A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> In this paper, adaptive neural network control is investigated for single-master-multiple-slaves teleoperation in consideration of time delays and input dead-zone uncertainties for multiple mobile manipulators carrying a common object in a cooperative manner. Firstly, concise dynamics of teleoperation systems consisting of a single master robot, multiple coordinated slave robots, and the object are developed in the task space. To handle asymmetric time-varying delays in communication channels and unknown asymmetric input dead zones, the nonlinear dynamics of the teleoperation system are transformed into two subsystems through feedback linearization: local master or slave dynamics including the unknown input dead zones and delayed dynamics for the purpose of synchronization. Then, a model reference neural network control strategy based on linear matrix inequalities (LMI) and adaptive techniques is proposed. The developed control approach ensures that the defined tracking errors converge to zero whereas the coordination internal force errors remain bounded and can be made arbitrarily small. Throughout this paper, stability analysis is performed via explicit Lyapunov techniques under specific LMI conditions. The proposed adaptive neural network control scheme is robust against motion disturbances, parametric uncertainties, time-varying delays, and input dead zones, which is validated by simulation studies. <s> BIB001 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> To achieve an excellent dual-arm coordination of the humanoid robot, it is essential to deal with the nonlinearities existing in the system dynamics. The literatures so far on the humanoid robot control have a common assumption that the problem of output hysteresis could be ignored. However, in the practical applications, the output hysteresis is widely spread; and its existing limits the motion/force performances of the robotic system. In this paper, an adaptive neural control scheme, which takes the unknown output hysteresis and computational efficiency into account, is presented and investigated. In the controller design, the prior knowledge of system dynamics is assumed to be unknown. The motion error is guaranteed to converge to a small neighborhood of the origin by Lyapunov’s stability theory. Simultaneously, the internal force is kept bounded and its error can be made arbitrarily small. <s> BIB002 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> Most studies on bilateral teleoperation assume known system kinematics and only consider dynamical uncertainties. However, many practical applications involve tasks with both kinematics and dynamics uncertainties. In this paper, trilateral teleoperation systems with dual-master-single-slave framework are investigated, where a single robotic manipulator constrained by an unknown geometrical environment is controlled by dual masters. The network delay in the teleoperation system is modeled as Markov chain-based stochastic delay, then asymmetric stochastic time-varying delays, kinematics and dynamics uncertainties are all considered in the force-motion control design. First, a unified dynamical model is introduced by incorporating unknown environmental constraints. Then, by exact identification of constraint Jacobian matrix, adaptive neural network approximation method is employed, and the motion/force synchronization with time delays are achieved without persistency of excitation condition. The neural networks and parameter adaptive mechanism are combined to deal with the system uncertainties and unknown kinematics. It is shown that the system is stable with the strict linear matrix inequality-based controllers. Finally, the extensive simulation experiment studies are provided to demonstrate the performance of the proposed approach. <s> BIB003 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> This paper addresses adaptive fuzzy control for multimaster–multislave teleoperation for multiple mobile manipulators carrying a common object in a cooperative manner that subjected to asymmetric time-varying delays and model parameter uncertainties. In the proposed control framework, a novel switched error filtering is designed. By introducing the filtering output in the control torque design, the complete closed-loop master/slave systems are modeled as a special class of switched system that are composed of two subsystems, i.e., the local master (slave) dynamics with well-defined auxiliary variable and the switched error filter subsystem, which is fairly different from the existing subsystem decomposition method. Utilizing the Lyapunov–Krasovskii method, the complete closed-loop master (slave) system is proved to be state-independent input-to-output stable. The proposed scheme has overcome some application limitations existing in the literature. It is shown that the position tracking errors and the parameter estimation errors can remain bounded under the proposed control laws, which are validated by simulation studies. <s> BIB004 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> For solving the singularity problem arising in the control of manipulators, an efficient way is to maximize its manipulability. However, it is challenging to optimize manipulability effectively because it is a nonconvex function to the joint angles of a robotic arm. In addition, the involvement of an inversion operation in the expression of manipulability makes it even hard for timely optimization due to the intensively computational burden for matrix inversion. In this paper, we make progress on real-time manipulability optimization by establishing a dynamic neural network for recurrent calculation of manipulability-maximal control actions for redundant manipulators under physical constraints in an inverse-free manner. By expressing position tracking and matrix inversion as equality constraints, physical limits as inequality constraints, and velocity-level manipulability measure, which is affine to the joint velocities, as the objective function, the manipulability optimization scheme is further formulated as a constrained quadratic program. Then, a dynamic neural network with rigorously provable convergence is constructed to solve such a problem online. Computer simulations are conducted and show that, compared to the existing methods, the proposed scheme can raise the manipulability almost 40% on average, which substantiates the efficacy, accuracy, and superiority of the proposed manipulability optimization scheme. <s> BIB005 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> This paper presents dynamic learning from adaptive neural control (ANC) with prescribed tracking error performance for an $ {n}$ -link robot manipulator subjected to unknown system dynamics and external disturbances. To achieve the prescribed performance, a performance function is introduced to describe the performance restrictions on tracking errors, and then specific performance requirements are served as a priori condition of tracking control design. By an error transformation method, the constrained tracking control problem of the original robot manipulator is transformed into the stabilization problem of an unconstrained augmented system. Then, a novel ANC scheme is proposed for the unconstrained system by combining a filter tracking error with radial basis function (RBF) neural network (NN) approximator, and all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. The external disturbances might make it difficult to achieve the accurate convergence of NN weight estimates. To overcome this difficulty, an appropriate state transformation is introduced to transform the closed-loop system into a linear time-varying system with small perturbed terms. Under partial persistent excitation condition of RBF NNs, the convergence of NN weight estimates is guaranteed, and then the experienced knowledge on the unknown robot manipulator dynamics can be stored with NN constant weights. Using the experienced knowledge, a static neural learning control is proposed to improve the system performances without time-consuming online parameter adjustment process, and the proposed learning control can also guarantee the prescribed transient and steady-state tracking control performance. Simulation results demonstrate the effectiveness of the proposed method. <s> BIB006 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> This paper addresses distributed coordination and cooperation control for networked mobile manipulators over a jointly connected topology with time delays. First, tracking control is proposed to guarantee the position and velocity synchronization of the networked mobile manipulators, while keeping a formation. For cooperation control, the decoupled dynamics is considered so that the task and null space of the mobile manipulators can be designed to achieve different missions. For end-effector motion, synchronization control works in combination with force controls to ensure that the network of mobile manipulators achieves cooperative manipulation and transportation. The motion of the mobile bases is controlled in the null space, which can be designed to track a trajectory, avoid colliding with obstacles, and achieve velocity consensus without influencing the main task. Numerical examples are addressed to demonstrate the performance of the proposed networked robotic system. <s> BIB007 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> This paper addresses the distributed formation control problem of a networked multi-agent system (MAS) subject to limited communication resources. First, a dynamic event-triggered communication mechanism (DECM) is developed to schedule inter-agent communication such that some unnecessary data exchanges among agents can be reduced so as to achieve better resource efficiency. Different from most of the existing event-triggered communication mechanisms, wherein threshold parameters are fixed all the time, the threshold parameter in the developed event triggering condition is dynamically adjustable in accordance with a dynamic rule. It is numerically shown that the proposed DECM can achieve a better tradeoff between reducing inter-agent communication frequency and preserving an expected formation than some existing ones. Second, an event-triggered formation protocol is delicately proposed by using only locally triggered sampled data in a distributed manner. Based on the formation protocol, it is shown that the state formation control problem is cast into an asymptotic stability problem of a reduced-order closed-loop system. Then, criteria for designing desired formation protocol and communication mechanism are derived. Finally, the effectiveness and advantages of the proposed approach are demonstrated through a comparative study in multirobot formation control. <s> BIB008 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> This paper is concerned with sampled-data leader-following consensus of a group of agents with nonlinear characteristic. A distributed consensus protocol with probabilistic sampling in two sampling periods is proposed. First, a general consensus criterion is derived for multiagent systems under a directed graph. A number of results in several special cases without transmittal delays or with the deterministic sampling are obtained. Second, a dimension-reduced condition is obtained for multiagent systems under an undirected graph. It is shown that the leader-following consensus problem with stochastic sampling can be transferred into a master–slave synchronization problem with only one master system and two slave systems. The problem solving is independent of the number of agents, which greatly facilitates its application to large-scale networked agents. Third, the network design issue is further addressed, demonstrating the positive and active roles of the network structure in reaching consensus. Finally, two examples are given to verify the theoretical results. <s> BIB009 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> In this paper, a distributed scheme is proposed for the cooperative motion generation in a distributed network of multiple redundant manipulators. The proposed scheme can simultaneously achieve the specified primary task to reach global cooperation under limited communications among manipulators and optimality in terms of a specified optimization index of redundant robot manipulators. The proposed distributed scheme is reformulated as a quadratic program (QP). To inherently suppress noises originating from communication interferences or computational errors, a noise-tolerant zeroing neural network (NTZNN) is constructed to solve the QP problem online. Then, theoretical analyses show that, without noise, the proposed distributed scheme is able to execute a given task with exponentially convergent position errors. Moreover, in the presence of noise, the proposed distributed scheme with the aid of NTZNN model has a satisfactory performance. Furthermore, simulations and comparisons based on PUMA560 redundant robot manipulators substantiate the effectiveness and accuracy of the proposed distributed scheme with the aid of NTZNN model. <s> BIB010 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> Joint-drift problem may lead to task execution failure or robot damage. To solve this problem, a finite-time varying-parameter recurrent neural network (FT-VP-RNN) is proposed and investigated in this paper. First, a quadratic programming (QP) based joint-drift-free (JDF) scheme is developed, which consists of an optimization criterion and a kinematic equation at velocity layer. A feedback control is then added into the kinematic equation as the equality constraint, and a feedback-considered joint-drift-free (FC-JDF) scheme is obtained. Second, a novel FT-VP-RNN is designed to solve the FC-JDF scheme and a corresponding finite-time convergence theorem is proposed. The outstanding advantages of the proposed FT-VP-RNN are the real-time computation, exponential convergence, and the ability to eliminate the initial errors. Finally, three path-tracking simulations and comparisons are conducted to verify the effectiveness, accuracy, practicability, and safety of the proposed FT-VP-RNN for solving the joint-drift problems of redundant robot manipulators. <s> BIB011 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> In this paper, a neural-dynamic distributed scheme is proposed for the cooperative control of multiple redundant manipulators with limited communications. It is guaranteed that, with the communication network being connected, all manipulators can jointly reach the same desired motion. The proposed distributed scheme is rearranged as a time-varying quadratic program and solved online by a Zhang neural network. Then, theoretical analyses show that, without noise, the proposed distributed scheme is able to execute a given task with exponentially convergent position errors. Moreover, an explicit bound relationship between the control input noise and the end-effector position error is analytically derived. Furthermore, numerical comparisons substantiate the superiority, effectiveness, and accuracy of the proposed distributed scheme. <s> BIB012 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> Nowadays, the control technology of the robotic manipulator with flexible joints (RMFJ) is not mature enough. The flexible-joint manipulator dynamic system possesses many uncertainties, which brings a great challenge to the controller design. This paper is motivated by this problem. In order to deal with this and enhance the system robustness, the full-state feedback neural network (NN) control is proposed. Moreover, output constraints of the RMFJ are achieved, which improve the security of the robot. Through the Lyapunov stability analysis, we identify that the proposed controller can guarantee not only the stability of flexible-joint manipulator system but also the boundedness of system state variables by choosing appropriate control gains. Then, we make some necessary simulation experiments to verify the rationality of our controllers. Finally, a series of control experiments are conducted on the Baxter. By comparing with the proportional-derivative control and the NN control with the rigid manipulator model, the feasibility and the effectiveness of NN control based on flexible-joint manipulator model are verified. <s> BIB013 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> This paper addresses the problem of robotic manipulators with unknown deadzone. In order to tackle the uncertainty and the unknown deadzone effect, we introduce adaptive neural network (NN) control for robotic manipulators. State-feedback control is introduced first and a high-gain observer is then designed to make the proposed control scheme more practical. One radial basis function NN (RBFNN) is used to tackle the deadzone effect, and the other RBFNN is also proposed to estimate the unknown dynamics of robot. The proposed control is then verified on a two-joint rigid manipulator via numerical simulations and experiments. <s> BIB014 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> This paper deals with the networked control of loosely or tightly connected cooperative manipulators in charge of achieving a cooperative task that is specified by means of proper task-oriented variables depending on the full state of the system. Since the full state is not known to robots, a two-layer architecture is designed. At the first level, each arm controller runs a distributed observer that estimates the system state. At the second level, this estimation is adopted to compute the local control input as in the case that a central unit is available. In addition, since the dynamic parameters of the arms might not be perfectly known, the local control law is made adaptive in order to counteract this uncertainty. The designed solution is suitable not only for pure motion coordination tasks but can also be exploited in those cases where a closed kinematic chain is generated by multirobot object manipulation. In this situation, the objective is to both move the object and limit the internal stresses on it that, however, cannot be locally computed. To overcome this issue, the wrench exerted by each robot on the object is decomposed in an external component (contributing to the motion of the object) and in an internal component that is locally estimated and, then, regulated. The approach was validated by simulation with 6-DOF serial chain manipulators mounted on a mobile platform and performing cooperative tasks. <s> BIB015 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> Event-triggered consensus of multiagent systems (MASs) has attracted tremendous attention from both theoretical and practical perspectives due to the fact that it enables all agents eventually to reach an agreement upon a common quantity of interest while significantly alleviating utilization of communication and computation resources. This paper aims to provide an overview of recent advances in event-triggered consensus of MASs. First, a basic framework of multiagent event-triggered operational mechanisms is established. Second, representative results and methodologies reported in the literature are reviewed and some in-depth analysis is made on several event-triggered schemes, including event-based sampling schemes, model-based event-triggered schemes, sampled-data-based event-triggered schemes, and self-triggered sampling schemes. Third, two examples are outlined to show applicability of event-triggered consensus in power sharing of microgrids and formation control of multirobot systems, respectively. Finally, some challenging issues on event-triggered consensus are proposed for future research. <s> BIB016 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> Abstract Distributed cooperative control of multi-agent systems has been one of the most active research topics in the fields of automatic control and robotics. This paper provides a survey on recent advances in distributed cooperative control under a sampled-data setting, with special emphasis on the published results since 2011. First, some typical sampling mechanisms related to this topic, such as uniform sampling, nonuniform sampling, random sampling, and event-triggered sampling, are summarized in both asynchronous and synchronous paradigms. Then, based on different coordinated tasks, recent results on distributed sampled-data cooperative control of multi-agent systems are categorized into four classes, i.e., sampled-data leaderless consensus, sampled-data leader-following consensus, sampled-data containment control, and sampled-data formation control. For each class, some explicit research lines are identified according to various sampling mechanisms. In particular, depending on definitions of event triggering conditions, some representative event-triggered sampling mechanisms are sorted out and discussed in detail. Finally, several challenging issues for future research are proposed. <s> BIB017 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 1) Distributed Control Based on CQP: <s> For the safe operation of redundant manipulators, physical constraints such as the joint angle, joint velocity, and joint acceleration limits should be taken into account when designing redundancy resolution schemes. Velocity-level redundancy resolution schemes are widely adopted in the kinematic control of redundant manipulators due to the existence of the well-tuned inner loop regarding the joint velocity control. However, it is difficult to deal with joint acceleration limits for velocity-level redundancy resolution methods. In this paper, a recurrent-neural-network-based velocity-level redundancy resolution method is proposed to deal with the problem, and theoretical results are given to guarantee its performance. By the proposed method, the end-effector position error is asymptotically convergent to zero, and all the joint limits are not violated. The effectiveness and superiority of the proposed scheme are validated via simulation results. <s> BIB018
For redundant manipulators, the purpose of the inverse-kinematics issue, one of the most fundamental issues, is to generate an ideal trajectory in the joint space according to the desired trajectories of manipulator's end effector being provided in the Cartesian space BIB010 . Note that the number of equations in such a problem is less than the number of decision variables, which proposes extra design freedom and thus increases the applicability. In other words, this property offers more design selections with the concern of certain optimum criteria (e.g., minimum joint velocity q and tracking error ṙ d −q ) and extra constraints from practical engineering requirements (e.g., joint limits and collision avoidance) BIB011 . In addition, solving the ideal trajectory can be easily reformulated as a constrained quadratic program (CQP) issue minq f (q,ṙ d −q) s.t.q ∈ Ω, and/or g(J(q)) = 0 where f is a convex function and g(J(q)) stands for the Jacobian equality constraint. According to derived Karash-Kuhn-Tucker conditions, the optimal solution can be obtained via constructed recurrent neural networks (NNs) BIB001 , BIB018 . When the local communication among neighbor manipulators is taken into consideration, the addressed issue has to be enslaved to a set of auxiliary constraints only dependent on the neighbor information BIB010 , BIB012 , BIB005 . For instance, considering the limited communication bandwidth and communication range as well as electromagnetic interferences, a distributed scheme via a noise-tolerant zeroing NN is developed in BIB010 to solve a CQP problem constructed by a Lagrange multiplier method. Theoretical analysis reveals that the proposed scheme without noises can make position errors exponentially convergent. 2) Distributed Control Based on NNs: Different from solving a CQP issue, NNs or adaptive NNs can be utilized to approximate the nonlinear kinematics function of manipulators involving various complex cases, such as modeling uncertainties, input deadzones and output constraints as well as torque disturbances BIB002 , BIB006 . The main idea is that an ideal controller is first derived via a constructed Lyapunov candidate and then its unknown part is approximated via NNs BIB013 , BIB014 . For instance, W σ(q,q) = C(q,q)q + G(q), where W is the NN weight, σ means the adopted activation function, C(q,q)q denotes the centripetal and Coriolis torques, and G(q) stands for the gravitational force. For distributed cooperative control, the developed control scheme makes manipulators realize position and velocity synchronization while guaranteeing a formation. In addition, the designed controller has to embed an error term relying on both received information and communication topology to compensate the drift from predetermined ideal trajectory and, at the same time, a decomposition in the null space is employed to handle the challenges from nonintegrable and independent constraints in BIB001 and BIB003 . Under this conception, a vector can be artificially introduced to construct a dynamic equation of motion in reduced feasible-space BIB007 , BIB001 . For instance, by resorting to a decoupled dynamics, the distributed control of both the end-effector motion and the mobile base motion is investigated in BIB007 to achieve different missions of mobile manipulators with a jointly connected topology. A master-slave framework based on NNs is adopted to handle the teleoperation subject to geometrically unknown constraints in BIB003 and both communication delays and input uncertainties in BIB001 . However, various network-induced phenomena and switching topologies as well as communication protocols have still not been fully taken into account mainly due to the difficulties of controller construction. 3) Distributed Control Based on MASs: The cooperative control of multiple manipulators is adopted to realize the position and velocity synchronization while guaranteeing a formation or the joint trajectory for a primary task. In the past few years, multiple mobile manipulators are widely utilized in material transportation in modern factories, space exploration, and dangerous fields for dismantling bombs and moving nuclear infected objects BIB004 . Formation control of vehicles or distributed cooperative control of various industrial mobile manipulators can be transformed into the consensus issues of MASs, each agent in which is described by an operational space model BIB007 , BIB015  where τ i is the input torque vector and other parameter matrices are dependent on both the EL equations of the ith manipulators and the nonlinear mapping function between the joint trajectory and the Cartesian coordinate. Recently, there are a rich body of results on consensus control of MASs with various networked-induced phenomena, switching network topologies, or sampling (see BIB008 , BIB009 , and the references therein). Furthermore, considering limited communication and energy resources, event-triggered consensus protocol receives considerable research attention and some interesting reviews on this topic are published in BIB016 . Specifically, the recent advancement is systematically surveyed in BIB017 according to different sampling mechanisms, especially event-triggered sampling with various thresholds. Based on the merit of event-triggered mechanism, the applications of consensus analysis in power sharing of microgrids and formation control of multirobot systems are summarized in BIB016 . It is worth noting that the fashionable results for linear multiagent systems cannot be effectively utilized to solve the specific challenges coming from the inherent nonlinearity of networked EL systems, not to mention that from various network-induced phenomena and communication protocols.