Cooperative Tracking Control Research Articles

Adaptive Cooperative Tracking Control of Multi-Agent Systems With Unknown Actuators Hysteresis

This paper considers cooperative tracking control of nonlinear multi-agent systems with actuators hysteresis over digraphs. Each agent is modeled by a higher-order nonlinear system in strict-feedback form with the generalized Prandtl–Ishlinskii hysteresis input and unknown time-varying virtual control coefficients. An online adaptive law is introduced for compensating the unknown hysteresis effect. A special Nussbaum-type function is developed to handle unknown time-varying virtual control coefficients. A switching mechanism is utilized to combine the neural networks approximation with an extra robust term, which can take over the authority outside the neural active region. In this sense, the globally uniformly ultimately bounded stability is guaranteed by the proposed distributed adaptive control law. Moreover, all agents ultimately synchronize to the leader node with bounded residual errors. Simulation results justify the proposed algorithm.

Asymptotical Cooperative Tracking Control for Unknown High-Order Multi-Agent Systems via Distributed Adaptive Critic Design

In this paper, a distributed adaptive critic design-based asymptotical cooperative tracking control scheme is established for a class of unknown high-order multi-agent systems with disturbances on undirected graphs. The cooperative tracking problem of high-order multi-agent systems is first transformed to the stabilizing problem of filtered tracking errors dynamic systems, which only depend on the information from neighboring agents. Then, a novel distributed adaptive critic design-based controller is developed for the newly obtained filtered tracking errors dynamic systems. The special local filtered tracking errors and local critic signals are defined for facilitating the implementation of distributed adaptive critic design. Novel distributed weights updating laws for critic neural networks, actor neural networks, and adaptive parameters are proposed. Furthermore, the RISE technique is introduced to suppress the external disturbances and neural network approximation errors. The asymptotical stability of a closed-loop system is demonstrated by using Lyapunov stability theory. Finally, a simulation example justifying the effectiveness of the proposed control scheme is given.

Consensus-based total-amount cooperative tracking control for multi-motor locomotive traction system

In locomotive traction system, unavoidable factors (such as idling and skidding) typically lead to the decline of traction performance of one or more motors, thereby resulting in the fluctuation of total torque traction amount. In this paper, the consensus-based total-amount cooperative tracking control (TACTC) is proposed to maintain the consensus of total torque traction amount with the given reference instruction. First, a disturbance observer is employed to estimate uncertain disturbances, then the output torque and observed values are fed back to design the total amount cooperative tracking control protocol, which is used to coordinate traction torque output redundancy of each individual motor. Simulation results show that the proposed approach is effective in reducing tracking time and tracking errors.

Adaptive cooperative tracking control for a class of nonlinear time-varying multi-agent systems

In this paper, an adaptive cooperative tracking control scheme is proposed for a class of high-order nonlinear time-varying multi-agent systems, where only the output of the leader is available for some followers. By introducing a bound estimation approach and a smooth function, the obstacle caused by unknown time-varying parameters is successfully circumvented without any restriction on their variation speed. With the aid of the dynamic surface control technique, simple distributed adaptive controllers are obtained and each follower needs only the first two states rather than the full states of its neighbor followers, which considerably reduces the computational and communication burden. It is shown that all tracking errors converge to a residual set which can be made arbitrarily small. Simulation results on robotic manipulators are presented to illustrate the effectiveness of the proposed scheme.

Neuro-adaptive cooperative tracking control with prescribed performance of unknown higher-order nonlinear multi-agent systems

ABSTRACTThis paper is concerned with the design of a distributed cooperative synchronisation controller for a class of higher-order nonlinear multi-agent systems. The objective is to achieve synchronisation and satisfy a predefined time-based performance. Dynamics of the agents (also called the nodes) are assumed to be unknown to the controller and are estimated using neural networks. The proposed robust neuro-adaptive controller drives different states of nodes systematically to synchronise with the state of the leader node within the constraints of the prescribed performance. The nodes are connected through a weighted directed graph with a time-invariant topology. Only few nodes have access to the leader. Lyapunov-based stability proofs demonstrate that the multi-agent system is uniformly ultimately bounded stable. Highly nonlinear heterogeneous networked systems with uncertain parameters and external disturbances were used to validate the robustness and performance of the new novel approach. Simulation results considered two different examples: single-input single-output and multi-input multi-output, which demonstrate the effectiveness of the proposed controller.

Cooperative tracking control for linear multi-agent systems with external disturbances under a directed graph

ABSTRACTThis paper studiesthe cooperative tracking control problem for multi-agent systems with unknown external disturbances under a directed graph. The leader's input is nonzero and unavailable to the followers. Based on the relative output measurements of neighbouring agents, a novel observer-based cooperative tracking protocol is presented, where the a group of intermediate estimators are constructed to estimate the tracking errors and the combined signal of the disturbances and the leader's input simultaneously, then decentralised tracking protocols are designed based on the obtained estimates. The states of the global tracking error system are proved to be uniformly ultimately bounded. A numerical example of aircraft illustrates the effectiveness of the cooperative tracking protocol.

Distributed tracking control of unmanned aerial vehicles under wind disturbance and model uncertainty

A distributed robust method is developed for cooperative tracking control of unmanned aerial vehicles under unknown wind disturbance and model uncertainty. The communication network among vehicles is a directed graph with switching topology. Each vehicle can only share its states with its neighbors. Dynamics of the vehicles are nonlinear and affected by the wind disturbance and model uncertainty. Feedback linearization is adopted to transform the dynamics of vehicles into linear systems. To account for the wind disturbance and model uncertainty, a robust controller is designed for each vehicle such that all vehicles ultimately synchronize to the virtual leader in the three-dimensional path. It is theoretically shown that the position states of the vehicles will converge to that of the virtual leader if the communication network has a directed spanning tree rooted at the virtual leader. Furthermore, the robust controller is extended to address the formation control problem. Simulation examples are also given to illustrate the effectiveness of the proposed method.

Robust cooperative path tracking control algorithm for multi-vessel

The issue of distributed cooperative path tracking control for multi-vessel in the presence of ocean currents has addressed in this article. The proposed cooperative control approach is achieved by designing the guidance system and the control system. In order to achieve the multi-vessel’s coordination with the desired spatial formation, the guidance system is designed based on the strategy of virtual leader for supplying the desire path and relevant parameters for each vessel. In addition, a robust cooperative path tracking controller is designed to reject the disturbance of unknown ocean currents using the backstepping method and the adaptive control technology. The synchronization between all the vessels is achieved by defining same path parameter and same speed along the path through the guidance system. Global asymptotic stability is guaranteed by Lyapunov-based technique for the whole control system. The effectiveness of the proposed cooperative path tracking control method is demonstrated by numerical simulation.

Merging Strategy for Vehicles by Applying Cooperative Tracking Control

This work presents a merging strategy for cooperative vehicles. In the proposed strategy, each vehicle possesses a tracking controller that considerers both tracking and coupling error signals, where all vehicles in the group know their positions. The trajectories of the cooperative vehicles are developed, to guarantee that each vehicle keeps a certain distance from the rest of the vehicles in the group, and are designed by using the virtual structure approach. The merging strategy is successfully validated in an experimental setup consisting of a group of nonholonomic mobile vehicles that represents the simplest bicycle model for cars with a zero vehicle length. It is shown using Lyapunov theory that this strategy is global asymptotically stable for the group.

Cooperative adaptive fuzzy control for a class of uncertain non-linear multi-agent systems with time delays

This paper studies the robust adaptive fuzzy cooperative tracking control problem for a class of uncertain non-linear multi-agent systems with multiple time delays and dead-zone non-linearities. First, based on the implicit function theorem, the non-affine form of the multi-agent system can be converted into the corresponding affine form. Then, using the local state information of neighbouring agents, a novel adaptive fuzzy cooperative tracking controller with the corresponding parameter-updated laws is designed based on undirected communication topologies. Furthermore, it is shown that all the closed-loop signals are bounded, and all follower nodes asymptotically tracking to the leader can be achieved in the presence of time-delayed perturbations and unknown dead-zone inputs. Finally, simulation results are given to demonstrate the effectiveness of the proposed adaptive control scheme.

Three-dimensional distributed tracking control for multiple quadrotor helicopters

This paper deals with the cooperative tracking control of a team of underactuated quadrotors in three-dimensional space when the reference signal is not available to all the vehicles. Using the Backstepping and filtering design technique and results from graph theory, a distributed cooperative controller consisting of two interconnected blocks is proposed. The first block, which is based on local distributed controllers, guarantees that the centroid of the three-dimensional formation asymptotically follows a desired path corresponding to the desired formation trajectory. The second block ensures that the attitude dynamics of the quadrotor will converge asymptotically to their actual values, which are constrained within a predefined set, such that singularities are avoided in the quadrotor׳s dynamics. Due to the coupling property between the translational and rotational dynamics, the equilibrium point of the complete closed-loop system is shown to be asymptotically stable. Numerical simulations are illustrated to show that the theoretical conclusions are effective.

Terminal sliding mode-based cooperative tracking control for non-linear dynamic systems

This paper investigates cooperative tracking problems for multiple non-linear dynamic systems. The desired trajectory is only available to a portion of the agents. Treating the desired trajectory as a virtual agent, a terminal sliding mode (TSM)-based distributed control algorithm is designed only using the neighbours’ information. A decentralized observer is provided firstly to estimate the unknown external disturbances. Then, the Gaussian functions are introduced to approximate the second-order derivative of the inaccessible states. On this basis, we further develop a TSM-based cooperative tracking control algorithm for the non-linear dynamic systems such that the tracking errors of each agent converge to an adjustable neighbourhood of the origin in finite time. Finally, a simulation example is presented to illustrate the feasibility and effectiveness of the proposed approaches.

Adaptive Task-Space Cooperative Tracking Control of Networked Robotic Manipulators Without Task-Space Velocity Measurements.

In this paper, the task-space cooperative tracking control problem of networked robotic manipulators without task-space velocity measurements is addressed. To overcome the problem without task-space velocity measurements, a novel task-space position observer is designed to update the estimated task-space position and to simultaneously provide the estimated task-space velocity, based on which an adaptive cooperative tracking controller without task-space velocity measurements is presented by introducing new estimated task-space reference velocity and acceleration. Furthermore, adaptive laws are provided to cope with uncertain kinematics and dynamics and rigorous stability analysis is given to show asymptotical convergence of the task-space tracking and synchronization errors in the presence of communication delays under strongly connected directed graphs. Simulation results are given to demonstrate the performance of the proposed approach.

Robust cooperative control of multiple heterogeneous Negative-Imaginary systems

This paper presents a consensus-based robust cooperative control framework for a wide class of linear time-invariant (LTI) systems, namely Negative-Imaginary (NI) systems. Output feedback, dynamic, Strictly Negative-Imaginary (SNI) controllers are applied in positive feedback to heterogeneous multi-input–multi-output (MIMO) plants through the network topology to achieve robust output feedback consensus. Robustness to external disturbances and model uncertainty is guaranteed via NI system theory. Cooperative tracking control of networked NI systems is presented as a corollary of the derived results by adapting the proposed consensus algorithm. Numerical examples are also given to demonstrate the effectiveness of proposed robust cooperative control framework.

Robust neuro‐adaptive cooperative control of multi‐agent port‐controlled Hamiltonian systems

SummaryThis paper presents the distributed cooperative tracking control of the multi‐agent port‐controlled Hamiltonian (PCH) systems that are networked through a directed graph. Controller is made robust against the parametric uncertainties using neural networks. Dynamics of the the proposed novel neural network tuning law is driven by both the position and the velocity errors owing to the information preserving filtering of the Hamiltonian gradient. In addition, the PCH structure of the closed‐loop system is preserved and the controller achieves the disturbance attenuation objective. Simulations are performed on a group of robotic manipulators to demonstrate the efficacy of the proposed controller. Copyright © 2015 John Wiley & Sons, Ltd.

Reinforcement learning-based asymptotic cooperative tracking of a class multi-agent dynamic systems using neural networks

In this paper, a novel reinforcement learning-based cooperative tracking control scheme is proposed for a class of multi-agent dynamic systems with disturbances and un-modeled dynamics on undirected graphs by using neural networks (NNs). For each agent, two NNs are employed, i.e., an actor NN which approximates the unknown nonlinearity and generates the control input, and a critic NN which evaluates the performance of the actor and updates the weights of actor NN. Further, a RISE technique is utilized in the design of the actor NN and the critic NN to compensate for the external disturbances and the NN approximation errors. Based on the Lyapunov theory, it is proved that the proposed control scheme can guarantee the tracking error of each agent to converge to zero asymptotically. Additionally, the proposed control scheme is distributed in the sense that the controller for each agent only uses the local neighbor information. Finally, two simulation examples are given to verify the effectiveness of the proposed control scheme.

Cooperative attitude tracking control for multiple spacecraft using vector measurements

We investigate the cooperative attitude tracking control problem of multiple spacecraft in this paper, and propose novel control schemes using vector measurements. The nonlinear dynamics describing the attitude tracking control of formation are considered, and rotation matrix is adopted to avoid singularity and non-uniqueness. The cooperative attitude tracking controllers are proposed by using time-varying sliding mode control method and vector measurement results. The information of vector measurements can be obtained by using star trackers or Earth-horizon sensors. Especially, the proposed control algorithm is proven to be robust to external disturbance torque, measurement uncertainty, and time delays in communication links. Numerical simulations demonstrate the effectiveness of the proposed control schemes for cooperative attitude tracking.

Cooperative Tracking Control for Networked Lagrange Systems: Algorithms and Experiments

This paper considers the coordinated tracking problem for a group of Lagrange systems in the presence of parametric uncertainties. Distributed adaptive controllers are proposed with the aid of Lyapunov techniques. Compared with the previous work in the context of networked Lagrange systems control, the results in this paper are suitable for the general digraph communication topologies. Under the condition that the desired trajectory is only available to a portion of Lagrange systems, we discuss the cooperative tracking problem with general digraph communication topology, which contains a spanning tree with the root node being the active target system. Under the case where the neighbor's velocity is unavailable, a distributed filter is introduced to overcome this deficiency. Experimental results on networked robot-arms are provided to show the effectiveness of the proposed control algorithms.

Adaptive coordinated tracking control of multiple autonomous underwater vehicles

A practical design method is developed for cooperative tracking control of multiple autonomous underwater vehicles (AUVs). Each AUV is modeled by a system with time-varying parameters, unknown nonlinear dynamics and unknown disturbance. A robust adaptive distributed controller is designed for each AUV such that all AUVs ultimately synchronize to the desired paths with required formation. Moreover, these controllers are distributed in the sense that the controller design for each AUV only requires relative state in formation between itself and its neighbors. Finally, a simulation example demonstrates the effectiveness of the control method.

Cooperative output feedback tracking control for multi-agent consensus with time-varying delays and switching topology

This paper investigates the consensus tracking problem for leader-following multi-agent systems with general dynamics. The agents that are at most critically unstable and with time-varying delays and arbitrary switching topology are considered in our work. A novel framework for cooperative tracking control with time-varying input delay and communication delay under switching topology is constructed. The distributed observer-based tracking protocol is proposed for desired tracking based on the truncated predictor feedback method, algebraic graph theory and Riccati equation. Moreover, we design the observer gain and feedback gain independent of each other. A simulation example is provided to demonstrate the effectiveness of our proposed method.