Control Gain Matrix Research Articles

Nonfragile Consensus of Multiagent Systems Based on Memory Sampled-Data Control

In this paper, we address the consensus tracking problem for the multiagent system (MAS) based on a nonfragile memory sampled-data controller. Considering the effect of controller gain fluctuation and communication delay, a novel sampled-data control scheme with variable sampling interval is designed for each agent. By developing some new terms, an improved piecewise Lyapunov–Krasovskii functional (LKF) is constructed to take full advantage of characteristic about real sampling pattern. Furthermore, some relaxed matrices constructed in the LKF are not necessarily positive definite. Making full use of the LKF and free-matrix-based integral inequality, some sufficient criteria are developed to ensure the consistency of the MAS. Then, by solving a group of linear matrix inequalities with the maximal sampling interval, the desired sampled-data control gain matrix is obtained. Finally, the numerical example of a 5-agent system is given to illustrate the effectiveness of the proposed approach in this paper.

Sampled-Based Consensus for Nonlinear Multiagent Systems With Deception Attacks: The Decoupled Method

In this paper, the sampled-based consensus problem is investigated for a class of nonlinear multiagent systems subjected to deception attacks. Due to network fluctuations and limited resources, deception attacks might destroy the sampled-data in communication networks. Additionally, the success of deception attacks greatly depends on some randomly fluctuated factors. This paper takes into account the deception attacks that are randomly launched at each sampling instant. The eigenvector of Laplacian matrix is utilized to construct a novel Lyapunov functional. Then, the decoupled criterion connected with eigenvalues of Laplacian matrix is obtained such that the addressed multiagent systems achieve the mean square consensus. Furthermore, the solutions of a set of matrix inequalities represent the controller gain matrix. Finally, a numerical example is provided to validate the effectiveness of the derived results.

New Delay-Dependent Synchronization Criteria of Complex Dynamical Networks With Time-Varying Coupling Delay Based on Sampled-Data Control via New Integral Inequality

In this work, the issue of synchronization control for complex dynamical networks with time-varying coupling delay based on sampled-data is addressed. First, the sampled-data control is transformed into the bounded sampling period with time-varying delay. As a result, this model is converted to the investigation for synchronization of complex networks with multiple time-varying delays. Second, an appropriate Lyapunov-Krasovkii functional (LKF) is constructed, which composites of double and triple integral terms in quadratic form. Third, we propose a new integral inequality including a reciprocally convex technique which leads to a better condition. Fourth, the solution for the controller gain matrix is obtained by solving linear matrix inequalities (LMIs) with available software such that the synchronization error system is exponentially stable. Finally, the effectiveness and less conservatism of our proposed method are demonstrated via numerical examples.

Event-Based Pinning Synchronization Control for Time-Delayed Complex Dynamical Networks: The Finite-Time Boundedness

The paper is concerned with the synchronization control issue for a kind of nonlinear discrete time-delayed complex dynamical networks. To improve energy efficiency, a dynamic event-triggering strategy is introduced to regulate the signal transmission from the controller to the actuator. Then, the event-based pinning feedback control strategy is adopted to control a small fraction of the network nodes with hope to reduce the frequency of updating and communication in control process. Subsequently, a new concept of finite-time boundedness in the mean square is put forward to evaluate the synchronization control performance by means of a settling-like time function. Furthermore, by using the Lyapunov stability theory and the stochastic analysis technique, a sufficient condition is provided to ensure that the synchronization error is finite-time bounded in the mean square with a prescribed error upper bound in the presence of both time-delay and external noise disturbances. By solving an optimization problem with some inequality constraints, the desired controller gain matrix is parameterized to minimize the settling-like time. Finally, a numerical simulation example is carried out to illustrate the effectiveness and usefulness of the obtained theoretical results.

Fuzzy Adaptive Control for Fractional Nonlinear Systems with External Disturbances and Unknown Control Directions

In this paper, the problem of fuzzy adaptive control of unknown nonlinear fractional-order systems with external disturbances and unknown control directions is studied. We exploit a decomposition of the control gain matrix into a symmetric positive-definite matrix, a diagonal matrix with diagonal entries + 1 or 1 , and a unity upper triangular matrix. Fuzzy logic systems are used for estimating the unknown nonlinear functions. Based on the fractional Lyapunov direct method and some proposed lemmas, a novel fuzzy adaptive controller is designed. The proposed method can guarantee that all the signals in the closed-loop systems remain bounded and the tracking errors converge to an arbitrary small region of the origin. In addition, for updating the parameters of the fuzzy system, fractional-order adaptations laws are proposed. Lastly, an illustrative example is given to demonstrate the effectiveness of the proposed results.

Interconnection structure preservation design for a type of port‐controlled hamiltonian systems—A parametric approach

It is a very important issue to minimise the change of the interconnect structure matrix when stabilising a port-controlled Hamiltonian (PCH) system. Toward this problem, a parametric design method is proposed in this paper for a type of PCH systems. First, concepts of H-damping-assignable and H-damping-assigning controller are introduced, and the stability of the closed-loop system resulting from this type of controller is discussed. Secondly, a necessary and sufficient condition for the system to be H-damping-assignable is given, and, when this condition is met, a parametric general expression of all the H-damping-assigning controllers is obtained. Thirdly, the free parameters are optimised to minimize the change of the interconnect structure matrix and also the norm of the control gain matrix. The parameter optimisation is formulated as a standard quadratic programming problem, to which analytical solutions are obtained. Finally, comparative simulations are carried out for a numerical example to verify the effect and the superiority of the proposed method.

Periodic Event-Triggered Integral Sliding-Mode Control for T-S Fuzzy Systems.

This article investigates the integral sliding-mode control (SMC) problem for T-S fuzzy systems via the periodic event-triggered method. First, in order to remove the assumption that the inter-execution time has a uniform upper bound, a novel sliding variable error function is added into the event-triggering mechanism. Second, in order to avoid the extra information transmission, a new sliding-mode switching function consisting of the triggering state information is proposed to design the event-triggered integral SMC (ISMC) law. In addition, the ultimate boundedness of sliding motion can be ensured via using a designed event-triggered ISMC law. A sufficient condition of boundedness is given in the form of linear matrix inequality, which is employed to solve the controller gain matrix. Finally, the effectiveness of theoretical results can be illustrated via three illustrative examples.

Observer-based control for nonlinear parameter-varying systems: A sum-of-squares approach

This paper investigates the design problem of nonlinear and time-varying observer-based controllers for nonlinear parameter-varying systems without/with input constraints. With the aid of Lyapunov stability theory, the state-and-parameter-dependent linear matrix inequality conditions are obtained. These conditions are developed as convex programming problems. And a feasible solution can be obtained via sum-of-squares techniques. Thus, the commonly used backstepping/iterative methods are avoided. In addition, the effect of the bilinear product forms for the controller gain matrix and the Lyapunov functional are eliminated. A remarkable advantage of this proposed approach is that the state-and-parameter-dependent observer and the state-feedback controller can be designed independently, which significantly reduces the computational complexity. Finally, the feasibility and validity of the proposed method can be illustrated by simulation results.

H 2/H ∞ formulation of LQR controls based on LMI for continuous-time uncertain systems

The classical theory of linear matrix inequality (LMI)-based linear quadratic regulator (LQR) control that is well established in literature does not provide, in the controller project phase, the occurrence of exogenous inputs acting on the plants. Therefore, this study proposes sufficient conditions for the robust synthesis of a mixed / control of the LQR problem. A new mixed polytopic and norm-bounded uncertainties representation for linear time-invariant uncertain systems allows to express different uncertainty models in one single LMI by using the S-procedure. As an additional objective, we propose the study of the robustness of controllers concerned with the sensibility of their coefficients, in such a way that the variations in controller gain matrix are described by norm-bounded uncertainties. A practical implementation in Quanser active suspension evaluates the control projects through the rejection level of vibrations caused by track irregularities.

Event-triggered control of positive Markov jump systems without/with input saturation

This paper proposes an event-triggered control for positive Markov jump systems without/with input saturation. First, an event-triggering condition is established in the form of 1-norm for positive Markov jump systems. Under the event-triggering condition, the term related to error signal between the sample state and the actual state is transformed into a form of interval uncertainty. Then, the positivity and stability of the systems are discussed by using the lower and upper bounds of interval uncertain systems, respectively. An event-triggered control law for the underlying systems is proposed by decomposing controller gain matrix into non-positive and non-negative parts. For positive Markov jump systems with input saturation, a design approach to the controller gain matrices and the corresponding controller auxiliary gain is presented. All conditions are described in terms of linear programming. Furthermore, the obtained approaches are developed for the discrete-time case. Finally, the effectiveness of the proposed design is verified via three examples.

Secure synchronization control for a class of cyber-physical systems with unknown dynamics

This paper investigates the secure synchronization control problem for a class of cyber-physical systems &#x0028 CPSs &#x0029 with unknown system matrices and intermittent denial-of-service &#x0028 DoS &#x0029 attacks. For the attack free case, an optimal control law consisting of a feedback control and a compensated feedforward control is proposed to achieve the synchronization, and the feedback control gain matrix is learned by iteratively solving an algebraic Riccati equation &#x0028 ARE &#x0029 . For considering the attack cases, it is difficult to perform the stability analysis of the synchronization errors by using the existing Lyapunov function method due to the presence of unknown system matrices. In order to overcome this difficulty, a matrix polynomial replacement method is given and it is shown that, the proposed optimal control law can still guarantee the asymptotical convergence of synchronization errors if two inequality conditions related with the DoS attacks hold. Finally, two examples are given to illustrate the effectiveness of the proposed approaches.

Reliable control for positive switched systems with random nonlinearities

This paper proposes a reliable control of positive switched systems with random nonlinearities which may induce the security problem of the systems. The random nonlinearities are governed by stochastic variables obeying the Bernoulli distribution. A switched linear copositive Lyapunov function is employed for the systems. Using a matrix decomposition approach, the gain matrix of controller is formulated by the sum of nonnegative and non-positive components. A reliable controller is designed for positive switched systems with actuator faults by virtue of linear programming. Under the designed reliable controller, the systems can resist some possible security risks triggered by random nonlinearities and actuator faults. The obtained approach is developed for systems subject to exogenous disturbances. Finally, two examples are provided to verify the validity of the obtained results.

Distributed model predictive control of positive Markov jump systems

This paper proposes a new distributed model predictive control (DMPC) for positive Markov jump systems subject to uncertainties and constraints. The uncertainties refer to interval and polytopic types, and the constraints are described in the form of 1-norm inequalities. A linear DMPC framework containing a linear performance index, linear robust stability conditions, a stochastic linear co-positive Lyapunov function, a cone invariant set, and a linear programming based DMPC algorithm is introduced. A global positive Markov jump system is decomposed into several subsystems. These subsystems can exchange information with each other and each subsystem has its own controller. Using a matrix decomposition technique, the DMPC controller gain matrix is divided into nonnegative and non-positive components and thus the corresponding stochastic stability conditions are transformed into linear programming. By virtue of a stochastic linear co-positive Lyapunov function, the positivity and stochastic stability of the systems are achieved under the DMPC controller. A lower computation burden DMPC algorithm is presented for solving the min-max optimization problem of performance index. The proposed DMPC design approach is extended for general systems. Finally, an example is given to verify the effectiveness of the DMPC design.

Synchronization of Stochastic Complex Dynamical Networks with Mixed Time-Varying Coupling Delays

Synchronization of complex networks with mixed time-varying coupling delays and stochastic perturbation. We constructed a novel Lyapunov functional with triple integral terms. By applying Jensen’s inequality and Lyapunov stability theory stability conditions are derived to check the asymptotical stability of the concerned system. By employing the stochastic evaluation and Kronecker product delay-dependent synchronization criteria of stochastic complex dynamical networks are derived. By using the derived conditions control gain matrix is obtained. Finally, numerical results are presented to demonstrate the effectiveness and usefulness of the proposed results.

Impulsive method to reliable sampled-data control for uncertain fractional-order memristive neural networks with stochastic sensor faults and its applications

This paper is devoted to investigate the issue of fault-tolerant sampled-data control for a class of uncertain fractional-order memristive neural networks with random switching topologies subject to stochastic sensor faults via impulsive method. Firstly, a fault detection sampled-data control strategy is proposed for sensor failure. Then, by utilizing the constructed quasi-periodic polynomial Lyapunov function, the criterion for ensuring that the transformed pulse system achieves asymptotic stability is established. Moreover, based on this criterion and with the help of the mechanism of sum of squares (SSs), the desired reliable control gain matrix is obtained. Finally, a numerical example is employed to demonstrate the validity of our method, and this method is applied to the well-known fractional-order Chua???s circuit system. Compared to large quantities of results for integer-order memristive neural networks, only a small number of results are for fractional order. In particular, the sampling-controlled fractional-order memristive neural networks have not been solved until now, let alone the novel impulive approach designed in this paper. This paper is the first attempt to make up for this vacancy in this topic.

New Decentralized Control of Interconnected Systems

In this paper, we present a new decentralized H∞ control for interconnected systems, the interconnected system consists of several subsystems. The proposed approach based on Lyapunov functional and a H∞ criterion, employed to reduce the effect of interconnections between subsystems. In the first, we study the stability of the global system in closed loop using a criterion H∞, the stability conditions are presented in terms of LMI. In the second, to improve this approach, a Finsler’s lemma is used for the stability analysis by LMIs. Some sufficient conditions, ensuring all the closed-loop stability are supplied in terms of Linear Matrix Inequalities (LMIs), and the new feedback gain matrix of each local controller is obtained by solving the LMIs. Finally, the practice examples are given to illustrate the efficiency of the present method.

Exponential Synchronization of Markovian Jump Complex Dynamical Networks with Uncertain Transition Rates and Mode-Dependent Coupling Delay

This paper aimed at investigating the exponential synchronization problem for a Markovian jump complex dynamical network through designing a state feedback controller. In this paper, it is supposed that both time delay and coefficient matrices switch between finite modes governed by a time-varying Markov process. The transition rate (TR) matrix of the Markov process is supposed to vary with time, and to be piecewise-constant. The time-varying transition rates are investigated under two cases: completely known TRs and partly unknown TRs, respectively. The synchronization problem of the proposed model is inspected by developing Lyapunov–Krasovski function with Markov-dependent Lyapunov matrices. The controller gain matrix for guaranteeing the synchronization problem is derived by using linear matrix inequalities. The resulted criteria depend on both delay size and the probability of the delay-taking value. Finally, a numerical example is provided to demonstrate the effectiveness of the theoretical results.

Positivity and Stability Analysis for Fractional-Order Delayed Systems: A T-S Fuzzy Model Approach

This article investigates positivity, external positivity, and asymptotic stability for a large class of incommensurate fractional-order nonlinear systems (FONSs) with bounded multiple time-varying delays by virtue of the T-S fuzzy method. The Laplace transformation technique is used to obtain the solutions of T-S fuzzy FONSs. A sufficient and necessary condition is derived for characterizing (internal) positivity, and certain criteria are also provided to guarantee external positivity of FONSs with or without time-varying delays. It is indicated that the positivity of the considered systems is determined purely by system matrices rather than the magnitudes of time-varying delays. Moreover, a sufficient and necessary condition for asymptotic stability of positive FONSs is obtained, and a state-feedback controller is also designed to guarantee that state variables not only converge to the origin asymptotically but also remain nonnegative, where the control gain matrix is obtained by solving an linear programming (LP) problem. Three numerical simulation examples are given to expound validity and feasibility of the theoretical results.

Synchronization of Delayed Neural Networks With Actuator Failure Based on Stochastic Sampled-Data Controller

This paper addresses the master-slave synchronization problems of delayed neural networks with actuator failure based on stochastic sampled-data controller. To simplify the analysis process, only two different sampling periods whose occurrence probabilities follow the Bernoulli distribution are considered. In addition, it can be further extended to cases with multiple random sampling periods. The sampling system with random parameters is transformed into a continuous system through applying the input delay method. The novelty of this article is to consider the problem of actuator failure which may exist in the real world. By constructing a new type of Lyapunov-Krasovskii function (LKF), a sampling controller for neural networks synchronization system is designed. Using Jensens's inequality, Wirtinger's inequality and convex optimization methods, the stability criterion of neural networks with low conservativeness is acquired. Meanwhile, the controller gain matrix can be obtained through solving the linear matrix inequalities (LMIs). One numerical example provides feasibility and advantages of theoretical results.

Stabilization for Networked Control System With Time-Delay and Packet Loss in Both S-C Side and C-A Side

The stabilization problem for a class of discrete network control system with time-delay and packet loss in both S-C side and C-A side is researched in this paper. Firstly, two independent discrete Markov chains are used to describe the network time-delay from sensor to controller and the network time-delay from controller to actuator. Two random variables obeying the Bernoulli distribution are employed to describe the packet loss between the sensor and the controller and the packet loss between the controller and the actuator. Secondly, a mathematical model for closed-loop system is established. By constructing the appropriate Lyapunov-Krasovskii functional, the sufficient conditions for the existence of the controller and observer gain matrix are obtained under the condition that the transition probabilities of S-C time-delay and C-A time-delay are both partly unknown. Finally, two examples are exploited to illustrate the effectiveness of the proposed method.