Asynchronous passive control under event‐triggered scheme for discrete‐time Markov jump systems with complex probabilities

This article addresses the dissipativity-based asynchronous repetitive control problem for networked Markovian jump systems subject to time delays and partly accessible mode detection probabilities. A hidden Markov model is introduced to describe the asynchronous phenomenon between the system modes and controller modes. Based on this, an asynchronous repetitive controller is proposed. By utilizing the lifting technique, the 1-D delayed Markovian jump system and controller governing equations are converted into a stochastic and closed-loop 2-D delayed model to describe the control and learning actions. Utilizing a stochastic Lyapunov functional, sufficient conditions in terms of matrix inequalities are derived such that the closed-loop system is mean-square stable and achieves the specified (W <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , W <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , W <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> ) -γ-dissipative performance. Under the assumption that the input matrix is full column rank in all modes of operation, a set of feasible sufficient conditions described by linear matrix inequalities is established by making use of the Schur complement. A procedure for synthesizing the controller parameters is also provided. A detailed numerical example with simulation results is presented to validate the proposed dissipativity-based asynchronous repetitive control design scheme.

This paper concerns the issue of finite-time dissipative asynchronous output feedback control for a wind turbine system that can be modelled as Markov jump Lur'e systems. Due to quantisation, time delays and ubiquitous data dropouts, the actual controller modes in practical application cannot always operate synchronously with the plant modes. To conquer this difficulty, a hidden Markov model is employed to provide some estimated modes information for controlling. In addition, by the Lyapunov function approach and linear matrix inequality technology, sufficient conditions are developed to guarantee finite-time boundedness of the continuous-time closed-loop system subject to strictly -α-dissipative performance. Finally, a simulation example of a wind turbine system is given to verify the correctness and applicability of the proposed controller.

This paper is concerned with the asynchronous dissipative control for discrete-time singular Markov jump systems with multiplicative noises. In a real set, noises always exist in the state or output measurement, which may cause some errors and decrease system performance. Without loss of generality, both state and output multiplicative noises are considered in this paper. The singular systems, which could widely describe more general systems and present traits of physical features, are discussed in this paper. Using a Markov chain to model the asynchronous jumps existing in system modes and controller modes. Through a method of LMI, the sufficient conditions are derived and the asynchronous controller is designed to ensure that the singular Markov jump systems are stochastically admissible and strictly dissipative.

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.

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.

The most important challenge of the spectrum sensing in cognitive radio (CR) is to find a way to share the licensed spectrum without interfering with the licensed user transmission. Predicting the near future of the licensed or primary user (PU) channel state can solve this problem. Many studies have investigated the primary user channel state prediction in recent literature, in this study we introduce new approach for PU channel state prediction in time domain based on hidden Markov model (HMM) and Markov switching model (MSM). In our new approach we use a time series to capture the primary user channel state detection sequence (PU channel “idle” or “occupied”). Then, we fed this time series as an observation sequence into HMM and MSM algorithm to predict the switching time between the two states, “idle and occupied” before it happens so that the secondary user (SU) can adjust its transmission strategies accordingly. The experimental results show that all HMM and MSM perform very well for PU channel state prediction. It has also shown in a simulation comparison between HMM and MSM algorithm that MSM algorithm can preform without need for training process and provide a smoother prediction with low computational complexity than HMM.

This article deals with the problem of multiple-event-triggered dissipative tracking control for nonlinear Markov jump systems with incomplete transition probabilities. An interval type-2 fuzzy model with partially known transition probability matrix is used to capture the underlying nonlinearities and a hidden Markov model with an incomplete conditional probability matrix is employed to describe the possible asynchronous phenomenon between the plant and the tracking controller. A multiple-event-triggered methodology involving two adaptive event-triggered schemes for the actuator channel and the sensor channel is proposed. By using the Lyapunov and dissipativity theory, sufficient conditions for the desired tracking controller are established in terms of linear matrix inequalities. Last, two examples, involving one numerical and one practical model named the Hénon system, are utilized to show the effectiveness of the proposed tracking control algorithm.

In this article, an investigation about the issue of fuzzy event-triggered asynchronous dissipative control for T–S fuzzy Markov jump systems (FMJSs) with unknown transition probabilities and nonuniform sampling is conducted. First of all, a mode-dependent looped Lyapunov–Krasovskii functional (LKF) is proposed, which takes full use of the available information not only from sawtooth structure characteristics but also from the inner sampling dynamics. Meanwhile, a hidden Markov chain is employed to depict the mismatch between the original system and the state-dependent fuzzy event-triggered controller. Then, based on the LKF methodology, matrix inequality techniques, and the reciprocally convex combination protocol, some relaxed criteria with respect to the stochastic stable of the considered system and the desired dissipative performance are derived, simultaneously. A numerical experiment is given to illustrate the significance of the theoretical results.

This paper is concerned with filtering of hidden Markov processes (HMP) which possess (or approximately possess) the property of lumpability. This property is a generalization of the property of lumpability of a Markov chain which has been previously addressed by others. In essence, the property of lumpability means that there is a partition of the (atomic) states of the Markov chain into aggregated sets which act in a similar manner as far as the state dynamics and observation statistics are concerned. We prove necessary and sufficient conditions on the HMP for exact lumpability to hold. For a particular class of hidden Markov models (HMM), namely finite output alphabet models, conditions for lumpability of all HMP representable by a specified HMM are given. The corresponding optimal filter algorithms for the aggregated states are then derived. The paper also describes an approach to efficient suboptimal filtering for HMP which are approximately lumpable. By this we mean that the HMM generating the process may be approximated by a lumpable HMM. This approach involves directly finding a lumped HMM which approximates the original HMM well, in a matrix norm sense. An alternative approach for model reduction based on approximating a given HMM by an exactly lumpable HMM is also derived. This method is based on the alternating convex projections algorithm. Some simulation examples are presented which illustrate the performance of the suboptimal filtering algorithms.

In recent years, the problems of asynchronous control and filtering for Markov jump systems (MJSs) have received great research attention from scientific and engineering communities. The asynchronous situation between the original MJSs and the controller/filter is modelled by the hidden Markov model (HMM). This work gives a survey on the recent development of the HMM-based asynchronous controller and filter design for different MJSs, covering linear MJSs, fuzzy MJSs, semi-MJSs and 2D MJSs. Finally, a conclusion is drawn and the potential future research directions of MJSs are also discussed.

The finite-time asynchronous strict passive control for fuzzy Markov jump systems via output feedback is studied in this paper. The asynchronization is between the controller mode and the system mode and it can be described by the hidden Markov model. Applying Takagi-Sugeno fuzzy techniques, we ensure the finite-time boundedness and strict passivity of the fuzzy Markov jump systems by a suitable Lyapunov function. Then, we obtain the asynchronous strictly passive controller gains by solving a train of linear matrix inequalities. Finally, the correctness and feasibility of this designed method are illustrated by an example.

This paper is concerned with the issue of hybrid‐triggered scheme asynchronous control for networked Markov jump systems (MJSs) with probabilistic cyber attacks. First, in view of the subsistent phenomenon that the controller cannot capture the system modes synchronously, the hidden Markov model (HMM) with partly unknown probabilities is introduced in this article to describe such asynchronous phenomenon. In addition, the hybrid‐triggered scheme includes time‐triggered scheme and event‐triggered scheme, in which the switching signal between two schemes obeys random Bernoulli distribution. By utilizing Lyapunov stability theory and matrix inequality technique, some sufficient conditions are developed, which can guarantee the networked MJSs mean‐square asymptotically stable (MSAS) and performance; also, the desired controller gains are obtained by singular value decomposition (SVD) methods. Moreover, as the special cases of the results above, three corollaries are given. Finally, a numerical example and a pulse width‐modulation‐driven boost converter (PWMDBC) model are provided to demonstrate the usefulness and reliability of our developed approaches.

Spectrum prediction plays a critical role in cognitive radio networks because it is promising to significantly speed up the sensing process and hence save energy as well as improve resource utilization. However, most existing spectrum prediction models are not able to fully explore the hidden correlation among adjacent observations or appropriately describe the channel behavior. In this paper, we propose a novel prediction approach termed high-order hidden bivariate Markov model (H^2BMM), by leveraging the advantages of both HBMM and high-order. H^2BMM applies two dimensional parameters, i.e., hidden process and underlying process, to more accurately describe the channel behavior. In addition, the current channel state is predicted by observing multiple previous states. Extensive simulations are conducted and results verify that the prediction accuracy is significantly improved using the proposed H^2BMM compared with traditional Hidden Markov Model (HMM) and Hidden Bivariate Markov Model (HBMM).

Asynchronous boundary stabilization for T-S fuzzy Markov jump delay reaction-diffusion neural networks

This paper considers the problem of asynchronous guaranteed cost control (GCC) for nonlinear Markov jump systems with stochastic quantization. Hidden Markov model is used to describe the nonsynchronous controller and the random quantization phenomenon. Based on Takagi-Sugeno fuzzy technique and Lyapunov function approach, a sufficient condition is obtained, which can not only ensure the asymptotic stability of the closed-loop system and existence of the desired controller, but also can yield the minimal upper bound of GCC performance. Finally, two examples are provided to demonstrate the correctness and reliability of our developed approaches.