An Improved Jump Model for Two-Dimensional Markov Jump Roesser Systems and Its H∞ Control.

Robust Control, Optimization, and Applications to Markovian Jumping Systems

This article intends to study the asynchronous control problem for 2-D Markov jump systems (MJSs) with nonideal transition probabilities (TPs) under the Roesser model. Two practical considerations motivate the current work. First, considering that the system mode cannot always be observed accurately, a hidden Markov model (HMM) is adopted to describe the relationship between the mismatched modes. Second, considering that the TPs information related to the Markov process and the observation process is difficult to obtain, the nonideal TPs (unknown or uncertain) are simultaneously considered on the two processes. Under the considerations, several new sufficient conditions are developed for concerned closed-loop 2-D MJSs with nonideal TPs, by which the asymptotic mean square stability is ensured with an H∞ performance index. A nonconservative separation strategy is utilized to decouple the system mode TPs and the observation TPs to facilitate the analysis of nonideal TPs. An unified LMI-based condition is finally developed for the concerned closed-loop 2-D MJSs with/without nonideal TPs, showing more satisfactory conservatism than that in the literature. In the end, we present two examples to validate the superiority of the proposed design method.

This paper investigates the consensus problem of second‐order Markovian jump multi‐agent systems with delays. Both network‐induced random delay and node‐induced state delay are considered, where the network‐induced random delay, subjected to a Markov chain, exists in the switching signal and the node‐induced state delay, related to switching topologies, is heterogeneous between any two linked agents. In order to reduce communication and control energy, an impulsive protocol is proposed, where each agent only can get delayed relative positions to neighbors and the velocity of itself at impulsive instants. By performing three steps of model transformation and introducing a mapping for two independent Markov chains, the consensus problem of the original continuous‐time system is equivalent to the stability problem of a discrete‐time expand error system with two Markovian jumping parameters and a necessary and sufficient criterion is derived. A numerical example is given to illustrate the effectiveness of the theoretical result.@@@@This work is supported by the National Natural Science Foundation of China under Grants 61374171, 61572210, and 51537003, the Fundamental Research Funds for the Central Universities (2015TS030), and the Program for Changjiang Scholars and Innovative Research Team in University (IRT1245).

Adaptive neural network control for Markov jumping systems against deception attacks

Output Feedback Stabilization of Networked Brushless DC Motor with Random Delay via Markovian Jump Systems

Stability analysis of two-dimensional Markovian jump state-delayed systems in the Roesser model with uncertain transition probabilities

A design procedure for state feedback controllers is derived for uncertain stochastic systems. The controller ensures that the closed loop system is asymptotical mean square stable with stabilizing degree α, and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> bound is less than some given scalars. Based on linear matrix inequalities (LMI) method and convex optimization algorithm, this paper gets one sufficient condition, which guarantees the closed-loop is with stabilizing degree α and the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> bound is least. Furthermore, the robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> optimization controller design and the least H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> bound are presented via solving one convex optimization problem with LMI constraints.

This paper is concerned with the stochastic stabilization problem for a class of networked control system (NCS) with destabilizing transmission factors. By introducing the effective sampling instant to model random time delays and successive packet dropouts as two independent Markov chains, NCS is modeled as a discrete-time Markovian jump linear system with mixed integrated Markovian jumping parameters. In this way, a novel framework to analyze the stochastic stabilization problem of NCS is provided. The necessary and sufficient conditions for the stochastic stabilization of the NCS are obtained by the Lyapunov method and the state-feedback controller gain that depends on the delay modes is obtained in terms of the linear matrix inequalities (LMIs) formulation via the Schur complement theory. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

This paper deals with the problem of simultaneously detecting and tracking multiple maneuvering targets. The multitarget, multi-Bernoulli (MeMber) filter based track-before-detect (TBD) is an attractive approach to detect and track targets at low signal-to-noise (SNR). However, MeMber-TBD with a fixed motion model is not general enough to accommodate maneuvering targets. In this paper, a new MeMber filter in the TBD context is proposed to cope with unknown and time-varying number of maneuvering targets. We extend the basic MeMber-TBD with Jump Markov System (JMS) multi-target models to accommodate target birth, death and switching dynamics. The recursive prediction and update equations of the proposed JMS-MeMber-TBD are derived and implemented using the sequential Monte Carlo (SMC) approximations. Simulation results for a challenging tracking scenario prove the effectiveness of the proposed algorithm.

This paper investigates the problem of state feedback controller design for discrete-time Markovian jump systems (MJSs) with time delay and two Markov chains under partly known transition probabilities. First, by constructing improved Lyapunov-Krasovskii functional (LKF), utilizing the properties that the sum of each row is one in a transition probability matrix and some tractable linear matrix inequalities (LMI), a sufficient condition is established such that the system under consideration is stochastically stable. Second, the design method of time-delay-dependent state feedback controller is proposed to ensure that the resulting closed-loop system is stochastically stable. Since no free matrix variables are applied under the proposed conditions, the method proposed reduce the complexity of calculations. Finally, two simulation examples are presented to show the effectiveness of the proposed method. Compared with the existing literature, in the proposed method not only the conservatism is reduced under the derived stability and stabilization conditions, but also the total number of matrix inequalities is less.

ABSTRACTThis study proposes a fault-tolerant control method for stochastic systems with multiple intermittent faults (IFs) and nonlinear disturbances, and both sensor and actuator faults are considered. The occurrence and disappearance of IFs are governed by Markov chain, and its transition probabilities are partly known. Hence, the faulty system can be described by a Markovian jump system (MJS). In order to ensure that the MJS is stochastically stable and satisfies H∞ performance index, mode-dependent output feedback controllers are modelled using linear matrix inequalities. Numerous sufficient conditions for stochastic stability are obtained on the basis of Lyapunov stability theory. Finally, the effectiveness of the developed method is evaluated on the three-tank system.

This paper investigates the problem of quantized filtering for a class of continuous‐time Markovian jump linear systems with deficient mode information. The measurement output of the plant is quantized by a mode‐dependent logarithmic quantizer, and the deficient mode information in the Markov stochastic process simultaneously considers the exactly known, partially unknown, and uncertain transition rates. By fully exploiting the properties of transition rate matrices, together with the convexification of uncertain domains, a new sufficient condition for quantized performance analysis is first derived, and then two approaches, namely, the convex linearization approach and iterative approach, to the filter synthesis are developed. It is shown that both the full‐order and reduced‐order filters can be obtained by solving a set of linear matrix inequalities (LMIs) or bilinear matrix inequalities (BMIs). Finally, two illustrative examples are given to show the effectiveness and less conservatism of the proposed design methods.

This paper is focused on the synchronous control problem of teleoperation robot arms based on Markov jump linear systems. More specifically, a drive-response Markov model is used to describe the master and slave teleoperation robot arms system. According to linear matrix inequalities (LMIs), we propose a stability condition for Markov jump systems using mode-dependent controllers based on a stochastic Lyapunov function. Singular value decomposition and sparse matrix structuring methods are used to prove the teleoperation control system is stochastically stable. Finally, a simulation example is presented to prove the correctness and truth of the inference.

The problems of delay‐dependent exponential passivity analysis and exponential passification of uncertain Markovian jump systems (MJSs) with partially known transition rates are investigated. In the deterministic model, the time‐varying delay is in a given range and the uncertainties are assumed to be norm bounded. With constructing appropriate Lyapunov‐Krasovskii functional (LKF) combining with Jensen’s inequality and the free‐weighting matrix method, delay‐dependent exponential passification conditions are obtained in terms of linear matrix inequalities (LMI). Based on the condition, desired state‐feedback controllers are designed, which guarantee that the closed‐loop MJS is exponentially passive. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.

This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems (MJSs) with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities (LMIs), which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.