A new Lyapunov functional approach to sampled-data synchronization control for delayed neural networks

This paper discusses the problem of synchronization for delayed neural networks using sampled-data control. We introduce a new Lyapunov functional, called complete sampling-interval-dependent discontinuous Lyapunov functional, which can adequately capture sampling information on both intervals from $r(t?\overline{\tau })$ to $r(t_k?\overline{\tau })$ and from $r(t?\overline{\tau })$ to $r(t_{k+1}?\overline{\tau })$. Based on this Lyapunov functional and an improved integral inequality, less conservative conditions are derived to ensure the stability of the synchronization error system, leading to the fact that the drive neural network is synchronized with the response neural network. The desired sampled-data controller is designed in terms of solutions to linear matrix inequalities. A numerical example is provided to demonstrate that the proposed approaches are effective and superior to some existing ones in the literature.     

A BP-PID controller-based multi-model control system for lateral stability of distributed drive electric vehicle

The lateral stability is the crucial feature in a distributed drive electronic vehicle (DDEV). A high speed DDEV in a sharp turn may lose the lateral stability when it encounters fast varied road adhesion coefficients. To solve this problem, a BP-PID controller-based multi-model control system (MMCS) is designed for DDEV via direct yaw-moment control (DYC) in this paper. Firstly, according to the varied road adhesion coefficients, the working circumstance of DDEV is summarized as seven kinds of typical types. A sub-model set is established to accurately describe the operating mode of the working circumstance. Secondly, based on the sub-model set, a nonlinear sub-controller set is constructed with seven off-line tuning BP-PID controllers and an on-line tuning one. The off-line tuning controller can fast calculate the required direct yaw-moment, and the on-line tuning controller is aimed to achieve a high control accuracy. Thirdly, a controller switching policy is composed of an error judgement policy and a model matching policy. Such switching policy is utilized to precisely identify the working circumstance of DDEV and implement switching control. Finally, simulation experiments prove that the designed MMCS shows a significant control performance and guarantees the lateral stability of DDEV under varied road adhesion coefficients.     

Event-triggered dissipative state estimation for Markov jump neural networks with random uncertainties

This paper is concerned with the problem of event-triggered dissipative state estimation for Markov jump neural networks with random uncertainties. The event-triggered mechanism is introduced to save the limited communication bandwidth resource and preserve the desired system performance. The phenomenon of randomly occurring parameter uncertainties is considered to increase utilizability of the proposed method. To describe such a randomly occurring phenomenon, some mutually independent Bernoulli distributed white sequences are adopted. A mode-dependent state estimator is designed in this paper, which ensures that the estimation error system is extended stochastically dissipative. By using the Lyapunov–Krasovskii functional approach and an optimized decoupling approach, an expected state estimator can be built by solving some sufficient conditions. Two numerical examples are presented to demonstrate the correctness and effectiveness of the proposed method.     

Optimal synchronization controller design for complex dynamical networks with unknown system dynamics

In this paper, the optimal synchronization controller design problem for complex dynamical networks with unknown system internal dynamics is studied. A necessary and sufficient condition on the existence of the optimal control minimizing a quadratic performance index is given. The optimal control law consists of a feedback control and a compensated feedforward control, and the feedback control gain can be obtained by solving the well-known Algebraic Riccati Equation (ARE). Especially, in the presence of unknown system dynamics, a novel adaptive iterative algorithm using the information of system states and inputs is proposed to solve the ARE to get the optimal feedback control gain. Finally, a simulation example shows the effectiveness of the theoretical results.     

Optimal control of stochastic functional neutral differential equations with time lag in control

In this work, we consider an optimal control problem of a class of stochastic differential equations driven by additive noise with aftereffect appearing in control. We develop a semigroup theory of the driving deterministic neutral system and identify explicitly the adjoint operator of the corresponding infinitesimal generator. We formulate the time delay equation under consideration into an infinite dimensional stochastic control system without time lag by means of the adjoint theory established. Consequently, we can deal with the associated optimal control problem through the study of a Hamilton–Jacob–Bellman (HJB) equation. Last, we present an example whose optimal control can be explicitly determined to illustrate our theory.     

Input-to-state stability of impulsive inertial memristive neural networks with time-varying delayed

The property of input-to-state stability (ISS) of inertial memristor-based neural networks with impulsive effects is studied. Firstly, according to the characteristics of memristor and inertial neural networks, the inertial memristor-based neural networks are built. Secondly, based on the impulsive control theory, the average impulsive interval approach, Halanay differential inequality, Lyapunov method and comparison property, some sufficient conditions ensuring ISS of the inertial memristor-based neural networks under impulsive controller are derived. In this paper, we consider two types of impulse, stabilizing impulses and destabilizing impulses. When the inertial memristor-based neural networks are originally not ISS, by choosing a suitable lower bound of the average impulsive interval, the stabilizing impulses can be used to stabilize the inertial memristor-based neural networks. On the contrary, the inertial memristor-based neural networks are originally ISS, by restricting the upper bound of the average impulsive interval, the ISS of inertial memristor-based neural networks with destabilizing impulses can be ensured. Finally, numerical results are presented to illustrate the main results.     

Adaptive synchronization of complex networks with general distributed update laws for coupling weights

This paper discusses adaptive synchronization control for complex networks interacted in an undirected weighted graph, and aims to provide a novel and general approach for the design of distributed update laws for adaptively adjusting coupling weights. The proposed updating laws are very general in the sense that they encompass most weight update laws reported in the literature as special cases, and also provide new insights in the analysis of network system evolution and graph weight convergence. We show a rigorous proof for the synchronization stability of the overall complex network to a synchronized state, and demonstrate the convergence of adaptive weights for each edge to some bounded constants. A detailed comparison with available results is provided to elaborate the new features and advantages of the proposed adaptive strategies as compared with conventional adaptive laws. The effectiveness of the proposed approach is also validated by several typical simulations.     

Guaranteed cost synchronization for second-order wireless sensor networks with given cost budgets

The current paper addresses leader-following guaranteed cost synchronization with the cost budget given previously for the second-order wireless sensor networks. The published researches on guaranteed cost synchronization design criteria usually are based on the linear matrix inequality (LMI) techniques and cannot take the cost budget given previously into consideration. Firstly, the current paper proposes a guaranteed cost synchronization protocol, which can realize the tradeoff design between the battery power consumption and the synchronization regulation performance. Secondly, for the case without the given cost budget, sufficient conditions for leader-following guaranteed cost synchronization are presented and an upper bound of the cost function is shown. Thirdly, for the case that the cost budget is given previously, the criterion for leader-following guaranteed cost synchronization is proposed. Especially, the value ranges of control gains in these criteria are determined, which means that the existence of control gains in synchronization criteria can be guaranteed, but the LMI techniques can only determine the gain matrix and cannot give the value ranges of control gains. Moreover, these criteria are only associated with the minimum nonzero eigenvalue and the maximum eigenvalue, which can ensure the scalability of the wireless sensor networks. Finally, numerical simulations are given to illustrate theoretical results.     

A cyclic pursuit framework for networked mobile agents based on vector field approach

This paper proposes a pursuit formation control scheme for a network of double-integrator mobile agents based on a vector field approach. In a leaderless architecture, each agent pursues another one via a cyclic topology to achieve a regular polygon formation. On the other hand, the agents are exposed to a rotational vector field such that they rotate around the vector field centroid, while they keep the regular polygon formation. The main problem of existing approaches in the literature for cyclic pursuit of double-integrator multiagent systems is that under those approaches, the swarm angular velocity and centroid are not controllable based on missions and agents capabilities. However, by employing the proposed vector field approach in this paper, while keeping a regular polygon formation, the swarm angular velocity and centroid can be determined arbitrary. The obtained results can be extended to achieve elliptical formations with cyclic pursuit as well. Simulation results for a team of eight mobile agents verify the accuracy of the proposed control scheme.     

State and unknown input estimations for discrete-time switched linear systems with average dwell time

In this paper, the problem of state and unknown input estimations for a class of discrete-time switched linear systems with average dwell time switching is investigated. First, a proportional integral observer with an exponential H_∞ performance is constructed to estimate the system state and unknown input simultaneously. Second, both of the observability and the stability of the estimation error system are analyzed, then the derivation of the observer gain matrices is transformed into the calculation of linear matrix inequalities. Third, the obtained results are extended to the systems with output disturbances. Finally, two simulation examples are provided to show the validity and effectiveness of the proposed methods.     

A new distributed Kalman filtering based on means-quare estimation upper bounds

In this paper, a novel distributed Kalman filter consisting of a bank of interlaced filters is proposed for a signal model whose dynamic equation and measurement equation are coupled. Each of the interlaced filters estimates a part of state rather than the global state using its and its neighbor information, which is different from other distributed filters already existed (e.g., distributed Kalman filter based on diffusion strategy or consensus strategy, distributed fuzzy filter and distributed particle filter with Gaussian mixer approximation, etc). This relieves the calculation and communication burden in networks. In addition, the proposed distributed Kalman filtering contains no consensus strategies, which is useful in some cases since consensus usually requires an infinite number of iterations.     

Recursive state estimation based-on the outputs of partial nodes for discrete-time stochastic complex networks with switched topology

In this paper, the state estimation problem is studied for a class of discrete-time stochastic complex networks with switched topology. In the network under consideration, we assume that measurement outputs can be got from only partial nodes, besides, the switching rule of this network is characterized by a sequence of Bernoulli random variables. The aim of the presented estimation problem is to develop a recursive estimator based on the framework of extended Kalman filter (EKF), such that the upper bound for the filtering error convariance is optimized. In order to address the nonlinear functions, the Taylor series expansion is utilized and the high-order terms of linearization errors are expressed in an exact way. Furthermore, by solving two Ricatti-like difference equations, the gain matrix can be acquired at each time instant. It is shown that the filtering error is bounded in mean square under some conditions with the aid of stochastic analysis techniques. A numerical example is given to demonstrate the validity of the proposed estimator.     

Distributed dynamic state estimation with parameter identification for large-scale systems

In this paper, we consider a distributed dynamic state estimation problem for time-varying systems. Based on the distributed maximum a posteriori (MAP) estimation algorithm proposed in our previous study, which studies the linear measurement models of each subsystem, and by weakening the constraint condition as that each time-varying subsystem is observable, this paper proves that the error covariances of state estimation and prediction obtained from the improved algorithm are respectively positive definite and have upper bounds, which verifies the feasibility of this algorithm. We also use new weighting functions and time-varying exponential smoothing method to ensure the robustness and improve the forecast accuracy of the distributed state estimation method. At last, an example is used to demonstrate the effectiveness of the proposed algorithm together with the parameter identification.     

Extended evidential cognitive maps and its applications

Evidential cognitive maps (ECMs) are uncertain graph structure for describing causal reasoning through the cognitive maps (CMs) and Dempster–Shafer (D-S) theory, and utilize the basic probability assignments (BPAs) and intervals to denote connections among concepts and the state of concepts, respectively. ECMs have been proved effective and convenient in modeling those systems with both subjective and objective uncertainty. However, ECMs may get unreasonable results in system modeling when facing the problem of combining knowledge. To overcome the drawbacks of ECMs, we present extended evidential cognitive maps (EECMs) based on evidential reasoning (ER) theory, distance measure and convex optimization for the development of ECMs. In contrast with ECMs, in the EECMs, the default connections are redefined, a scheme of combining knowledge is established through the ER theory, and a convex-optimization-based approach is proposed for determining the weights of different EECMs. Both theoretical analysis and numerical examples indicate that EECMs not only develop ECMs, but also can overcome the limitations suffered by ECMs and other high-order cognitive maps including fuzzy grey cognitive maps (FGCMs), interval-valued fuzzy cognitive maps (IVFCMs) and intuitionistic fuzzy cognitive maps (IFCMs).     

Stability analysis of continuous-time systems with time-varying delay using new Lyapunov–Krasovskii functionals

This paper studies the stability of linear continuous-time systems with time-varying delay by employing new Lyapunov–Krasovskii functionals. Based on the new Lyapunov–Krasovskii functionals, more relaxed stability criteria are obtained. Firstly, in order to coordinate with the use of the third-order Bessel-Legendre inequality, a proper quadratic functional is constructed. Secondly, two couples of integral terms $\{{\int }_{t?h_t}^{s}x\left(s\right)ds,{\int }_s^{t}x\left(s\right)ds\}$ and $\{{\int }_{t?h_M}^{s}x\left(s\right)ds,{\int }_s^{t?h_t}x\left(s\right)ds\}$ are involved in the integral functionals ${\int }_{t?h_t}^t(·)ds$ and ${\int }_{t?h_M}^{t?h_t}(·)ds,$ respectively, so that the coupling information between them can be fully utilized. Finally, two commonly-used numerical examples are given to demonstrate the effectiveness of the proposed method.     

Robust adaptive control for prescribed performance tracking of constrained uncertain nonlinear systems

This paper proposes a robust adaptive control strategy for a class of state-constrained uncertain nonlinear systems with prescribed transient and steady-state behavior. The prescribed tracking performance can be characterized by constraints on an output tracking error. Both state and output constraints are achieved by bounding integral barrier Lyapunov functions in the backstepping procedure. A robust adaptive term is designed to compress auxiliary system uncertainties without the knowledge of their bounds. The satisfaction of control constraints and tracking error convergence are verified by theoretical analysis and are illustrated by simulation results.     

Distributed sensor fault diagnosis for a formation of multi-vehicle systems

In the paper, a distributed sensor fault detection and isolation scheme is presented for a network of second-order integrators. A new distributed control law is developed to achieve formation of the system. By using the integration information of distributed formation errors, the control law improves the robustness of the formation. A distributed observer is then designed in each vehicle based on the closed-loop dynamic model of the vehicle. Each vehicle updates the states of the distributed observer by employing the measurements of itself and the transmitted state estimations from its neighbors. Based on the distributed observer, a distributed fault detection observer and a distributed fault isolation observer are designed. The presented distributed fault detection observer in each vehicle is able to be sensitive to the faults of all vehicles in the system. By using the distributed fault isolation observers, each vehicle is able to be sensitive to the faults of itself, its neighbors and its neighbors’ neighbors and to be robust to the faults of other vehicles. Although the fault isolation of the proposed scheme is simple, computation loads of the scheme are lower than the current ones since only the model of the individual vehicle is used. Finally, the effectiveness of the control law and the fault diagnosis scheme is demonstrated by simulations and real-time experiments carried out based on a formation of three quadrotors.     

Orbit consensus of quantum networks based on interaction design

For a general quantum network system with a non-zero Hamiltonian H composed of n identical m-level quantum subsystems, any symmetric consensus state in the interaction picture exactly corresponds to an orbit in the Schrödinger picture, which is called the H-orbit of the symmetric consensus state. By using the interaction picture transformation and the tool of the LaSalle invariance principle, this paper analyzes the orbit consensus of this quantum network and designs the corresponding swapping operators such that the system converges to the H-orbit of the target symmetric consensus state that exists in the interaction picture. In particular, we prove the convergence of the quantum network to the H-orbit when the quantum interaction graph is connected and the system Hamiltonian is permutation invariant. The orbit consensuses of a four-qubit network system and a quantum network of three identical three-level subsystems are achieved numerically, which verifies the correctness of our theoretical results and the effectiveness of the designed swapping operators.     

Event-triggered non-fragile H∞ fault detection for discrete time-delayed nonlinear systems with channel fadings

In this paper, the event-triggered non-fragile H_∞ fault detection filter is designed for a class of discrete-time nonlinear systems subject to time-varying delays and channel fadings. The Lth Rice fading model is utilized to reflect the actual received measurement signals, and its channel coefficients own arbitrary probability density functions on interval [0,1]. The event-based filter is constructed to reduce unnecessary data transmissions in the communication channel, which only updates the measurement signal to the filter when the prespecified “event” is triggered. Multiplicative gain variations are utilized to describe the phenomenon of parameter variations in actual implementation of the filter. Based on Lyapunov stability theory, stochastic analysis technology along with linear matrix inequalities (LMIs) skills, sufficient conditions for the existence of the non-fragile fault detection filter are obtained which make the filtering error system stochastically stable and satisfy the H_∞ constraint. The gains of the filter can be calculated out by solving the feasible solution to a certain LMI. A simulation example is given to show the effectiveness of the proposed method.     

Synergetic governing controller design for the hydraulic turbine governing system with complex conduit system

The hydraulic turbine governing system plays an indispensable role in maintaining the stability of electrical power system. In this paper, synergetic control theory is introduced to enhance the regulating ability of the hydraulic turbine governing system. For the purpose of describing the characteristics of objective system and deducing the synergetic control rule, a nonlinear mathematic model of a hydraulic turbine governing system with long tail race and two surge tanks is established. Furthermore, the nonlinear characteristic of the hydraulic turbine is described by six variable partial derivatives. For further investigation, the hydraulic turbine governing system is conducted to running under load condition when its coaxial generator connects to an infinite bus. Simulation experiments have been made under both load disturbance and three-phase short circuit fault conditions to compare the dynamic performances of proposed synergetic governing controller and classic PID controller. The results indicate that the proposed synergetic governing controller is an effective alternative in normal condition and a superior one in emergency. Moreover, the robustness of synergetic governing controller has also been discussed at the end of this paper.