Dynamic event-based reliable dissipative asynchronous control for stochastic Markov jump systems with general conditional probabilities

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.

This paper investigates the issue of observer-based [Formula: see text] control for a class of continuous-time-switched systems with a dynamic event-triggered strategy (DETS). First, we design a DETS that introduces an internal dynamic variable (IDV) into the event-triggered condition, which can improve data transmission efficiency and decrease the cost of the system operation by expanding the interevent intervals. Second, we establish a state observer based on the DETS and further construct an observer-based state feedback controller. It is worth noting that asynchronous switching may occur between the subsystems and the controllers under the DETS. Third, by utilizing novel Lyapunov-like functions (LLFs) with IDV and the signal-combining approach, sufficient conditions to ensure the [Formula: see text] performance of the closed-loop system are presented. Moreover, we verify that Zeno phenomenon does not exist. Finally, the effectiveness of the proposed method is verified by two examples.

In this article, the sliding mode control (SMC) problem is addressed for a class of Markovian jump systems via the T–S fuzzy model. First, in order to reduce the frequency of state transmission for alleviating congestion phenomenon in the bandwidth-limited communication network, a dynamic event-triggered (DET) strategy is introduced into the sensor-to-controller channel, in which an additional internal dynamical variable is employed to adjust the event-triggered condition adaptively. A fundamental issue resulting from the event-triggered strategy is that the controller cannot obtain the information about system mode during the triggering interval. Aiming at the phenomenon, this work utilizes a mode detector to estimate the unavailable system mode. Then, this article proposes a detected-mode-dependent event-triggered sliding mode controller whose membership grades are determined only via the transmitted state at the triggering instant. By constructing a relation on the membership functions (MFs) between the fuzzy model and the controllers for MF-dependent analysis, the conditions on the reachability and stability conditions are relaxed. Furthermore, an optimization algorithm is provided for the minimum control power via a high-dimensional grid searching for the coefficients of the internal dynamic variables, which, together with the designed detected-mode-dependent sliding mode controller, constitutes the novel SMC scheme under the DET strategy. Finally, the simulation results via the single-link arm system are provided to illustrate the efficiency of the proposed method.

Distributed Consensus Control for General Linear Multi-agent Systems via a Dynamic Event-triggered Strategy

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 considers the problem of adaptive reliable guaranteed cost controller design for linear time-delay systems against actuator faults via dynamic output feedback. Based on indirect adaptive method, a new reliable dynamic output feedback controller is established. The controller gains are affinely dependent on the estimations of fault parameters, which are updating automatically according to the proposed adaptive laws. New delay-dependent sufficient conditions for the existence of the reliable guaranteed cost dynamic output feedback controller are derived in terms of linear matrix inequalities, which have less conservativeness than the corresponding reliable dynamic output feedback controller with fixed gains. An example is presented to show the effectiveness of the proposed method.

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 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.

Allowing for simultaneous occurrence of multiple actuator faults in signal channels, the problem of robust reliable tracking controller design for a class of uncertain systems with polytopic type uncertainty is investigated. Based an unstructured quadratic separator, a less conservative condition for the existence of a reliable tracking control is derived. In order to reduce the design conservatism, a parameter dependent formation is introduced in construction of the quadratic separator, which can give rise to the improvement in degree of freedom for controller synthesis. In addition, the condition mentioned above can be reduced to linear matrix inequalities (LMI). Finally an example is given to demonstrate the effectiveness and superiority of presented robust reliable tracking controller.

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.

The problem of reliable controller design for two-dimensional (2-D) systems subject to extended dissipativity is investigated in this paper. Considering the wide usage of Roesser state-space model, a discrete-time Roesser model is introduced to describe 2-D systems. To reinforce the reliability of the system under consideration, actuator-failure model which may severely degrade performance, or even destabilize the system is introduced. Finally, the sufficient condition for the existence of reliable controller is presented to guarantee the mean square asymptotic stability and 2-D extended dissipativity of the closed-loop system under admissible actuator failures. The gains of 2-D controller are derived by means of the convex optimization method. A simulation result is exploited to verify the effectiveness and merits of the theoretical findings.

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.

This paper studies the problem of reliable Hinfin state feedback controller design for linear continuous-time systems. Actuator partial failures and actuator lock-in-place failures are simultaneously considered, and the signals in the case of certain actuators being locked in place are treated as zero-frequency disturbances, which gives an exact description for the lock-in- place failures. Based on the generalized KYP lemma in finite frequency domain, the controller design is developed in the framework of linear matrix inequality (LMI) approach, which can guarantee the asymptotic stability and Hinfin performances of the resulting closed-loop systems when all control components are operational as well as when some actuators fail. Finally, the design procedure and the effectiveness of the proposed method in comparison with the entire frequency approach by using bounded real lemma are illustrated via a numerical example of flight tracking control of an F-16 aircraft.

This paper addresses a novel state estimation design in a linear programming (LP) form for positive systems based on functional observers under dynamic event-triggered strategy (DETS). Firstly, a novel dynamic event-triggered condition is proposed for positive systems. Then, sufficient conditions of positivity and exponential stability are provided for the resulting dynamic error system under the designed DETS, and LP design is further proposed by applying the matrix decomposition technology. Finally, an example with comparison is given to illustrate the validity and superiority.