Dissipativity-based finite-time asynchronous output feedback control for wind turbine system via a hidden Markov model

This paper deals with the asynchronous passive control based on event‐triggered scheme for Markov jump systems with complex probabilities. A hidden Markov model with uncertain and unknown conditional probabilities is presented to describe the asynchronization. The complex probabilities consider that both transition probability matrix and conditional probability matrix in hidden Markov model contain uncertain and unknown elements simultaneously, with the former governing the jump of system mode and the latter representing the asynchronous relation between the system mode and the controller mode. Asynchronous control strategies based on hidden Markov model with complex probabilities are proposed under event‐triggered scheme. Furthermore, sufficient conditions are established to guarantee the stochastic passivity, under which the mode‐dependent controller gains and weighting matrices in the event‐triggered scheme are co‐designed. Theoretical results are finally verified via an example.

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.

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 this article, the issue of dissipative asynchronous control for continuous-time T–S fuzzy singular Markov jump linear parameter-varying systems against dual deception attacks under the dynamic event-triggered transmission protocol (DETP) is investigated. Firstly, the DETP is offered to further abate the channel congestion caused by the limited bandwidth. Meanwhile, the mutually independent random variables subject to Bernoulli distribution are utilized to model the dual deception attacks, which can destroy the integrity of the considered system to some degree. Besides, since the controller can not accurately receive the system information, a hidden Markov model is established to depict the asynchronous phenomenon. Specifically, in the light of the parameter-dependent Lyapunov functional, the stochastic admissible criterion of the closed-loop system with certain dissipative performance and uncertain transition rates is obtained. Ulteriorly, based on the parameter-dependent linear matrix inequalities, a cooperative design technique of asynchronous controller and the weighting matrix of the DETP is proposed. Finally, two examples of chaotic systems and electric truck-trailer systems under the DETP are given to illustrate the feasibility of the proposed method.

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.

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

The paper concerns the problem of reliable dissipative asynchronous controller design for a type of stochastic Markov jump systems (MJSs) with general conditional probabilities in the presence of the dynamic event-triggered rule. Since the mode information of the stochastic MJS is impossible to obtain, a reliable asynchronous controller is established such that the phenomena of nonsynchronous modes between the original stochastic MJS and the developed controller is formulated as a hidden Markov model. A novel dynamic event-triggered strategy is constructed to further decrease the data transmission frequency over the communication network. By taking the internal dynamic variable into account, the criteria of stochastically stable with the reliable dissipativity performance for the resulting closed-loop stochastic MJS are provided based on a collection of linear matrix inequalities. Further, the designs of reliable dissipative asynchronous controller and the dynamic event-triggered strategy are developed simultaneously. Lastly, a numerical instance is supplied to elucidate the superiority of proposed method.

This thesis is concerned with the dissipative control and filtering problems of singular systems. Four classes of singular systems are considered: delay-free singular systems, singular systems with constant time-delay, uncertain singular systems with time-varying delay and sensor failures, and singular Markovian jump systems with actuator failures.&#13;\nFor delay-free singular systems, the system augmentation approach is employed to study the dissipative control and filtering problems. First, the approach is used to solve the dissipative control problem by static output-feedback for standard state-space systems which are the special cases of singular systems. For a continuous-time standard state-space system, the closed-loop system is represented in an augmented system form. Based on the augmented system, a necessary and sufficient dissipativity condition is proposed, which decouples the Lyapunov matrix and controller matrix. To further separate the Lyapunov matrix and the system matrices, an equivalent condition is obtained by introducing some slack matrices. Then, a necessary and sufficient condition for the existence of a static output-feedback controller is proposed, and an iterative algorithm is given to solve the condition. For discrete-time singular systems, by giving an equivalent representation of the solution set, a necessary and sufficient dissipativity condition is proposed in terms of strict linear matrix inequality (LMI) which can be easily solved by standard commercial software. Then a state-feedback controller design method is given based on the augmentation system approach. The method is extended to the static output-feedback control problem and the reduced-order dissipative filtering problem.&#13;\nFor continuous-time singular time-delay systems, the problem of state-feedback dissipative control is considered. An improved delay-dependent dissipativity condition in terms of LMIs is established by employing the delay-partitioning technique, which guarantees a singular system to be admissible and dissipative. Based on this, a delay-dependent sufficient condition for the existence of a state-feedback controller is proposed to guarantee the admissibility and dissipativity of the closed-loop system. In addition to delay-dependence, the obtained results are also dependent on the level of dissipativity. Moreover, the results obtained unify existing results on H∞ performance analysis and passivity analysis for singular systems.&#13;\nFor discrete-time singular systems with polytopic uncertainties, time-varying delay and sensor failures, the problem of robust reliable dissipative filtering is considered. The filter is designed by the reciprocally convex approach such that the filtering error singular system is admissible and strictly (Q, S, R)-dissipative. For singular systems with time-varying delay and sensor failures, a sufficient condition of reliable dissipative analysis is obtained in terms of LMIs. Then the result is extended to the uncertain case by introducing some variables to decouple the Lyapunov matrices and the filtering error system matrices. Moreover, a desired filter for uncertain singular systems with time-varying delay and sensor failures is obtained by solving a set of LMIs.&#13;\nFor continuous-time singular Markovian jump systems with actuator failures, the problem of reliable dissipative control is addressed. Attention is focused on the state-feedback controller design method such that the closed-loop system is admissible and strictly (Q, S, R)-dissipative. A sufficient condition is obtained in terms of strict LMIs. Moreover, the results obtained unify existing results on H∞control and passive control on singular Markovian jump systems.

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 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.

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.

SummaryIn this article, an asynchronous adaptive tracking control approach is presented for a type of hidden Markov jump nonlinear systems with external disturbances. In this joint jump process model, hidden Markov model signifies the dynamics of the actual system, whereas the signal emits from the detector symbolizes the transmitted information. This leads to the phenomenon of asynchronization between the modes of the system and that of the controller. Accordingly, an asynchronous observer is developed by using the mode information from the detector to develop an asynchronous control approach. The observer contains a disturbance estimation part, to compensate the unknown external inputs. Utilizing the backstepping scheme, a strict‐feedback asynchronous tracking controller is formulated, guaranteeing that all signals within the closed‐loop system are semi‐globally uniformly ultimately bounded in probability. Finally, the validity of the presented methodology is illustrated by means of a simulation example.

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.

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.