This study proposes a novel distributed economic model predictive control (EMPC) strategy for energy-efficient cooperative formation of decoupled multi-agent non-linear systems with transmission delay. In this system, each subsystem is controlled to maximise the economic performance during tracking the reference trajectory and maintaining its relative position to the neighbouring subsystems. The cooperation between subsystems is executed through the cost functions and coupled constraints associated with the delayed information. A Lyapunov-based contractive constraint is introduced to establish recursive feasibility of the proposed EMPC strategy. Moreover, stability of any single subsystem with the EMPC is proved rigorously by exploiting the idea of input-to-state stability and for both strongly and weakly connected networks, stability of the whole system is then proved by using the generalised small gain condition. The effectiveness of the proposed strategy is illustrated by two numerical simulation experiments.

In this study, distributed, event-based network flows are studied for solving the linear algebraic equation over an undirected network. Each node holds a dynamic state, which is broadcast to its neighbours at a sequence of event-based time instants in an asynchronous manner, at both its own and its neighbours' event times. Each node then updates its control rule for its dynamic states. It is shown that if the linear algebraic equation has a unique solution or an infinite set of solutions, all nodes states converge to a unique/common solution if the applied network is connected and the trigger function is well constructed. Convergence rates are established explicitly as a result of the linear equation, the network structure and the triggering conditions. An explicit lower bound on the time interval between consecutive events is obtained, and therefore the proposed network flow does not exhibit Zeno behaviour. Simulations are provided to illustrate the effectiveness of the proposed network flow. Additionally, they also investigate the scenario where nodes are only allowed to update their states at their own events, and demonstrate the similarity and difference compared to the proposed solution.

The bearing-based coordinated circumnavigation control for networked multi-agent systems with only bearing measurements in the presence of moving target is studied. First, a distributed algorithm is proposed to estimate the target's velocity and the distances between the agents and the target, based on the velocity and the bearing information of the local network. Then, a distributed circumnavigation algorithm is designed to drive the agents to circumnavigate around a moving target at a desired distance. The stability of the proposed control algorithm is proven by employing the newly developed bearing rigidity theory. Finally, the simulation experiment is performed based on the Gazebo simulator to illustrate the effectiveness of the proposed circumnavigation control law.

Based on the improved radial basis function (RBF) neural networks, the distributed three-dimension formation control scheme in the presence of dynamic uncertainties is studied for non-linear multi-agent systems with time delay. A virtual leader which tracks the desired signal is followed by all agents adaptively. Linear reduced-order observers are designed on the basis of absolute and local state errors of each agent. The local state error and absolute state error are generated between neighbouring agents and each individual agent in formation, respectively. The time delay for each agent in the formation can be offset by designing a Lyapunov function, which can simplify the controller design. To deal with non-linear dynamic uncertainties and unavoidable disturbance, improved RBF neural networks are employed. In comparison with traditional RBF neural networks, improved RBF neural networks can provide better convergence performance. Subsequently, the formation controller is designed and the stability of the systems is validated by using a new Lyapunov function. Numerical simulation is conducted to demonstrate the effectiveness of the proposed method for non-linear multi-agent time-delay systems.

In this study, the velocity tracking control of electric multiple units (EMUs) with non-linearity and uncertainty during braking is investigated. A consensus braking algorithm with distributed sliding mode observers is proposed. Firstly, a multi-agent model with non-linear coupling and uncertain external disturbances is established. Secondly, distributed observers are designed, in which a real-time estimation equation for coupling force and disturbances is established based on the equivalent control principle of sliding mode variable structure. Finally, a robust consensus algorithm is proposed to achieve a consensus velocity tracking of each carriage on the target braking curve. The distances between the adjacent carriages are stabilised at stationary distances in a safe range by an artificial potential field function. Experiments show that the algorithm has high accuracy and anti-interference ability in the braking process.

The analysis and synthesis of cyber-physical systems (CPSs) require an integrative approach of the study of the underlying physical and cyber components and their intricate and interactive interconnections. Their implementation using distributed embedded systems (DESs) requires the modelling and control of the entire CPS, where uncertainties may occur both in the physical and in the cyber parts. The focus of this study is on the adaptive control of such CPS. When multiple applications have to be controlled using a DES, often the underlying resources are shared. One of the main implications of this resource contention is the introduction of delays in the control messages reaching their intended destination. The specific set of problems the authors consider here are those where a control implementation leads to delays that are unknown. By separating the known part of the delay from the uncertain part, the authors propose a delay-aware design for the controller. They derive the underlying models, the requisite adaptive control designs, and the stability of the adaptive system. The authors showed effectiveness of the result and its improvement over non-adaptive designs using simulation.

This study addresses the issue of distributed event-triggered state estimators subject to deception attacks for sensor networked systems. A decentralised event-triggered scheme (ETS) is introduced to determine whether the sampling data of each sensor is transmitted or not, respectively. In this scheme, each sensor node is independent to decide to deliver the local measurement output through the corresponding ETS. Due to the insertion of the network, the effect of the deception attacks along with time delay and packet dropouts are considered in this study. A novel estimator network is established to realise the estimation of the decoupling output measurements and coupling intercommunication measurements. Firstly, a distributed event-triggered estimating system with deception attacks is constructed in a mathematical model. Secondly, sufficient conditions are derived, which can ensure the stability of the designed estimating error systems and the related parameters of the desired distributed estimators are presented in an accurate form. Finally, a simulated example is given to demonstrate the effectiveness of the designed event-triggered distributed state estimator systems under the deception attacks.

The process of enhancing the ability of a complex network against various malicious attacks through link addition/rewiring has been the subject of extensive interest and research. The performance of existing methods often highly depends on full knowledge about the network topology. In this study, the authors devote ourselves to developing new distributed strategies to perform link manipulation sequentially using only local accessible topology information. This strategy is concerned with a matrix-perturbation-based approximation of the network-based optimisation problems and a distributed algorithm to compute eigenvectors and eigenvalues of graph matrices. In addition, the development of a distributed stopping criterion, which provides the desired accuracy on the distributed estimation algorithm, enables us to solve the link-operation problem in a finite-time manner. Finally, all results are illustrated and validated using numerical demonstrations and examples.

The problem of distributed constrained optimisation over a network of agents, where the goal is to cooperatively minimise the sum of all local convex objective functions is studied. Each agent in the network possesses only its private local convex objective function and is constrained to a coupling equality constraint and its local inequality constraint. Moreover, the authors particularly focus on the scenario where each agent is only allowed to interact with their in-neighbours over a series of time-varying directed unbalanced networks. To collectively address the optimisation problem, a novel distributed primal-dual push-DIGing (integrated push-sum strategy with distributed inexact gradient tracking method) algorithm (termed as DPD-PD) in which agents employ uncoordinated step-sizes is proposed. Unlike other methods, DPD-PD allows not only the mixing matrices are column-stochastic, but also the step-sizes are uncoordinated. An important feature of DPD-PD is handling distributed constrained optimisation problems in the case of time-varying directed unbalanced networks. When objective functions are strongly convex and smooth, the authors demonstrate that DPD-PD converges linearly to the optimal solution given that the uncoordinated step-sizes are smaller than an upper bound. Explicit convergence rate is also conducted. Preliminary results on some numerical experiments validate the theoretical findings.

In this study, the distributed optimisation problem for linear multi-agent systems with disturbance rejection is considered. The topology graph is assumed to be uniformly jointly strongly connected and the disturbance is not limited to satisfy the matching condition. Each agent is assigned with a local quadratic cost function and the objective is to minimise the sum of local cost functions based on information exchange. The authors propose a distributed observer for each agent such that other agents' cost functions are obtained. Then, the state feedback and output feedback optimal algorithms are designed based on the output of the distributed observer. The theoretical results are validated by simulations.

The path optimisation problem of mobile sensor networks for arrival-of-angle (AOA) target localisation, using the consensus-based extended information filter is considered, in this study. A new idea of equipping sensors with information-driven mobility to improve the estimation accuracy with respect to a stationary target is proposed by the authors. A gradient descent method is used for mobile sensors, which are subject to geometric constraints, to choose the next optimal waypoints. The corresponding optimisation problem is solved in a distributed manner, by selecting a proper cost function for each mobile sensor. It is shown that the boundedness of the estimation error is guaranteed. Moreover, they find that the mobility of sensors does decrease the estimation error bounds compared with the static sensor networks, which is beneficial for the localisation performance. Simulation is carried out to show the effectiveness of the proposed method.

In this study, the solution of a convex distributed optimisation problem with a global coupling inequality constraint is considered. By using the Lagrange duality framework, the problem is transformed into a distributed consensus optimisation problem and then based on the recently proposed Hybrid Alternating Direction Method of Multipliers (H-ADMM), which merges distributed and centralised optimisation concepts problems, a novel distributed algorithm is developed. In particular, the authors offer a reformulation of the original H-ADMM in an operator theoretical framework, which exploits the known relationship between ADMM and Douglas–Rachford splitting. In addition, the authors' formulation allows us to generalise the H-ADMM by including a relaxation constant, not present in the original design of the algorithm. Moreover, an adaptive penalty parameter selection scheme that consistently improves the practical convergence properties of the algorithm is proposed. Finally, the convergence results of the proposed algorithm are discussed and moreover, in order to present the effectiveness and the major capabilities of the proposed algorithm in off-line and on-line scenarios, distributed quadratic programming and distributed model predictive control problems are considered in the simulation section.

In this study, an online distributed optimal adaptive algorithm is introduced for continuous-time non-linear differential graphical games under unknown systems subject to external disturbances. The proposed algorithm learns online the approximate solution to the coupled Hamilton–Jacobi–Isaacs equations. Each of the players in the game uses an actor-critic network structure and an intelligent identifier to find the unknown parameters of the systems. The authors use recorded past observations concurrently with current data to speed up convergence by exploring the state space. The closed-loop stability and convergence of the policies to Nash equilibrium are ensured by using Lyapunov stability theory. Finally, a simulation example shows the efficiency of the proposed algorithm.

Predictive cruise control concerns designing controllers for autonomous vehicles using the broadcasted information from the traffic lights such that the idle time around the intersection can be reduced. This study proposes a novel adaptive optimal control approach based on reinforcement learning to solve the predictive cruise control problem of a platoon of connected and autonomous vehicles. First, the reference velocity is determined for each autonomous vehicle in the platoon. Second, a data-driven adaptive optimal control algorithm is developed to estimate the gains of the desired distributed optimal controllers without the exact knowledge of system dynamics. The obtained controller is able to regulate the headway, velocity, and acceleration of each vehicle in a suboptimal sense. The goal of trip time reduction is achieved without compromising vehicle safety and passenger comfort. Numerical simulations are presented to validate the efficacy of the proposed methodology.

This study is concerned with a joint localisation and tracking problem for autonomous underwater vehicle (AUV), subject to asynchronous clock and stratification effect in cyber channels as well as the model disturbances in physical channels. The authors first construct an integrated state and clock model, which allows the co-design of communication and control strategies. Then, an asynchronous localisation algorithm is developed to estimate the position of AUV, where the asynchronous clock and the stratification effect are both considered. With the estimated position information, a reinforcement learning based tracking controller is developed for the AUV to track the reference point. Particularly, the multivariate probabilistic collocation method is adopted to evaluate the model uncertainty. Moreover, the convergence analyses for the localisation algorithm and tracking controller are also given. Finally, simulation results are presented to show the effectiveness of the proposed method. It is demonstrated that the communication energy consumption and tracking error can be significantly reduced, through the co-design of localisation and tracking strategies.

This study proposes a model-free distributed output feedback control scheme that achieves synchronisation of the outputs of the heterogeneous follower agents with that of the leader agent in a directed network. A distributed two degree of freedom approach is presented that separates the learning of the optimal output feedback and the feedforward terms of the local control law for each agent. The local feedback parameters are learned using the proposed off-policy Q-learning algorithm, whereas a gradient adaptive law is presented to learn the local feedforward control parameters to achieve asymptotic tracking of each agent. This learning scheme and the resulting distributed control laws neither require access to the local internal state of the agents nor do they need an additional distributed leader state observer. The proposed approach has the advantage over the previous state augmentation approaches as it circumvents the need of introducing a discounting factor in the local performance functions. It is shown that the proposed algorithm converges to the optimal solution of the algebraic Riccati equation and the output regulator equations without explicitly solving them as long as the leader agent is reachable directly or indirectly from all the follower agents. Simulation results validate the proposed scheme.

The authors analyse the contour error dynamics in contouring control of dual-arm robotic manipulators with holonomic constraints. With the modified dynamics of robot, the dynamics of dual-arm robot with holonomic constraints is symetrically transformed into dynamics error problem by considering the equivalent error method. It becomes the control problem of stabilisation such that it is suitable for robust control approach to improve control performance in terms of contouring control, i.e. contour accuracy with high speed. The proposed method can deal with both analytic and non-analytic functions of desired path in task space. The experimental results reveal that the proposed method yields excellent performance in comparison to conventional distributed control. As a result, the proposed method can lead to the development of a modified distributed control for high degree of freedom robot manipulators.

This study investigates the task assignment problem where a fleet of dispersed vehicles needs to visit multiple target locations in a time-invariant drift field with obstacles while trying to minimise the vehicles' total travel time. The vehicles have different capabilities, and each kind of vehicles can visit a certain type of the target locations; each target location might require to be visited more than once by different kinds of vehicles. The task assignment problem has been proven to be NP-hard. A path planning algorithm is first designed to minimise the time for a vehicle to travel between two given locations through the drift field while avoiding any obstacle. The path planning algorithm provides the travel cost matrix for the target assignment, and generates routes once the target locations are assigned to the vehicles. Then, a distributed algorithm is proposed to assign the target locations to the vehicles using only local communication. The algorithm guarantees that all the visiting demands of every target will be satisfied within a total travel time that is at worst twice of the optimal when the travel cost matrix is symmetric. Numerical simulations show that the algorithm can lead to solutions close to the optimal.

Practical formation-containment tracking issues for the multiple autonomous surface vessels system with multiple leader vessels are considered. The follower vessels' states are designed to track the convex combination of the leader vessels' states, which are required to actualise the predefined time-varying formation tracking. Firstly, this study establishes the dynamic models of the multiple vessels system, where the outer-loop kinematic model and inner-loop dynamic model are considered simultaneously. Then, the practical formation-containment tracking protocols are devised based on distributed extended state observers, where the mismatched uncertainties and leader vessels' control input signals are estimated and compensated. Thirdly, an algorithm is presented to give the procedures for designing the control protocols, in which the feasible time-varying formations of leader's vessels are raised. A series of linear matrix inequalities are solved for obtaining the control parameters. Sufficient conditions for actualising the practical formation-containment tracking are derived. Finally, numerical simulation results reveal the effectiveness of the acquired theories.

To support an increasing number of commercial multi-unmanned aerial vehicle (UAV) applications, robust UAV-to-UAV communication is critical. A promising solution is aerial communication using directional antennas (ACDA), with features like long communication distance, low power consumption, broad bandwidth, and interference rejection. Nevertheless, ACDA requires the automatic alignment of directional antennas, which is not easy to achieve considering the imperfect communication environment unknown in advance and the limited sensing devices onboard due to the constrained payloads and power sources. In this study, the authors design and implement a new ACDA system, including the platform, communication, computing, control, middleware, and interface components. Practical implementation issues for the emergency response application are also considered. The ACDA system features a communication and control co-design, where the communication quality indicator, received signal strength indicator, serves as the goal function for antenna alignment. The solution also features a reinforcement learning-based directional antenna control algorithm that learns the unknown communication environment models. The performance of the ACDA system is verified using simulation studies, field tests, and disaster drills.

This study presents a distributed fault-tolerant cooperative control (FTCC) strategy to achieve the attitude synchronisation tracking control of networked unmanned aerial vehicles (UAVs) in the presence of actuator faults and model uncertainties. By utilising the fuzzy neural networks (FNNs), the unknown non-linear terms induced by actuator faults and model uncertainties are estimated as lumped uncertainties. A set of distributed sliding-mode estimators (DSMEs) is then employed to estimate the leader UAV's attitudes for the follower UAVs via a distributed communication network. Based on the estimated knowledge from FNNs and DSMEs, a group of distributed FTCC laws is developed for all follower UAVs by using the fractional-order calculus. It is proven that with the proposed control scheme, all follower UAVs can track the attitudes of the leader UAV and the tracking errors are uniformly ultimately bounded even when a portion of networked UAVs encounters multiple actuator faults. Comparative simulation results are presented to demonstrate the effectiveness of the proposed approach.

A distributed cooperative control paradigm is proposed to handle the load sharing and transmission power loss optimisation-based optimal power flow (OPF) problems in DC microgrids, which is based on a distributed finite-time average consensus algorithm and a linear variable weighted summation algorithm. Firstly, an OPF problem is formulated to minimise the global transmission power loss, which is then solved by a novel distributed OPF regulator in secondary control. Furthermore, a distributed OPF considering load sharing controller is proposed in secondary control, which aims to guarantee that the load sharing deviation is limited to the assigned permissible range and the global transmission power loss is reduced to a minimum simultaneously. Compared to existing methods, these two control algorithms are developed in a completely distributed fashion, and the load distribution matrix and conductance matrix of DC microgrids are not needed. The effectiveness of the proposed control methods is verified by simulation results.

The existing economic dispatch (ED) control structures in power systems are based on solving a quadratic optimisation problem, which can only guarantee the optimal steady-state performance. In this study, the authors formulate the real-time ED problem for the transient operation of power systems as a dynamic model predictive control (MPC) optimisation problem. A novel MPC solving method, named backwards square completion (BSC) is thereby proposed to solve it with guaranteed transient economic performance. Meanwhile, it satisfies the input and state security constraints. Conventional linear MPC algorithms routinely involve with inverse matrix calculation, which is computationally expensive and may result in singularity. By contrast, BSC algorithm replaces the inverse matrix calculation by recursive receding horizon optimisation problem solving, which significantly reduces the computational complexity in terms of the control horizon. The proposed BSC-MPC solution for real-time ED is applied to an IEEE 39-bus benchmark power network system to show its effectiveness and efficiency.

This work focuses on Distributed Secondary Control (DSC) technique, for frequency regulation and Economic Load Dispatch of Microgrid (MG). The fluctuating nature and large quantity of Distributed Energy Resources (DER) in an autonomous MG result in complex control requirements, demanding fast and robust response. The contemporary DSC schemes are mostly based on Distributed Averaging Integration techniques, with slow response. This paper proposes Distributed Model Predictive based Secondary Control (DMPSC) which effectively complies with the control requirements of MG. DMPSC requires each DER-node to solve a local optimization problem with the cost function penalizing the deviation of states from their desired values and the differences between the assumed and predicted values. The desired-states are based on local intermediate-optimum values, computed using local and neighbouring information. Equality based terminal constraints are introduced to ensure the stability, where each node is forced to reach the desired-state value at the end of prediction horizon. The terminal-consensus of the network affirms convergence of the desired-states to a global optimal point of the network. The asymptotic stability of the proposed control is proved by using the sum of local cost-functions as a candidate Lyapunov function. Simulation results validate the effectiveness of the proposed control scheme.

This study examines a distributed direct load control (DLC) problem for maximising customer welfare in a power system for the network communication of energy management controllers (EMCs). A model is first built to describe the dynamics and communication intervals of the EMCs with a distributed and uniform controller. The controller conditions are then derived to stabilise the system and to converge the power imbalance to zero at an assigned rate. The control condition that maximises customer welfare is then found. Furthermore, an optimal controller that maximises customer welfare over a given network communication is proposed, and the performance degradation caused by distributed management is evaluated. This study reveals that even though moving from a centralised to a distributed DLC can degrade customer welfare, this degradation can be reduced by considering consumer properties and network topologies of the EMCs. Numerical examples with real consumption data are also presented to demonstrate the effectiveness of the proposed method.