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Power consumption and data redundancy of wireless sensor networks (WSN) are widely considered for a distributed state monitoring network. For reducing the energy consumption and data amount, we propose a topology optimisation and an iterative parameter identification method for estimating the common model factors in WSN. The former method optimises the decentralised topology such that all the leaf nodes in a community connect to the head node directly. A circle topology is built to enable the remote leaf nodes to link to the head node through two adjoining relay nodes to reduce the whole communication distance and power consumption. Based on the optimised topology, an iterative identification method is proposed to minimise the information capacity by transmitting the processed results instead of raw data to reduce the data amount for calculation and storage. Then, we prove the consensus and convergence of the proposed identification method. Finally, two simulations verify the effectiveness of the proposed method and the comparative results present the data reduction for the on-board calculation, communication, and storage in the practical use of WSN.

A finite-time geometric control of quadrotor has been proposed in this paper by representing the attitude using rotation matrices to avoid the singularities and ambiguities associated with Euler an...

Many engineering optimisation problems can be summarised as mixed-integer optimal control problems (MIOCPs) owing to the needs for mixed-integer dynamic control decisions. However, the convergence ...

This paper investigates the convergence characteristics of the conventional P-type iterative learning control (ILC) scheme and exploits a gain-adaptive iterative learning control mechanism for a cl...

This paper concentrates on the suboptimal state estimation problem for systems without acknowledgement (ACK). The ACK signal is used for informing the estimator of whether control-input packets hav...

In this paper, we study distributed multiagent optimisation over undirected graphs. The optimisation problem is to minimise a global objective function, which is composed of the sum of a set of loc...

In this paper, we improve an earlier iterative successive approximation method for solving the Hamilton–Jacobi equation (HJE) arising in deterministic optimal control of affine nonlinear systems. T...

Having the capability to estimate parametric and non-parametric uncertainties, this paper investigates a regressor-free adaptive model-reference scheme for impedance control of robotic systems inte...

In this paper, two iterative algorithms are constructed to obtain the positive definite solutions of the discrete periodic algebraic Riccati matrix equations. In these two algorithms, the estimatio...

In the presence of probabilistic communication networks between agents, the convergence analysis of max-consensus algorithm (MCA) is addressed in this paper. It is considered that at each iteration of MCA, all agents share their measurements with adjacent agents via local communication networks which is applicable in many multi-agent systems (MASs). It is assumed that the communication networks have Bernoulli dropouts, i.e. the information exchanged between agents may be lost with Bernoulli distribution. In the proposed method, the information topology of MAS is modelled as a dynamic graph with the Bernoulli adjacency matrix. It is proved that in the presence of Bernoulli dropouts and under non-restrictive assumptions concerning the MAS features and communication topology, the MCA converges with a probability one in the finite time. Furthermore, the upper bounds are provided by means of deterministic and probabilistic expressions for the expectation and dispersion of convergence time, respectively...

This paper is concerned with convergence characterisation of an iterative algorithm for a class of reverse discrete periodic Lyapunov matrix equation associated with discrete-time linear periodic s...

This paper is to investigate the linear minimum mean square error estimation for Markovian jump linear system subject to unknown Markov chains, multi-channel mode and observation delays, and packet...

This paper addresses convergence issue of two networked iterative learning control (NILC) schemes for a class of discrete-time nonlinear systems with random packet dropout occurred in input and out...

Leaderless consensus for the fractional-order nonlinear multi-agent systems is investigated in this paper. At the first part, a control protocol is proposed to achieve leaderless consensus for the nonlinear single-integrator multi-agent systems. At the second part, based on sliding mode estimator, a control protocol is given to solve leaderless consensus for the the nonlinear single-integrator multi-agent systems. It shows that the control protocol can improve the systems’ convergence speed. At the third part, a control protocol is designed to accomplish leaderless consensus for the nonlinear double-integrator multi-agent systems. To judge the systems’ stability in this paper, two classic continuous Lyapunov candidate functions are chosen. Finally, several worked out examples under directed interaction topology are given to prove above results.

In order to cope with system disturbances in multi-phase batch processes with different dimensions, a hybrid robust control scheme of iterative learning control combined with feedback control is proposed in this paper. First, with a hybrid iterative learning control law designed by introducing the state error, the tracking error and the extended information, the multi-phase batch process is converted into a two-dimensional Fornasini–Marchesini (2D-FM) switched system with different dimensions. Second, a switching signal is designed using the average dwell-time method integrated with the related switching conditions to give sufficient conditions ensuring stable running for the system. Finally, the minimum running time of the subsystems and the control law gains are calculated by solving the linear matrix inequalities. Meanwhile, a compound 2D controller with robust performance is obtained, which includes a robust extended feedback control for ensuring the steady-state tracking error to converge rap...

This paper investigates the distributed optimisation problem for the multi-agent systems (MASs) with the simultaneous presence of external disturbance and the communication delay. To solve this problem, a two-step design scheme is introduced. In the first step, based on the internal model principle, the internal model term is constructed to compensate the disturbance asymptotically. In the second step, a distributed optimisation algorithm is designed to solve the distributed optimisation problem based on the MASs with the simultaneous presence of disturbance and communication delay. Moreover, in the proposed algorithm, each agent interacts with its neighbours through the connected topology and the delay occurs during the information exchange. By utilising Lyapunov–Krasovskii functional, the delay-dependent conditions are derived for both slowly and fast time-varying delay, respectively, to ensure the convergence of the algorithm to the optimal solution of the optimisation problem. Several numerica...

An observer-based controller for Lipschitz nonlinear systems is presented. The necessary and sufficient condition to ensure stability of state-observer as well as nonlinear system with state-feedback control law is derived. According to the separation principle, the closed-loop stability is guaranteed based on dual problems concerning stability of state-observer and stability of state-feedback parts. Also, the stability region for locally Lipschitz nonlinearities is obtained. A practical synthesis approach to achieve controller parameters is then given which yields the closed-loop convergence with less conservative results. The effectiveness of the proposed synthesis method is finally demonstrated by simulation results.

The problems of the constraints and the vibration suppression are investigated for the flexible Timoshenko robotic manipulator in this paper. Robust adaptive boundary control laws with the disturbance observes are designed to guarantee the convergence of the feedback flexible Timoshenko robotic manipulator system with the uncertain parameters and the states are proven to be uniform bounded. In addition, the proposed boundary controls are verified to be effectiveness by the numeral experiments.

The iterative learning control (ILC) is investigated for a class of nonlinear systems with measurement noises where the output is subject to sensor saturation. An ILC algorithm is introduced based on the measured output information rather than the actual output signal. A decreasing sequence is also incorporated into the learning algorithm to ensure a stable convergence under stochastic noises. It is strictly proved with the help of the stochastic approximation technique that the input sequence converges to the desired input almost surely along the iteration axis. Illustrative simulations are exploited to verify the effectiveness of the proposed algorithm.

This study investigated the multi-target circumnavigation problem. The multi-target circumnavigation problems involve a group of agents circumnavigating moving targets in a coordinated fashion. To address the problem, a decentralised estimator is first constructed at each agent to estimate the geometric centre of the targets. Then, the distributed control strategy is developed by means of the estimator, which guarantees that the agents preserve the desired distance to the target centre and rotate around the targets at uniformly spaced angles. In particular, the topology structure of the agents only needs to be a tree rather than the ring. Thus, the control scheme is more feasible and robust and requires less information. The convergence of the proposed algorithms is demonstrated based on Lasalle's invariance principle and algebraic graph theory. Several numerical simulations are provided to validate the results.

This paper considers the continuous–discrete-time adaptive observer (CDAO) design for a class of nonlinear systems with unknown constant parameters and sampled output measurements. The proposed observer is actually an impulsive system, since the observer state flows according to a set of differential equations and with instantaneous state jumps corresponding to measured samples and their estimates, and an inter-sample output predictor is used to predict the output during sampling intervals. By assuming appropriate persistent excitation conditions and following a technical lemma, an upper bound of the sampling intervals is derived, with which the convergence of the observer state and unknown parameters can be ensured. Finally, the proposed observer is used in examples of chaotic oscillators and single-link flexible-joint robot manipulator to show the effectiveness.

This paper presents a new design condition for the multivariable filtered Smith predictor (MFSP) in order to achieve sinusoidal disturbance rejection in steady state. The proposed MFSP strategy is based on a transfer matrix description with multiple delays. A suitable prediction error filter is presented to deal with this new design condition. The proposed design requirement can be used in model predictive controllers with inactive constraints in steady state. Two case studies are used to illustrate the main benefits of the proposed framework.

This paper investigates the problem of periodic motion control of second-order multi-agent systems in three dimensions under directed interaction topologies. Distributed algorithms for periodic rotating motion around a static and moving target were proposed by exploring the introduction of Cartestian coordinate coupling for each agent. In case of a static target, we show that when the nonsymmetric Laplacian matrix has certain properties, the damping gain is above a certain bound, and the Euler angle is equal to a critical value, all the agents will eventually rotate around the target periodically. In case of a moving target, the composite motion behaviours with translation and rotation will emerge, when this moving target's information can only be available to one or one subset of these agents and all agents have only local interactions. Tools like matrix theory, linear system theory and other mathematical skills were used for convergence analysis. Simulation results were provided to illustrate th...

This paper addresses a distributed consensus optimisation problem over networks with time-varying topologies based on Zero-Gradient-Sum ZGS algorithm. First, the exponential convergence of the algorithm is guaranteed under a new condition on network topologies, called cooperatively connected. This condition does not require the topology constantly connected or jointly connected but only requires the integral of the Laplacian matrix of the network topology over a period of time is connected. Hence, it is suitable for more general time-varying topologies. Second, by establishing a key mathematical lemma, we develop a convergence analysis technique which is based on the difference of the Lyapunov function rather than its differentiation. Finally, a simulation example is also provided to verify the results obtained in this paper.

This work presents the design and the corresponding analysis of a nonlinear robust adaptive controller for model reference tracking of an aircraft that has parametric uncertainties in its system matrices and additive state- and/or time-dependent nonlinear disturbance-like terms in its dynamics. Specifically, robust integral of the sign of the error feedback term and an adaptive term is fused with a proportional integral controller. Lyapunov-based stability analysis techniques are utilised to prove global asymptotic convergence of the output tracking error. Extensive numerical simulations are presented to illustrate the performance of the proposed robust adaptive controller.

In this paper, a novel iterative adaptive dynamic programming ADP algorithm, called generalised policy iteration ADP algorithm, is developed to solve optimal tracking control problems for discrete-time nonlinear systems. The idea is to use two iteration procedures, including an i-iteration and a j-iteration, to obtain the iterative tracking control laws and the iterative value functions. By system transformation, we first convert the optimal tracking control problem into an optimal regulation problem. Then the generalised policy iteration ADP algorithm, which is a general idea of interacting policy and value iteration algorithms, is introduced to deal with the optimal regulation problem. The convergence and optimality properties of the generalised policy iteration algorithm are analysed. Three neural networks are used to implement the developed algorithm. Finally, simulation examples are given to illustrate the performance of the present algorithm.

In this paper, a robust unknown input observer (UIO) for the joint state and fault estimation in discrete-time Takagi-Sugeno (TS) systems is presented. The proposed robust UIO, by applying the framework, leads to a less restrictive design procedure with respect to recent results found in the literature. The resulting design procedure aims at achieving a prescribed attenuation level with respect to the exogenous disturbances, while obtaining at the same time the convergence of the observer with a desired bound on the decay rate. An extension to the case of unmeasurable premise variables is also provided. Since the design conditions reduce to a set of linear matrix inequalities that can be solved efficiently using the available software, an evident advantage of the proposed approach is its simplicity. The final part of the paper presents an academic example and a real application to a multi-tank system, which exhibit clearly the performance and effectiveness of the proposed strategy., This work has been funded by the National Science Centre in Poland under the grant 2013/11/B/ST7/01110, by the Spanish Government (MINECO) through the project CICYT ECOCIS (ref. DPI2013-48243-C2-1-R), by MINECO and FEDER through the project CICYT HARCRICS (ref. DPI2014-58104-R), by AGAUR through the contracts FI-DGR 2014 (ref. 2014FI_B1 00172) and FIDGR 2015 (ref. 2015FI_B2 00171), and by the DGR of Generalitat de Catalunya (SAC group Ref. 2014/SGR/374).

The paper considers the issues of state estimation and output disturbance reconstruction for a class of switched linear systems with unknown inputs. A singular switched system is derived from the original switched system by taking the output disturbance as a part of a new extended state vector. For the constructed singular switched system, a robust sliding-mode switched observer which can not only estimate the states of original switched system but also reconstruct output disturbances is proposed, where the switching of the observer is synchronous with that of the switched system. A sufficient condition is provided to guarantee the existence of the switched observer by the feasibility of an optimisation problem with linear matrix inequality constraint, and the corresponding switching signal with average dwell time is designed such that the convergence of the estimation error system is proven to be exponential. Based on the state estimation of singular switched system, the methods of state estimation and output disturbance reconstruction of original switched system are proposed. Finally, the simulation results confirm the predicted performance of the proposed methods.

The problem of designing linear functional observers for discrete time-delay systems with unknown-but-bounded disturbances in both the plant and the output is considered for the first time in this paper. A novel approach to design a minimum-order observer is proposed to guarantee that the observer error is e-convergent, which means that the estimate converges robustly within an e-bound of the true state. Conditions for the existence of this observer are first derived. Then, by utilising an extended Lyapunov–Krasovskii functional and the free-weighting matrix technique, a sufficient condition for e-convergence of the observer error system is given. This condition is presented in terms of linear matrix inequalities with two parameters needed to be tuned, so that it can be efficiently solved by incorporating a two-dimensional search method into convex optimisation algorithms to obtain the smallest possible value for e. Three numerical examples, including the well-known single-link flexible joint robotic system, are given to illustrate the feasibility and effectiveness of our results.

This paper deals with the adaptive control of a class of stochastic Hammerstein–Wiener nonlinear systems with measurement noise. Despite the fundamental progress achieved so far, a general theory framework about adaptive control of Hammerstein–Wiener models is still absent. Such situation is mainly due to the lack of an appropriate parameterisation model. To this end, this paper presents a novel parameterisation model that is to replace unmeasurable internal variables with their estimations. Then, the adaptive control algorithm to be applied is derived on the basis of self-tuning control. In addition, due to the use of the internal variable estimations, the stability and convergence properties are different from the self-tuning control. Our aim, in theoretical analysis, is to discover what limitations are in using the estimations instead of the true values in a control algorithm. Representative numerical examples are given and the simulation results verify the theoretical analysis.

In this paper, the unknown input observer (UIO) design for singular delayed linear parameter varying (LPV) systems is considered regarding its application to actuator fault detection and isolation. The design procedure assumes that the LPV system is represented in the polytopic framework. Existence and convergence conditions for the UIO are established. The design procedure is formulated by means of linear matrix inequalities (LMIs). Actuator fault detection and isolation is based on using the UIO approach for designing a residual generator that is completely decoupled from unknown inputs and exclusively sensitive to faults. Fault isolation is addressed considering two different strategies: dedicated and generalised bank of observers' schemes. The applicability of these two schemes for the fault isolation is discussed. An open flow canal system is considered as a case study to illustrate the performance and usefulness of the proposed fault detection and isolation method in different fault scenarios.

This paper proposes a successive approximation design approach of observer-based optimal tracking controllers for time-delay systems with external disturbances. To solve a two-point boundary value problem with time-delay and time-advance terms and obtain the optimal tracking control law, two sequences of vector differential equations are constructed first. Second, the convergence of the sequences of the vector differential equations is proved to guarantee the existence and uniqueness of the control law. Third, a design algorithm of the optimal tracking control law is presented and the physically realisable problem is addressed by designing a disturbance state observer and a reference input state observer. An example of an industrial electric heater is given to demonstrate the efficiency of the proposed approach.

In this paper, the problem of distributed consensus estimation with randomly missing measurements is investigated for a diffusion system over the sensor network. A random variable, the probability of which is known a priori, is used to model the randomly missing phenomena for each sensor. The aim of the addressed estimation problem is to design distributed consensus estimators depending on the neighbouring information such that, for all random measurement missing, the estimation error systems are guaranteed to be globally asymptotically stable in the mean square. By using Lyapunov functional method and the stochastic analysis approach, the sufficient conditions are derived for the convergence of the estimation error systems. Finally, a numerical example is given to demonstrate the effectiveness of the proposed distributed consensus estimator design scheme.

Artificial bee colony ABC optimisation algorithm is a relatively simple and recent population-based probabilistic approach for global optimisation. The solution search equation of ABC is significantly influenced by a random quantity which helps in exploration at the cost of exploitation of the search space. In the ABC, there is a high chance to skip the true solution due to its large step sizes. In order to balance between diversity and convergence in the ABC, a Levy flight inspired search strategy is proposed and integrated with ABC. The proposed strategy is named as Levy Flight ABC LFABC has both the local and global search capability simultaneously and can be achieved by tuning the Levy flight parameters and thus automatically tuning the step sizes. In the LFABC, new solutions are generated around the best solution and it helps to enhance the exploitation capability of ABC. Furthermore, to improve the exploration capability, the numbers of scout bees are increased. The experiments on 20 test problems of different complexities and five real-world engineering optimisation problems show that the proposed strategy outperforms the basic ABC and recent variants of ABC, namely, Gbest-guided ABC, best-so-far ABC and modified ABC in most of the experiments.

The Hammerstein–Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein–Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.

Consensus problem of high-order integral multi-agent systems under switching directed topology is considered in this study. Depending on whether the agent’s full state is available or not, two distributed protocols are proposed to ensure that states of all agents can be convergent to a same stationary value. In the proposed protocols, the gain vector associated with the agent’s estimated state and the gain vector associated with the relative estimated states between agents are designed in a sophisticated way. By this particular design, the high-order integral multi-agent system can be transformed into a first-order integral multi-agent system. Also, the convergence of the transformed first-order integral agent’s state indicates the convergence of the original high-order integral agent’s state, if and only if all roots of the polynomial, whose coefficients are the entries of the gain vector associated with the relative estimated states between agents, are in the open left-half complex plane. Therefore, many analysis techniques in the first-order integral multi-agent system can be directly borrowed to solve the problems in the high-order integral multi-agent system. Due to this property, it is proved that to reach a consensus, the switching directed topology of multi-agent system is only required to be ‘uniformly jointly quasi-strongly connected’, which seems the mildest connectivity condition in the literature. In addition, the consensus problem of discrete-time high-order integral multi-agent systems is studied. The corresponding consensus protocol and performance analysis are presented. Finally, three simulation examples are provided to show the effectiveness of the proposed approach.

This article addresses the ultra-fast consensus problem of high-order discrete-time multi-agent systems based on a unified consensus framework. A novel multi-step predictive output mechanism is proposed under a directed communication topology containing a spanning tree. By predicting the outputs of a network several steps ahead and adding this information into the consensus protocol, it is shown that the asymptotic convergence factor is improved by a power of q + 1 compared to the routine consensus. The difficult problem of selecting the optimal control gain is solved well by introducing a variable called convergence step. In addition, the ultra-fast formation achievement is studied on the basis of this new consensus protocol. Finally, the ultra-fast consensus with respect to a reference model and robust consensus is discussed. Some simulations are performed to illustrate the effectiveness of the theoretical results.

This paper investigates the robust finite-time consensus problem of multi-agent systems in networks with undirected topology. Global nonlinear consensus protocols augmented with a variable structure are constructed with the aid of Lyapunov functions for each single-integrator agent dynamics in the presence of external disturbances. In particular, it is shown that the finite settling time of the proposed general framework for robust consensus design is upper bounded for any initial condition. This makes it possible for network consensus problems to design and estimate the convergence time offline for a multi-agent team with a given undirected information flow. Finally, simulation results are presented to demonstrate the performance and effectiveness of our finite-time protocols.

This paper deals with the problem of varying initial state shifts in continuous-time iterative learning control (ILC) by employing the two-dimensional (2D) analysis approach. Two PD-type ILC algorithms are considered based on an average operator, where the second one is combined with an initial rectifying action. For both ILC algorithms, 2D Roesser systems are applied to develop sufficient conditions to guarantee their convergence. It is shown that the ILC processes converge with the increasing of iteration, and the converged tracking error can be formulated in terms of the mean of the initial output error and the learning parameters. Numerical simulations are given to illustrate that both ILC algorithms are robust against varying initial state errors, and the second one can achieve uniform convergence over any specified time interval with good learning transients.

In this paper, an adaptive iterative learning control scheme is proposed for a class of non-linearly parameterised systems with unknown time-varying parameters and input saturations. By incorporating a saturation function, a new iterative learning control mechanism is presented which includes a feedback term and a parameter updating term. Through the use of parameter separation technique, the non-linear parameters are separated from the non-linear function and then a saturated difference updating law is designed in iteration domain by combining the unknown parametric term of the local Lipschitz continuous function and the unknown time-varying gain into an unknown time-varying function. The analysis of convergence is based on a time-weighted Lyapunov–Krasovskii-like composite energy function which consists of time-weighted input, state and parameter estimation information. The proposed learning control mechanism warrants a L2[0, T] convergence of the tracking error sequence along the iteration axis. Simulation results are provided to illustrate the effectiveness of the adaptive iterative learning control scheme.

This paper presents a kind of state observer for a velocity-sensorless vertical take-off and landing VTOL aircraft with bounded time-varying delay in its measurement outputs. The proposed observer predicts current state variables based on the delayed outputs, and the estimated state variables can be considered as the actual state variables for feedback control scheme design. Since the delay is time-varying, compared to the constant delay case, different analysis theory must be employed. Under the assumption that the delays are identical for different outputs and bounded input, the asymptotic convergence property of the estimation error based on Lyapunov–Razumikhin theorem is proved. A relative large time delay for the VTOL aircraft in the outputs has been tested in the numerical simulation, and the simulation results show the effectiveness of the proposed observer.

This paper poses the enclosing control problem with identical geometry for a group of targets which are either stationary or moving and offers consensus-based distributed control protocols. An estimator is first introduced to estimate the central position of the targets. We then propose a target-enclosing control law with velocity information based on the centre estimating algorithm and consensus theory. A target-enclosing control law without the velocity information is further designed. The Lyapunov theory and Lasalle’s invariance principle are applied to show the convergence of the proposed control algorithms. Finally, numerical simulations are given to illustrate the effectiveness of our proposed strategy.

In this paper, we mainly focus on the problem of quantised feedback stabilisation of a stochastic discrete-time linear system with white noise input. The dynamic quantiser is used here. The stability of the system under state quantisation and input quantisation is analysed in detail, respectively. Both the convergence of the state's mean and the boundedness of the state's covariance matrix norm should be considered when analysing its stability. It is shown that for the two situations of the state quantisation and the input quantisation, if the system without noise input can be stabilised by a linear feedback law, it must be stabilised by the dynamic quantised feedback control policy. The sufficient conditions that the dynamic quantiser should satisfy are given. Using the results obtained in this paper, one can test whether the stochastic system is stabilisable or not. Numerical examples are given to show the effectiveness of the results.

In this research, we apply a scenario aggregation approach to solving the supply chain contract model formulated by two-stage stochastic programming problem. The supply chain contract can achieve the coordination between the buyer and the supplier. We formulate the stochastic programming model for a quantity-flexibility contract. The scenario aggregation method called the progressive hedging method is used to solve this problem. Experimental results show the convergence behaviour of the algorithm and the sensitivity of parameters.

Recent applications call for distributed weighted average estimation over sensor networks, where sensor measurement accuracy or environmental conditions need to be taken into consideration in the final consensused group decision. In this paper, we propose new dynamic consensus filter design to distributed estimate weighted average of sensors’ inputs on directed graphs. Based on recent advances in the filed, we modify the existing proportional-integral consensus filter protocol to remove the requirement of bi-directional gain exchange between neighbouring sensors, so that the algorithm works for directed graphs where bi-directional communications are not possible. To compensate for the asymmetric structure of the system introduced by such a removal, sufficient gain conditions are obtained for the filter protocols to guarantee the convergence. It is rigorously proved that the proposed filter protocol converges to the weighted average of constant inputs asymptotically, and to the weighted average of time-varying inputs with a bounded error. Simulations verify the effectiveness of the proposed protocols.

This paper presents a consensus-based stochastic subgradient algorithm for multi-agent networks to minimise multiple convex but not necessarily differential objective functions, subject to an intersection set of multiple closed convex constraint sets. Compared with the existing results an alternative subgradient algorithm is first introduced based on two level subgradient iterations, where the first level is to minimise the component functions, and the second to enforce the iterates not oscillate from the constraint set wildly. In addition, a distributed consensus-based type of the proposed subgradient algorithm is constructed within the framework of multi-agent networks for the case when the iteration index of local objective functions and local constraint sets is not homologous. Detailed convergence analysis of the proposed algorithms is established using matrix theories and super-martingale convergence theorem. In addition, a pre-step convergence factor is obtained in this study to characterise the dis...

This article investigates the problem of accelerating average consensus in undirected and connected networks. The protocol using the information of second-order neighbours with communication delays is proposed and the delay effects on stability and the convergence speed are analysed, respectively, under an assumption about the network topologies. It is proved that, for appropriate communication delays, networks reach average consensus faster under the proposed protocol than the standard protocol using only the information of first-order neighbours. Finally, a simulation example is presented to illustrate the proposed results.

Mean square average consensus for multi-agent systems with measurement noise and time delay under fixed digraph is studied in this article. The time-varying consensus-gain is introduced to attenuate the measurement noise. By combining the tools of algebraic graph theory, matrix theory and stochastic analysis, consensus protocols for multi-agent systems with measurement noise and time delay are elaborately analysed. The example and simulation results are given to illustrate the effectiveness of the obtained theoretical results. Moreover, the simulations demonstrate that, the proper consensus-gain function in the consensus protocol is the necessary and sufficient condition for the convergence of the multi-agent systems.

This paper investigates the stochastic bounded consensus tracking problems of second-order multi-agent systems, where the control input of an agent can only use the information measured at the sampling instants from its neighbours or the virtual leader with a time-varying reference state, the measurements are corrupted by random noises and the signal sampling process induces the general sampling delay. First, the stochastic bounded consensus tracking protocol based on sampled-data with the general sampling delay is presented by using the delay decomposition technique. Second, the augmented matrix method, the probability limit theory and some other techniques are employed to derive the necessary and sufficient conditions guaranteeing the mean square bounded consensus tracking. The theoretical results show that the convergence of the proposed protocol simultaneously depends on the constant feedback gains, the network topology, the sampled period and the sampling delay, and that the static consensus tracking...