Adaptive pinning control of deteriorated nonlinear coupling networks with circuit realization

Distributed Adaptive Output Feedback Consensus of Parabolic PDE Agents on Undirected Networks

In this article, we investigate the distributed adaptive consensus problem of parabolic partial differential equation (PDE) agents by output feedback on undirected communication networks, in which two cases of no leader and leader-follower with a leader are taken into account. For the leaderless case, a novel distributed adaptive protocol, namely, the vertex-based protocol, is designed to achieve consensus by taking advantage of the relative output information of itself and its neighbors for any given undirected connected communication graph. For the case of leader-follower, a distributed continuous adaptive controller is put forward to converge the tracking error to a bounded domain by using the Lyapunov function, graph theory, and PDE theory. Furthermore, a corollary that the tracking error tends to zero by replacing the continuous controller with the discontinuous controller is given. Finally, the relevant simulation results are further demonstrated to demonstrate the theoretical results obtained.

Adaptive NN-Based Consensus for a Class of Nonlinear Multiagent Systems With Actuator Faults and Faulty Networks

This article addresses the problem of fault-tolerant consensus control of a general nonlinear multiagent system subject to actuator faults and disturbed and faulty networks. By using neural network (NN) and adaptive control techniques, estimations of unknown state-dependent boundaries of nonlinear dynamics and actuator faults, which can reflect the worst impacts on the system, are first developed. A novel NN-based adaptive observer is designed for the observation of faulty transformation signals in networks. On the basis of the NN-based observer and adaptive control strategies, fault-tolerant consensus control schemes are designed to guarantee the bounded consensus of the closed-loop multiagent system with disturbed and faulty networks and actuator faults. The validity of the proposed adaptively distributed consensus control schemes is demonstrated by a multiagent system composed of five nonlinear forced pendulums.

Analog Control Circuit Designs for a Class of Continuous-Time Adaptive Fault-Tolerant Control Systems

This article is concerned with the robust adaptive fault-tolerant control (FTC) circuit designs for a class of continuous-time disturbed systems. A circuit realization method is investigated to convert the robust adaptive FTC control schemes into analog control circuits. An adaptive compensation control scheme against state-dependent and partially bounded actuator faults and disturbances is first developed to demonstrate the approach clearly, then its equivalent control circuits are implemented by using the circuit theory. Compared with simulation results achieved by MATLAB and professional circuit simulation software, the effectiveness of the proposed robust adaptive FTC circuits is validated by a rocket fairing system and a Chua's circuit system.

A Partial-Node-Based Approach to State Estimation for Complex Networks With Sensor Saturations Under Random Access Protocol

In this article, the robust finite-horizon state estimation problem is investigated for a class of time-varying complex networks (CNs) under the random access protocol (RAP) through available measurements from only a part of network nodes. The underlying CNs are subject to randomly occurring uncertainties, randomly occurring multiple delays, as well as sensor saturations. Several sequences of random variables are employed to characterize the random occurrences of parameter uncertainties and multiple delays. The RAP is adopted to orchestrate the data transmission at each time step based on a Markov chain. The aim of the addressed problem is to design a series of robust state estimators that make use of the available measurements from partial network nodes to estimate the network states, under the RAP and over a finite horizon, such that the estimation error dynamics achieves the prescribed H_∞ performance requirement. Sufficient conditions are provided for the existence of such time-varying partial-node-based H_∞ state estimators via stochastic analysis and matrix operations. The desired estimators are parameterized by solving certain recursive linear matrix inequalities. The effectiveness of the proposed state estimation algorithm is demonstrated via a simulation example.

Variance-Constrained Recursive State Estimation for Time-Varying Complex Networks With Quantized Measurements and Uncertain Inner Coupling

In this paper, a new recursive state estimation problem is discussed for a class of discrete time-varying stochastic complex networks with uncertain inner coupling and signal quantization under the error-variance constraints. The coupling strengths are allowed to be varying within certain intervals, and the measurement signals are subject to the quantization effects before being transmitted to the remote estimator. The focus of the conducted topic is on the design of a variance-constrained state estimation algorithm with the aim to ensure a locally minimized upper bound on the estimation error covariance at every sampling instant. Furthermore, the boundedness of the resulting estimation error is analyzed, and a sufficient criterion is established to ensure the desired exponential boundedness of the state estimation error in the mean square sense. Finally, some simulations are proposed with comparisons to illustrate the validity of the newly developed variance-constrained estimation method.

Trajectory Tracking on Uncertain Complex Networks via NN-Based Inverse Optimal Pinning Control

A new approach for trajectory tracking on uncertain complex networks is proposed. To achieve this goal, a neural controller is applied to a small fraction of nodes (pinned ones). Such controller is composed of an on-line identifier based on a recurrent high-order neural network, and an inverse optimal controller to track the desired trajectory; a complete stability analysis is also included. In order to verify the applicability and good performance of the proposed control scheme, a representative example is simulated, which consists of a complex network with each node described by a chaotic Lorenz oscillator.

Model-Free Fault Tolerant Control for a Class of Complex Dynamical Networks With Derivative Couplings

This paper studies the fault tolerant synchronization control for a class of derivative coupled complex dynamical networks (CDNs). Different from the existing results, each subsystem model is assumed to be completely unknown and the coupling terms are mismatched with the control input. Within this framework, a novel model-free fault tolerant controller is designed. Under the proposed control law, the synchronization errors of CDNs are proved to asymptotically converge to zero, which means that the synchronization is successfully achieved. Especially, by combining an important spectral decomposition technique and some properties of Laplacian matrix, a data-based algorithm is provided to derive the controller parameter. In addition, the proposed method is also valid for the CDNs with unknown coupling weights. Finally, examples on circuit systems are given to verify the theoretical results, and some circuit realizations of the proposed control law are implemented based on the circuit theory.

Closed-loop control of nonlinear neural networks: The estimate of control time and energy cost

This paper concentrates on an estimate of the upper bounds for control time and energy cost of a class of nonlinear neural networks (NNs). By constructing the appropriate closed-loop controller u^S and utilizing the inequality technique, sufficient conditions are proposed to guarantee achieving control target in finite time of the considered systems. Then, the estimate of the upper bounds for the control energy cost of the designed controller u^S is proposed. Our results provide a new controller which can ensure the realization of finite time control and energy consumption control for a class of nonlinear NNs. Meanwhile, the obtained results contribute to qualitative analysis of some nonlinear systems. Finally, numerical examples are presented to demonstrate the effectiveness of our theoretical results.

Analysis and Pinning Control for Output Synchronization and H∞ Output Synchronization of Multiweighted Complex Networks

The output synchronization and H_∞ output synchronization problems for multiweighted complex network are discussed in this paper. First, we analyze the output synchronization of multiweighted complex network by exploiting Lyapunov functional and Barbalat's lemma. In addition, some nodes- and edges-based pinning control strategies are developed to ensure the output synchronization of multiweighted complex network. Similarly, the H_∞ output synchronization problem of multiweighted complex network is also discussed. Finally, two numerical examples are presented to verify the correctness of the obtained results.

Global Pinning Synchronization of Complex Networks With Sampled-Data Communications

This paper investigates the global pinning synchronization problem for a class of complex networks with aperiodic samplings. Combined with the Writinger-based integral inequality, a new less conservative criterion is presented to guarantee the global pinning synchronization of the complex network. Furthermore, a novel condition is proposed under which the complex network is globally pinning synchronized with a given performance index. It is shown that the performance index has a positive correlation with the upper bound of the sampling intervals. Finally, the validity and the advantage of the theoretic results obtained are verified by means of the applications in Chua's circuit and pendulum.

Cluster Synchronization for Interacting Clusters of Nonidentical Nodes via Intermittent Pinning Control

The cluster synchronization problem is investigated using intermittent pinning control for the interacting clusters of nonidentical nodes that may represent either general linear systems or nonlinear oscillators. These nodes communicate over general network topology, and the nodes from different clusters are governed by different self-dynamics. A unified convergence analysis is provided to analyze the synchronization via intermittent pinning controllers. It is observed that the nodes in different clusters synchronize to the given patterns if a directed spanning tree exists in the underlying topology of every extended cluster (which consists of the original cluster of nodes as well as their pinning node) and one algebraic condition holds. Structural conditions are then derived to guarantee such an algebraic condition. That is: 1) if the intracluster couplings are with sufficiently strong strength and the pinning controller is with sufficiently long execution time in every period, then the algebraic condition for general linear systems is warranted and 2) if every cluster is with the sufficiently strong intracluster coupling strength, then the pinning controller for nonlinear oscillators can have its execution time to be arbitrarily short. The lower bounds are explicitly derived both for these coupling strengths and the execution time of the pinning controller in every period. In addition, in regard to the above-mentioned structural conditions for nonlinear systems, an adaptive law is further introduced to adapt the intracluster coupling strength, such that the cluster synchronization for nonlinear systems is achieved.

On Group Synchronization for Interacting Clusters of Heterogeneous Systems

This paper investigates group synchronization for multiple interacting clusters of nonidentical systems that are linearly or nonlinearly coupled. By observing the structure of the coupling topology, a Lyapunov function-based approach is proposed to deal with the case of linear systems which are linearly coupled in the framework of directed topology. Such an analysis is then further extended to tackle the case of nonlinear systems in a similar framework. Moreover, the case of nonlinear systems which are nonlinearly coupled is also addressed, however, in the framework of undirected coupling topology. For all these cases, a consistent conclusion is made that group synchronization can be achieved if the coupling topology for each cluster satisfies certain connectivity condition and further, the intra-cluster coupling strengths are sufficiently strong. Both the lower bound for the intra-cluster coupling strength as well as the convergence rate are explicitly specified.

On the Bipartite Consensus for Generic Linear Multiagent Systems With Input Saturation

The bipartite consensus problem for a group of homogeneous generic linear agents with input saturation under directed interaction topology is examined. It is established that if each agent is asymptotically null controllable with bounded controls and the interaction topology described by a signed digraph is structurally balanced and contains a spanning tree, then the semi-global bipartite consensus can be achieved for the linear multiagent system by a linear feedback controller with the control gain being designed via the low gain feedback technique. The convergence analysis of the proposed control strategy is performed by means of the Lyapunov method which can also specify the convergence rate. At last, the validity of the theoretical findings is demonstrated by two simulation examples.

Adaptive Fault-Tolerant Synchronization Control of a Class of Complex Dynamical Networks With General Input Distribution Matrices and Actuator Faults

This paper is concerned with the problem of adaptive fault-tolerant synchronization control of a class of complex dynamical networks (CDNs) with actuator faults and unknown coupling weights. The considered input distribution matrix is assumed to be an arbitrary matrix, instead of a unit one. Within this framework, an adaptive fault-tolerant controller is designed to achieve synchronization for the CDN. Moreover, a convex combination technique and an important graph theory result are developed, such that the rigorous convergence analysis of synchronization errors can be conducted. In particular, it is shown that the proposed fault-tolerant synchronization control approach is valid for the CDN with both time-invariant and time-varying coupling weights. Finally, two simulation examples are provided to validate the effectiveness of the theoretical results.

Graph Theory-Based Pinning Synchronization of Stochastic Complex Dynamical Networks

This paper is concerned with the adaptive pinning synchronization problem of stochastic complex dynamical networks (CDNs). Based on algebraic graph theory and Lyapunov theory, pinning controller design conditions are derived, and the rigorous convergence analysis of synchronization errors in the probability sense is also conducted. Compared with the existing results, the topology structures of stochastic CDN are allowed to be unknown due to the use of graph theory. In particular, it is shown that the selection of nodes for pinning depends on the unknown lower bounds of coupling strengths. Finally, an example on a Chua's circuit network is given to validate the effectiveness of the theoretical results.

FLS-Based Adaptive Synchronization Control of Complex Dynamical Networks With Nonlinear Couplings and State-Dependent Uncertainties

This paper is concerned with the problem of synchronization control of complex dynamical networks (CDN) subject to nonlinear couplings and uncertainties. An fuzzy logical system-based adaptive distributed controller is designed to achieve the synchronization. The asymptotic convergence of synchronization errors is analyzed by combining algebraic graph theory and Lyapunov theory. In contrast to the existing results, the proposed synchronization control method is applicable for the CDN with system uncertainties and unknown topology. Especially, the considered uncertainties are allowed to occur in the node local dynamics as well as in the interconnections of different nodes. In addition, it is shown that a unified controller design framework is derived for the CDN with or without coupling delays. Finally, simulations on a Chua's circuit network are provided to validate the effectiveness of the theoretical results.

Model-free optimal controller design for continuous-time nonlinear systems by adaptive dynamic programming based on a precompensator

In this paper, we consider the problem of developing a controller for continuous-time nonlinear systems where the equations governing the system are unknown. Using the measurements, two new online schemes are presented for synthesizing a controller without building or assuming a model for the system, by two new implementation schemes based on adaptive dynamic programming (ADP). To circumvent the requirement of the prior knowledge for systems, a precompensator is introduced to construct an augmented system. The corresponding Hamilton-Jacobi-Bellman (HJB) equation is solved by adaptive dynamic programming, which consists of the least-squared technique, neural network approximator and policy iteration (PI) algorithm. The main idea of our method is to sample the information of state, state derivative and input to update the weighs of neural network by least-squared technique. The update process is implemented in the framework of PI. In this paper, two new implementation schemes are presented. Finally, several examples are given to illustrate the effectiveness of our schemes.

Synchronization of nonlinear coupled networks via aperiodically intermittent pinning control

In this paper, pinning synchronization problem for nonlinear coupled networks is investigated, which can be recurrently connected neural networks, cellular neural networks, Hodgkin-Huxley models, Lorenz chaotic oscillators, and so on. Nodes in the network are assumed to be identical and nodes' dynamical behaviors are described by continuous-time equations. The network topology is undirected and static. At first, the scope of accepted nonlinear coupling functions is defined, and the effect of nonlinear coupling functions on synchronization is carefully discussed. Then, the pinning control technique is used for synchronization, especially the control type is aperiodically intermittent. Some sufficient conditions to guarantee global synchronization are presented. Furthermore, the adaptive approach is also applied on the pinning control, and a centralized adaptive algorithm is designed and its validity is also proved. Finally, several numerical simulations are given to verify the obtained theoretical results.

Synchronization and adaptive control of an array of linearly coupled reaction-diffusion neural networks with hybrid coupling

In this paper, we propose a general array model of coupled reaction-diffusion neural networks with hybrid coupling, which is composed of spatial diffusion coupling and state coupling. By utilizing the Lyapunov functional method combined with the inequality techniques, a sufficient condition is given to ensure that the proposed network model is synchronized. In addition, when the external disturbances appear in the network, a criterion is obtained to guarantee the H∞ synchronization of the network. Moreover, some adaptive strategies to tune the coupling strengths among network nodes are designed for reaching synchronization and H∞ synchronization. Some criteria for synchronization and H∞ synchronization are derived by using the designed adaptive laws. Numerical simulations are presented finally to demonstrate the effectiveness of the obtained theoretical results.

Novel adaptive strategies for synchronization of linearly coupled neural networks with reaction-diffusion terms

In this paper, two types of linearly coupled neural networks with reaction-diffusion terms are proposed. We respectively investigate the adaptive synchronization of these two types of complex network models. With local information of node dynamics, some novel adaptive strategies to tune the coupling strengths among network nodes are designed. By constructing appropriate Lyapunov functionals and using inequality techniques, several sufficient conditions are given for reaching synchronization by using the designed adaptive laws. Finally, two examples with numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

H∞ state estimation for complex networks with uncertain inner coupling and incomplete measurements

In this paper, the H∞ state estimation problem is investigated for a class of complex networks with uncertain coupling strength and incomplete measurements. With the aid of the interval matrix approach, we make the first attempt to characterize the uncertainties entering into the inner coupling matrix. The incomplete measurements under consideration include sensor saturations, quantization, and missing measurements, all of which are assumed to occur randomly. By introducing a stochastic Kronecker delta function, these incomplete measurements are described in a unified way and a novel measurement model is proposed to account for these phenomena occurring with individual probability. With the measurement model, a set of H∞ state estimators is designed such that, for all admissible incomplete measurements as well as the uncertain coupling strength, the estimation error dynamics is exponentially mean-square stable and the H∞ performance requirement is satisfied. The characterization of the desired estimator gains is derived in terms of the solution to a convex optimization problem that can be easily solved using the semidefinite program method. Finally, a numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach.

Distributed consensus tracking for multiple uncertain nonlinear strict-feedback systems under a directed graph

In this brief, we study the distributed consensus tracking control problem for multiple strict-feedback systems with unknown nonlinearities under a directed graph topology. It is assumed that the leader's output is time-varying and has been accessed by only a small fraction of followers in a group. The distributed dynamic surface design approach is proposed to design local consensus controllers in order to guarantee the consensus tracking between the followers and the leader. The function approximation technique using neural networks is employed to compensate unknown nonlinear terms induced from the controller design procedure. From the Lyapunov stability theorem, it is shown that the consensus errors are cooperatively semiglobally uniformly ultimately bounded and converge to an adjustable neighborhood of the origin.