantee the stochastic stability of fuzzy nonlinear MJSs, relying on the mode-dependent Lyapunov-Krasovskii functional (LKF) approach. Standard Chua’s circuit has been used to show the reliability and value of the developed results. Also, the Lorentz system has been explored to demonstrate the non-stochastic case.

Dynamic Event-Triggered Control for Delayed Nonlinear Markov Jump Systems under Randomly Occurring DoS Attack and Packet Loss

This paper aims to address the exponential stability and stabilization problems for a class of delayed nonlinear Markov jump systems under randomly occurring Denial-of-Service (DoS) attacks and packet loss. Firstly, the stochastic characteristics of DoS attacks and packet loss are depicted by the attack success rate and packet loss rate. Secondly, a Period Observation Window (POW) method and a hybrid-input strategy are proposed to compensate for the impact of DoS attack and packet loss on the system. Thirdly, A Dynamic Event-triggered Mechanism (DETM) is introduced to save more network resources and ensure the security and reliability of the systems. Then, by constructing a general common Lyapunov functional and combining it with the DETM and other inequality analysis techniques, the less conservative stability and stabilization criteria for the underlying systems are derived. In the end, the effectiveness of our result is verified through two examples.

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 Asynchronous Fault Detection for Nonlinear Markov Jump Systems With Its Application: A Zonotopic Residual Evaluation Approach

In this paper, the event-triggered asynchronous fault detection (FD) problem is investigated for a class of nonlinear Markov jump systems (NMJSs) via zonotopic residual evaluation (ZRE). An adaptive event-triggered scheme (AETS) is utilized to reduce the redundant data releasing frequency such that both communication resources and network bandwidth can be saved as much as possible. The hidden Markov model (HMM) with generally hybrid probabilities is introduced into the FD framework to fully characterize the asynchronization phenomenon between the plant and the FD filter as well as the event generator and to address both the general transition and mode detection information issues simultaneously. By applying the double variables-based decoupling principle and variable substitution principle, a co-design criterion of optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{1}/H_{\infty }$</tex-math></inline-formula> asynchronous reduced-order FD filter and AETS is derived fully considering accessible mode information, such that the generated residual signal is sensitive to system faults while being robust to amplitude-bounded exogenous disturbances and measurement noise. Furthermore, a novel ZRE strategy with dynamic thresholds is developed for FD in NMJSs. Finally, an application of automotive electronic throttle body is used to illustrate the effectiveness of the proposed approach.

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.

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.

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.

A novel system identification algorithm for nonlinear Markov jump system

System identification of nonlinear Markov jump systems (NMJSs) is crucial in modeling complex systems that contain unknown continuous and discrete states. In this system, the dynamics of continuous states is governed by the discrete states, which means the system can operate among different modes. The existing studies primarily identify the mode transition probability and noise model, whereas the parameters concerning the nonlinear continuous state transition function and observation function are commonly not considered. To identify all the parameters, a novel NMJSs identification algorithm based on a new particle system is proposed. The hidden state inference is implemented via an extended smoother that embodies the new particle system and Rao-Blackwellized particle Gibbs ancestor sampling kernel. The smoother not only estimates hidden state but also enables parameter update of the nonlinear functions. After inferencing the hidden states’ posterior density, a log-likelihood-based loss function is utilized to reduce the uncertainty of identifying the parameters related to the continuous state transition function. Then expectation–maximization and gradient descent are adopted to update the parameters. Finally, different experiments are conducted to verify the proposed algorithm. The results show that the proposed algorithm can approximate the parameter that well describes the data, and outperform other related approaches.

Event-Based Asynchronous Output Feedback Control for Nonlinear Markov Jump Systems With Partially Unknown Transition Probabilities

This brief investigates the event-triggered output feedback control problem for nonlinear Markov jump systems (NMJSs) with unknown probabilities. The NMJSs with parameter uncertainties are characterized by using the interval type-2 (IT2) fuzzy model. An adaptive event-triggered strategy is utilized to decide when to transmit, which can reduce communication costs. The output feedback controller is designed, where the modes can be allowed different with the system, and the conditional probability matrix does not require completely known. Then, an event-based asynchronous output feedback control approach is proposed for obtaining the required result. With the aid of an example, we demonstrate the effectiveness of the event-based asynchronous output control algorithms.

A variational marginalized particle filter for jump Markov nonlinear systems with unknown transition probabilities

This paper studies a new variational marginalized particle filter for jointly estimating the state and the system mode parameters of jump Markov nonlinear systems. Contrary to the Markovian assumption usually considered to model the evolution of the system modes, we introduce conjugate prior distributions for the system mode parameters. The joint posterior distribution of the state and system mode parameters is then marginalized with respect to the mode variables. The remaining state vector is sampled using a sequential Monte Carlo algorithm, and the mode parameters are sampled using variational Bayesian inference. In order to obtain analytical solutions for the different variational distributions, we use an extended factorized approximation simplifying the variational distributions. A comprehensive simulation study is conducted to compare the performance of the proposed approach with the state-of-the-art for a modified nonlinear benchmark model and maneuvering target tracking scenarios.

Filter for Positive Stochastic Nonlinear Switching Systems With Phase-Type Semi-Markov Parameters and Application

In this article, the issue of positive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L}_{1}$ </tex-math></inline-formula> filter design is investigated for positive nonlinear stochastic switching systems subject to the phase-type semi-Markov jump process. Many complicated factors, such as semi-Markov jump parameters, positivity, T–S fuzzy strategy, and external disturbance, are taken into consideration. Practical systems under positivity constraint conditions and unpredictable structural changes are characterized by positive semi-Markov jump systems (S-MJSs). First, by the key properties of the supplementary variable and the plant transformation technique, phase-type S-MJSs are transformed into Markov jump systems (MJSs), which means that, to an extent, these two kinds of stochastic switching systems are mutually represented. Second, with the help of the normalized membership function, the associated nonlinear MJSs are transformed into the local linear MJSs with specific T–S fuzzy rules. Third, by choosing the linear copositive Lyapunov function (LCLF), stochastic stability (SSY) criteria are given for the corresponding system with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L}_{1}$ </tex-math></inline-formula> performance. Some solvability conditions for positive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L}_{1}$ </tex-math></inline-formula> filter are constructed under a linear programming framework. Finally, an epidemiological model illustrates the effectiveness of the theoretical findings.

Adaptive optimization algorithm for nonlinear Markov jump systems with partial unknown dynamics

AbstractAn online adaptive optimal control problem for a class of nonlinear Markov jump systems (MJSs) is studied. It is worth noting that the dynamic information of MJSs is partially unknown. Applying the neural network linear differential inclusion techniques, the nonlinear terms in MJSs are approximately converted to linear forms. By using subsystem transformation schemes, we can transfer the nonlinear MJSs to N new coupled linear subsystems. Then a new online policy iteration algorithm is put forward to obtain the adaptive optimal controller. Some theorems are given afterward to ensure the convergence of the new algorithm. At last, a simulation example is provided to verify the applicability of the algorithm.

State estimation for jump markov nonlinear systems of unknown measurement data covariance

For state estimation of high accuracy, prior knowledge of measurement noise is necessary. In this paper, a method for solving the joint state estimation problem of jump Markov nonlinear systems (JMNSs) without knowing the measurement noise covariance is developed. By using the Inverse-Gamma distribution to describe the dynamics of measurement noise covariance, the joint conditional posterior distribution of the state variable and measurement noise covariance is approximated by a product of separable variational Bayesian (VB) marginals. In the newly constructed approach, the interacting multiple model (IMM) algorithm, as well as the particle-based approximation strategy, is employed to handle the computationally intractable problem and the nonlinear characteristics of systems, respectively. An interesting feature of the proposed method is that the distribution of states is spanned by a set of particles with weights, while the counterpart of measurement noise covariance is obtained analytically. Moreover, the number of particles is fixed under each mode, indicating a reasonable computational cost. Simulation results based on a numerical example and a tunnel diode circuit (TDC) system are presented to demonstrate that the proposed method can estimate the measurement noise covariance well and provide satisfied state estimation when the statistics of the measurement are unavailable.

Fixed-time sliding mode controller design for a class of nonlinear Markovian jumping systems

In this paper, a sliding mode control (SMC) strategy is applied to investigate the fixed-time stabilization (FTS) problems for nonlinear Markovian jumping systems (NMJSs) with nonlinear parts satisfying conic conditions. We aim to design a suitable SMC law to drive the system state trajectories onto the specified sliding mode surfaces (SMS) within a specified fixed-time interval. Then, by using the slack matrix approach, the sufficient conditions are derived to ensure the FTS of MJSs during the reaching phase. An appropriate Lyapunov-Krasovskii functional method is given to guarantee the FTS of the NMJSs during the slidinging motion phase. Finally, the FTS condition of the NMJSs in the whole fixed-time interval is given and proved. The effectiveness of the method is verified by a simulation result related to the Chua’s circuit.

Robust Control for Nonlinear Markov Jump Systems with Partially Unknown Transition Probabilities

This note focuses on the finite horizon H2/H∞ control for stochastic nonlinear jump systems with partially unknown transition probabilities. We derive the nonlinear stochastic bounded real lemma and the nonlinear optimal regular result for the considered system at first. A sufficient condition and a necessary condition for the solution of H2/H∞ control are, respectively, offered by four cross-coupled Hamilton–Jacobi equations (HJEs). Besides, numerical examples show the effectiveness of the obtained results.

Sliding Mode Control of One-Sided Lipschitz Nonlinear Markovian Jump Systems With Partially Unknown Transition Rates

This paper investigates the problem of sliding mode control (SMC) for one-sided Lipschitz (OSL) nonlinear Markovian jump systems with partially unknown transition rates. Unmatched norm-bounded uncertainties of state matrices and output matrices are considered. First, a suitable integral-type sliding surface is proposed and a sufficient condition is given such that the sliding mode dynamics is stochastically stable with an H ∞ performance level γ. Next, an SMC law is synthesized such that reachability of the specified sliding surface can be ensured. Finally, two simulation examples are provided to prove the effectiveness of the proposed approach.

Novel mixed-triggered filter design for interval type-2 fuzzy nonlinear Markovian jump systems with randomly occurring packet dropouts

This paper is aimed at investigating the problem of mixed-triggered filter design for interval type-2 (IT2) fuzzy nonlinear Markovian jump systems (MJSs) with randomly occurring packet dropouts. First, an IT2 fuzzy nonlinear MJSs model with parameter uncertainties is established by using IT2 fuzzy model, and the fuzzy filter is designed with different premise variables. Second, a novel mixed-triggered scheme is addressed, which can reduce the needless waste of network resources. Then, two Bernoulli stochastic variables are employed, one to randomly switch the different modes of the mixed-triggered scheme, the other to describe the randomly occurring packet dropouts. Next, in order to ensure that IT2 fuzzy filtering error system is asymptotically stable, sufficient conditions are presented. Moreover, the existence conditions for the fuzzy filter are given by the linear matrix inequalities. Finally, simulation results are given to verify the validity of the proposed method.

Bayesian State Estimation for Markovian Jump Systems: Employing Recursive Steps and Pseudocodes

In this article, we review several existing Bayesian state-estimation algorithms for Markovian jump systems (MJSs) and illustrate their distinctive properties. Specifically, we analyze the jump Markov linear systems (JMLSs), for which autonomous multiple-model (AMM) algorithms, first-order generalized pseudo-Bayesian (GPB1) algorithms, secondorder generalized pseudo-Bayesian (GPB2) algorithms, interacting multiple-model (IMM) algorithms, and reweighed IMM (RIMM) algorithms are introduced. For nonlinear MJSs, we consider the sampling importance resampling (SIR) particle filter (PF) as well as the IMM PF to demonstrate how to handle nonlinearity in the framework of MJSs. For convenience, the realization codes of GPB1 and IMM algorithms and SIR PFs are provided.