Mode-dependent Controller Research Articles

Stabilization of Discrete-Time Hidden Semi-Markov Jump Linear Systems With Partly Unknown Emission Probability Matrix

This paper studies the stabilization problem for a class of discrete-time hidden semi-Markov jump linear systems with partly unknown emission probability matrix. By virtue of the improved semi-Markov kernel approach and emission probability approach, the less conservative sufficient stability conditions are proposed on the basis of emission probability matrix with partly unknown elements. With the aid of an improved eliminating matrix product technique, the nonlinear matrix terms with respect to system coefficient matrix and controller gain matrix in the above conditions are decoupled into the linear matrix forms, and the numerically testable existence conditions of the observed mode dependent controller for the corresponding closed-loop systems are obtained. An example is given to illustrate the effectiveness of our results.

Model predictive control for asynchronously switched linear systems with mode-dependent dwell time

This paper presents a model predictive control (MPC) approach for a class of asynchronously switched linear systems with mode-dependent dwell time (MDT). Asynchronous switching which refers to the mismatch between system modes and desired mode-dependent controllers may result in infeasibility of the conventional switched MPC design or even make the closed-loop system unstable. To handle this problem, the concept of stage MDT is employed and its minimum admissible value is determined offline so as to ensure the reachable set of a starting region is included in a target region. Then, we compute a constraint admissible contractive asynchronous switching MDT invariant (AMI) set as the common terminal constraints for all the switching modes and find out an important property: The existence of such an AMI set is equivalent to the asymptotic stability of the asynchronously switched closed-loop system. By letting the reachable set be contained in the AMI set, we present two criteria to determine the minimum admissible stage MDT offline such that the closed-loop system is asymptotically stable. Finally, a numerical example is given to verify the theoretical results.

Observer-based output feedback event-triggered bounded consensus of multi-agent systems under DoS attacks

This paper is concerned with observer-based output feedback event-triggered bounded consensus problem for linear multi-agent systems. The original multi-agent systems are transformed into the switched systems due to DoS attacks, the fast switching is applied to multi-agent systems with DoS attacks, and slow switching is applied to multi-agent systems with no DoS attacks. A novel mode-dependent dynamic event-triggered scheme and a distributed mode-dependent control protocol are proposed by using the relative output, which include some existing results as special cases. It is shown that bounded consensus can be achieved if each agent is both stabilizable and detectable, the appropriate mode-dependent average dwell time and the co-designed feedback matrices are chosen. Two algorithms are also provided to obtain the lower consensus bound. The above results are also extended to undirected topology. Finally, our theoretical results can be verified by two simulation examples.

Linear programming-based stochastic stabilization of hidden semi-Markov jump positive systems

<p>This paper focuses on the stochastic stabilization of hidden semi-Markov jump nonlinear positive systems. First, a notion of stochastic stability is introduced for this class of systems. A criterion is addressed to ensure the stochastic stability using a stochastic copositive Lyapunov function. Then, an observed mode is proposed to estimate the emitted value of the hidden semi-Markov process and the mode-dependent controller is designed using an improved matrix decomposition approach. Some auxiliary variables are added to decouple the coupling terms in hidden semi-Markov jump nonlinear positive systems into a tractable condition. All conditions are described in terms of linear programming. Moreover, the proposed design is developed for systems with partially known emission probabilities. Two examples are provided to show the validity of the obtained results.</p>

Forward sensitivity analysis and mode dependent control for closure modeling of Galerkin systems

Forward sensitivity analysis and mode dependent control for closure modeling of Galerkin systems

Decentralized $H_{\infty }$ Control for Switched Interconnected Large-Scale Systems: A Computationally Attractive Method

This article investigates the decentralized <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> controller design problems for switched interconnected large-scale systems (ILSSs). The designed decentralized controllers are dependent on the switching modes which can reduce the conservatism. Sufficient conditions are established for ensuring the asymptotic stability and <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 of the studied switched ILSSs. Novel computationally attractive mode-dependent controller deign method is derived. The established controller design conditions eliminate the computationally expensive matrix inversion terms and are given in terms of linear matrix inequalities. Finally, the validness of the proposed decentralized controller design method is verified by the interconnected continuous stirred-tank reactor systems. Other three numerical examples are also performed to show the advantages and superiorities of the derived theoretical results.

Event-based asynchronous dissipative control for nonhomogeneous Markov jump systems

In this paper, the problem of the asynchronous dissipative control is investigated for a class of discrete-time nonhomogeneous Markov jump systems. Hidden Markov model is introduced to represent the asynchronization between the designed controller and the system. On the contrary, the mode-dependent event-triggered mechanism is formulated to alleviate the burden of data transmission in the communication channel. The Lyapunov function, which is dependent on both mode and uncertain parameters, is considered to obtain the sufficient conditions that make the system with strictly [Formula: see text]-[Formula: see text]-dissipative performance. Moreover, gains of the mode-dependent controller and coefficients of the event-triggered mechanism can be co-designed simultaneously. Finally, illustrative simulation and practical examples are provided to demonstrate the effectiveness of the proposed results.

The observed mode dependent controller design problem for a class of continuous‐time hidden semi‐Markov jump systems

SummaryThis paper studies the stability analysis and stabilization synthesis problems for a class of continuous‐time jump systems with hidden system modes. To precisely model the switching signals of the considered systems, a novel definition of continuous‐time hidden semi‐Markov process is proposed based on the notions of emission probability and time varying dual‐index transition rate. By virtue of such definition, a dual‐index Lyapunov function is utilized to derive the sufficient stability conditions of the considered systems. By adopting a technology that can decouple the nonlinear terms in the above conditions, the numerically testable existence conditions of the controller for the resulting stabilizing systems are presented. An example is given to illustrate the effectiveness of our results.

Adaptive learning nonsynchronous control of nonlinear hidden Markov jump systems with limited mode information

&lt;abstract&gt;&lt;p&gt;In this paper, an adaptive neural network learning based nonsynchronous control method is developed for hidden Markov jump systems with unmodeled nonlinear dynamics. In particular, the system modes are not directly accessible and the limited mode information can be partly estimated by the nonsynchronous controller. More precisely, the mode information with partly accessible transition rates is utilized based on the transition probability matrix. Moreover, the unmodeled nonlinear dynamics are more general in practical applications. Based on the designed mode-dependent controllers with mode observation, sufficient conditions are first exploited by means of the Lyapunov method, such that the desired control performance could be ensured in the mean-square sense. Then, the nonsynchronous mode-dependent controllers are further determined in terms of convex optimization. In the end, our proposed control strategy is applied to a robotic manipulator with varying loads to validate the feasibility with simulation results.&lt;/p&gt;&lt;/abstract&gt;

Asynchronous Control of Switched Discrete-Time Positive Systems With Delay

This article considers the stabilization issue of switched discrete-time positive systems (SDPSs) with delay by using asynchronous control. Combining transition probability (TP) with mode-dependent average dwell time (MDADT), called TP-based MDADT switching, the SDPSs are more practical than classical models with average dwell-time (ADT) switching. With the aid of a co-positive Lyapunov–Krasovskii functional (CLKF), sufficient conditions ensuring the exponential stability almost surely (ES a.s.) of the SDPSs without control is studied, where the mode is not necessary to be stable. After that, a mode-dependent controller with switching delay is designed to stabilize the SDPSs in the case that there are unstable subsystems. An algorithm is provided to design the control gains. It is discovered that the mode in the closed-loop SDPSs is not required to be stable on synchronous and asynchronous switching intervals. Numerical simulations verify the merits of the new results.

Adaptive Event-Triggered [formula omitted] Control of Semi-Markov Jump Distributed Parameter Systems

This paper focuses on the problem of adaptive event-triggered L2−L∞ control for distributed parameter systems with semi-Markov jump parameters. An event-triggered transmission scheme, whose threshold function can be adaptively adjusted, is established to decrease the frequency of data transmission. Simultaneously, the utilization of limited network bandwidth resources is also improved due to plenty of “unnecessary” packets being discarded before accessing networks. Furthermore, the jumping of stochastic parameters in networks can be described by a semi-Markov jump model, in which the sojourn-time is considered subject to the Weibull distribution instead of the exponential distribution. Based on the aforesaid discussions, a mode-dependent controller is designed under an adaptive event-triggered scheme. Whereafter, some criteria are constructed based on the Lyapunov stability theory to guarantee stochastic stability and a prescribed L2−L∞ performance of the system. Ultimately, two simulation examples are provided to verify the feasibility of the proposed design approach.

Formula omitted] and [formula omitted] Control with sector bound optimization for Continuous Time Markov Jump Lur’e Systems

This paper addresses the H2 and H∞ control of Markov Jump Systems subject to a class of nonlinearities that include them on the Lur’e system framework, with sector slope optimization. The proposed controllers are robust to nonlinearities belonging to a sector. We propose mode-dependent controllers; in other words, the Markov mode θ(t) is available to controllers. The design of such controllers considers the optimization of the H2 and H∞ costs as well as the sector slope, which determines the class of accepted nonlinearities. The results are illustrated through two practical examples: coupled electrical machines and the semi-active suspension of a quarter car.

Nonfragile H∞ Synchronization of BAM Inertial Neural Networks Subject to Persistent Dwell-Time Switching Regularity.

This article concentrates on the synchronization of discrete-time persistent dwell-time (PDT) switched bidirectional associative memory inertial neural networks with time-varying delays. Through the use of the switched system theory related to the PDT, the convex optimization technique together with some straightforward decoupling methods, an appropriate mode-dependent controller with nonfragility is developed to acclimatize itself to some practical circumstances. Simultaneously, sufficient conditions of ensuring the H∞ performance and exponential stability for the resulting switched synchronization error system are derived. Finally, a numerical example is utilized to show the validity of the model constructed and the influence of the PDT on the H∞ performance. In addition, an image encryption example is employed to show the potential application prospect of the investigated system.

Finite-frequency control for nonlinear semi-Markov jump systems with piecewise transition probabilities

Considering the frequency effect of external disturbances, this paper concerns the finite-frequency control problem for nonlinear semi-Markov jump systems (SMJSs) with piecewise transition probabilities (TPs) via the Takagi–Sugeno (T–S) fuzzy modeling approach. More precisely, the piecewise TPs are assumed to switch stochastically within limits, which implies that the corresponding distributions of sojourn time (ST) also vary randomly. Furthermore, another upper semi-Markov chain is utilized to characterize TPs variation in a finite set. With the aid of Finsler’s lemma and Parseval’s theorem, sufficient criteria for the controlled SMJS are constructed to meet the desired disturbance attenuation performance in the frequency domain. Then, the mode-dependent controllers are developed to use the TP information more efficiently. In particular, a novel matrix method is proposed to decouple the mode-dependent variables and controller gains by selecting slack matrices. Eventually, a numerical example is transmitted to demonstrate the validity and merits of established results.

Uncertainty and disturbance estimator-based resilient tracking control design for fuzzy semi-Markovian jump systems

The focus of this paper is on solving the state tracking control problem for a class of fuzzy semi-Markovian jump systems with the aid of fuzzy modeling approach. Besides, the impact of both unexpected disturbances and uncertainties in fuzzy semi-Markovian jump systems is considered. In particular, the nonlinearity in the addressed system is represented by the T-S fuzzy model, wherein the disturbances and uncertainties are estimated by precisely considering uncertainty and disturbance estimator (UDE)-based control approach. Whilst, the desired fuzzy rule-based mode-dependent control law is formulated by exploiting the parallel distributed compensation strategy and estimated output of disturbances and uncertainties. In the proposed tracking control scheme, the resilient strategy is considered to overcome the impact of gain perturbations. Further, in terms of LMIs, a set of sufficient constraints is derived in accordance with the appropriate selection of mode-dependent fuzzy rule-based Lyapunov function. Under which, the asymptotic tracking and enhanced disturbance rejection performances are guaranteed for the system under consideration. Notably, the desired control gain matrices are determined by solving the derived sufficient conditions via MATLAB LMI toolbox. Conclusively, a single-link robot arm model is adopted to justify the practicability and efficacy of the theoretical findings.

Semi-Markov jump linear systems with bi-boundary sojourn time: Anti-modal-asynchrony control

This paper investigates the problem of control synthesis for a class of discrete-time semi-Markov jump linear systems, in which the sojourn time of each mode is bi-boundary (with upper and lower bounds). The system is subject to modal asynchrony, which means that the switchings of the mode-dependent controller to be designed lag behind the ones of the controlled plant, and the lag is mode-dependent. In contrast with the traditional mode-independent lag commonly assumed in the existing studies, not only is the modal lag more practical and general, but also it yields less conservatism of the controller design. By virtue of the semi-Markov kernel approach, the conditions on the existence of the anticipated stabilizing controllers capable of overcoming the modal asynchrony are derived. Illustrative examples including a class of vertical take-off and landing (VTOL) helicopter models are presented to demonstrate the necessity and the validity of the designed anti-modal-asynchrony controllers.

Asynchronous partially mode-dependent control for switched larger-scale nonlinear systems with bounded sojourn time

In this paper, the asynchronous partially mode-dependent control problem is investigated for switched larger-scale systems (SLSSs) with inherent nonlinearities, known sojourn probabilities and bounded sojourn time. The interconnection among subsystems is nonlinear and subject to stochastic switching. The resultant part available mode information is that the modes of controllers and the plant are asynchronous. By introducing a mode storage rule and transforming the asynchronous system into a general switched system, the stability criteria is obtain with available modes, the sum of these modes’ sojourn probabilities and the bounds of sojourn time. Then, some sufficient conditions are derived to guarantee the mean-square stability (MSS) by employing Young inequality and the desired asynchronous controller is designed by using available softwares. At last, an example is provided to illustrate the main methods in this paper.

H ∞ asynchronous synchronisation control for Markovian coupled delayed neural networks with missing information

This paper first studies asynchronous synchronisation control problem for Markovian coupled neural networks with missing information. As information exchanges among neural networks, which can help achieving synchronisation, are conducted via a generally unprotected communication network with limited bandwidth, nodes' state information and the synchronised state information may not be available to node i, and a Bernoulli process is used to model this phenomenon. Furthermore, considering that the amount of information needs to be transmitted is decided by the coupling relationship, missing information rate is assumed to be node- and coupling dependent. By introducing another nonhomogeneous Markov chain with transition probability matrix depending on coupling mode, the asynchronous synchronisation controller is designed, which can describe complex asynchronous switch phenomenon between system and controller modes and covers mode-dependent controller and mode-independent one as two special cases. Three sufficient conditions respectively guaranteeing the global synchronisation and the global synchronisation of the addressed networks are obtained, and then the asynchronous synchronisation controller design method is proposed. Finally, an illustrative example with results demonstrating the effectiveness of the given controller design approach is provided.

Robust Nonfragile Guaranteed Cost Control for Uncertain Fuzzy Markov Jump Systems with Time-Varying Delays

This paper aims to investigate the problem of robust nonfragile guaranteed cost control for uncertain discrete-time Takagi–Sugeno fuzzy systems with Markov jumping parameters and time-varying delay. A nonfragile fuzzy-basis-dependent and mode-dependent controller is designed and a sufficient condition is developed to ensure that the resulting closed-loop system is robust asymptotically stable in mean square with guaranteed cost index not exceeding the specified upper bound. Subsequently, the controller gain and minimum upper bound of the guaranteed cost index can be obtained by solving a set of linear matrix inequalities. Compared with the existing literature, this paper enormously reduces the conservatism of the result obtained. Finally, numerical and practical examples are provided to demonstrate the performance of the proposed approach.

Stabilization of semi-Markovian jump systems via a quantity limited controller

This paper addresses the stabilization problem of continuous-time semi-Markovian jump systems (s-MJSs), where the quantity of a controller to be designed has a limitation. A principle designing such a controller is proposed based on its stationary probability sequence. Sufficient conditions for the existence of the designed controller are obtained by applying a Lyapunov function approach and presented with LMIs. The controller mentioned above is proved to be a minimal variance approximation of mode-dependent controllers having total modes. More special cases about Markovian switching and without minimal variance approximation are further studied. A practical example is used to demonstrate the effectiveness and superiority of the proposed methods.