Adaptive Consensus Tracking Research Articles

Event-triggered adaptive consensus tracking control for non-affine multi-agent systems

This paper presents the event-triggered consensus control problem for a class of multi-agent systems (MASs) in the non-affine form. An error-transformation-based design method is presented in the non-affine MASs. The radial basis function neural networks (RBFNNs) are used to approximate the unknown nonlinear functions. The dynamic surface control (DSC) technique is adopted to obtain parameters of the virtual controller through a first-order filter, which can make the calculation easier. An event-triggered control strategy is proposed to reduce communication frequency. Furthermore, it is further shown that the consensus tracking errors are semi-globally uniformly ultimately bounded (SGUUB). Finally, simulation results illustrate the effectiveness of the designed controller.

Consensus Tracking Control of Uncertain Multiagent Systems With Sampled Data and Time-Varying Delay.

In this article, the adaptive consensus tracking control is developed for uncertain multiagent systems with time-varying state delay in the case that leader's state is accessible at sampling instants. By proposing a distributed sampled observer with hybrid form, adaptive tracking controller with the complementary term is designed for first-order multiagent systems, and then is extended to high-order multiagent systems with the aid of dynamic surface control. Through the complementary term, the effects of parameter estimation error as well as dynamical terms with time-varying delays are eliminated and thus less conservative condition on time delays is required. It is proved that, under criteria in terms of linear matrix inequalities (LMIs), tracking error and estimation error exponentially converge to zero for first-order systems, and to a sufficiently small neighborhood of zero for high-order systems.

Event-Triggered Consensus Tracking Control of Stochastic Nonlinear Multiagent Systems

This paper addresses the event-triggered consensus tracking problem for a class of higher order stochastic nonlinear multiagent systems. First, we propose a new protocol design framework. Then, a novel adaptive consensus tracking protocol, under which the continuous communication is not required, is developed for the stochastic nonlinear multiagent systems. Using the Lyapunov functional approach and the stochastic theory, it is proven that the consensus tracking control objective can be achieved by the designed control law. The Zeno behavior was excluded by showing that there exists a lower bound for interevent instants. Finally, to verify the effectiveness of the given event-triggered control scheme, two numerical examples are provided.

Distributed adaptive consensus tracking control for uncertain non‐linear multi‐agent systems with input saturation

This study proposes a novel distributed adaptive consensus control scheme for a class of uncertain non-linear multi-agent systems with unknown control gains and input saturation. The radial basis function-neural networks are used to approximate the uncertain dynamics of the follower agents, as well as the effect of the neighbour agents of each agent. The dead-zone operator-based model is proposed to provide a smooth model of the saturation non-linearity. Then, the consensus strategy is proposed based on the minimal learning parameter algorithm and the dynamic surface control method. The stability analysis shows that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded and the consensus tracking error converges to a small vicinity of the origin. The proposed scheme solves the ‘singularity’ problem without using the projection operator. Furthermore, it avoids the ‘explosion of complexity’ and ‘explosion of learning parameters’ problems, simultaneously, and reduces the computational burden. Simulation results performed on a set of single-link robots composed of four followers and one leader verify the effectiveness of the proposed method.

Cooperative adaptive consensus tracking for multiple nonholonomic mobile robots

ABSTRACTThis paper addresses the cooperative adaptive consensus tracking for a group of multiple nonholonomic mobile robots, where the nonholonomic robot model is assumed to be a canonical vehicle having two actuated wheels and one passive wheel. By integrating a kinematic controller and a torque controller for the nonholonomic robotic system, a cooperative adaptive consensus tracking strategy is developed for the uncertain dynamic models using Lyapunov-like analysis in combination with backstepping approach and sliding mode technique. A key feature of the developed adaptive consensus tracking algorithm is the introduction of a directed network topology into the control constraints based on algebraic graph theory to characterise the communication interaction among robots, which plays an important role in realising the cooperative consensus tracking with respect to a specific common reference trajectory. Furthermore, a novel framework is proposed for developing a unified methodology for the convergence analysis of the closed-loop control systems, which can fully ensure the desired adaptive consensus tracking for multiple nonholonomic mobile robots. Subsequently, illustrative examples and numerical simulations are provided to demonstrate and visualise the theoretical results.

Observer-based adaptive consensus tracking control for nonlinear multi-agent systems with actuator hysteresis

This paper addresses the consensus tracking problem of a class of nonlinear multi-agent systems by using observer-based control. The systems are in output-feedback form with both actuator hysteresis and external disturbances. Radial basis function neural networks are used to approximate unknown nonlinear functions. By constructing a state observer and using the backstepping technique, a distributed adaptive neural output-feedback control scheme is proposed to solve the consensus tracking problem. Approximation errors of neural networks together with external disturbances are adaptively estimated and counteracted. For a communication graph containing a spanning tree, we show that the proposed controller guarantees all signals of the closed-loop system are semi-globally uniformly ultimately bounded, and the consensus tracking error and the observer error converge to an adjustable neighborhood of the origin. Finally, two simulation examples are provided to verify the performance of the control design.

Prescribed performance global stable adaptive neural dynamic surface consensus tracking control of stochastic multi-agent systems with hysteresis inputs and nonlinear dynamics

ABSTRACT This paper focuses on the leader-following consensus control problem of stochastic multi-agent systems with hysteresis inputs and nonlinear dynamics. A leader-following consensus scheme is presented for stochastic multi-agent systems directions under directed graphs, which can achieve predefined synchronisation error bounds. By mainly activating an auxiliary robust control component for pulling back the transient escaped from the neural active region, a multi-switching robust neuro adaptive controller in the neural approximation domain, which can achieve globally uniformly ultimately bounded tracking stability of multi-agent systems recently. A specific Nussbaum-type function is introduced to solve the problem of unknown control directions. Using a dynamic surface control technique, distributed consensus controllers are developed to guarantee that the outputs of all followers synchronise with that of the leader with prescribed performance. Based on Lyapunov stability theory, it is proved that all signals in closed-loop systems are uniformly ultimately bounded and all the follower agents can keep consensus with the leader. Two simulation examples are provided to illustrate the effectiveness and advantage of the proposed control scheme.

Distributed adaptive consensus tracking control for nonlinear multi-agent systems with state constraints

This paper investigates the consensus tracking problem of nonlinear multi-agent systems with state constraints and unknown disturbances. An observer is presented for the case that the states of each follower and its neighbors are unmeasurable. State constraint for multi-agent systems is a challenging problem. Barrier Lyapunov functions are applied in this paper to deal with this difficulty. Then based on adaptive back-stepping control approach and dynamic surface control technique, an adaptive fuzzy distributed controller is proposed to guarantee that the tracking errors between all followers and the leader converge to a small neighborhood of the origin. Moreover, it is proved that all the signals in the multi-agent systems are semi-globally uniformly ultimately bounded (SUUB). Finally, some numerical simulation results are presented to testify the effectiveness of the proposed algorithm.

Connectivity-Preserving Consensus Tracking of Uncertain Nonlinear Strict-Feedback Multiagent Systems: An Error Transformation Approach.

This brief addresses a distributed connectivity-preserving adaptive consensus tracking problem of uncertain nonlinear strict-feedback multiagent systems with limited communication ranges. Compared with existing consensus results for uncertain nonlinear lower triangular multiagent systems, the main contribution of this brief is to present an error-transformation-based design methodology to preserve initial connectivity patterns in the consensus tracking field, namely, both connectivity preservation and consensus tracking problems are considered for uncertain nonlinear lower triangular multiagent systems. A dynamic surface design based on nonlinearly transformed errors and neural network function approximators is established to construct the local controller of each follower. In addition, a technical lemma is derived to analyze the stability of the proposed connectivity-preserving consensus scheme in the Lyapunov sense.

Adaptive consensus tracking of non-square MIMO nonlinear systems with input saturation and input gain matrix under directed graph

This paper deals with the leader-following consensus problems of non-square multi-input/multi-output multi-agent systems in the presence of control input saturation and uncertain external disturbances. The agents have unknown high-order nonlinear dynamics and communicate together under any directed graph containing a spanning tree. A distributed adaptive method is designed to solve the problem. Moreover, a constant full-rank matrix with an adaptive gain is used instead of approximation of the unknown gain matrix by neural networks. Therefore, the proposed controller’s structure simplifies its implementation. The unknown nonlinearities are estimated by a radial basis function neural network. The ultimate boundness of the closed-loop system is guaranteed through Lyapunov stability analysis by introducing suitably driven adaptive rules. Finally, the simulation results verify the performance of the proposed control method.

Output‐feedback adaptive consensus tracking control for a class of high‐order nonlinear multi‐agent systems

SummaryIn this paper, an output‐feedback adaptive consensus tracking control scheme is proposed for a class of high‐order nonlinear multi‐agent systems. The agents are allowed to have unknown parameters, unknown nonlinearities, and input quantization simultaneously. The desired trajectory to be tracked is available for only a subset of agents, and only the relative outputs and the quantized inputs need to be measured or transmitted as signal exchange among neighbors regardless of the system order. By introducing a kind of high‐gain K‐filters and a smooth function, the effect among agents caused by the unknown nonlinearities is successfully counteracted, and all closed‐loop signals are proved to be globally uniformly bounded. Moreover, it is shown that the tracking errors converge to a residual set that can be made arbitrarily small. Simulation results on robot manipulators are presented to illustrate the effectiveness of the proposed scheme. Copyright © 2017 John Wiley & Sons, Ltd.

Minimal-Approximation-Based Distributed Consensus Tracking of a Class of Uncertain Nonlinear Multiagent Systems With Unknown Control Directions.

A minimal-approximation-based distributed adaptive consensus tracking approach is presented for strict-feedback multiagent systems with unknown heterogeneous nonlinearities and control directions under a directed network. Existing approximation-based consensus results for uncertain nonlinear multiagent systems in lower-triangular form have used multiple function approximators in each local controller to approximate unmatched nonlinearities of each follower. Thus, as the follower's order increases, the number of the approximators used in its local controller increases. However, the proposed approach employs only one function approximator to construct the local controller of each follower regardless of the order of the follower. The recursive design methodology using a new error transformation is derived for the proposed minimal-approximation-based design. Furthermore, a bounding lemma on parameters of Nussbaum functions is presented to handle the unknown control direction problem in the minimal-approximation-based distributed consensus tracking framework and the stability of the overall closed-loop system is rigorously analyzed in the Lyapunov sense.

Neutral Networks-Based Adaptive Fixed-Time Consensus Tracking Control for Uncertain Multiple AUVs

Neutral Networks-Based Adaptive Fixed-Time Consensus Tracking Control for Uncertain Multiple AUVs

Distributed adaptive asymptotically consensus tracking control of nonlinear multi-agent systems with unknown parameters and uncertain disturbances

Different from traditional centralized control, one major challenge of distributed consensus tracking control lies in the constraint that the desired reference trajectory is only accessible by part of the subsystems. Currently, most existing schemes require the availability of partial knowledge of the reference trajectories to all of the subsystems or information exchange of local control inputs. In this paper, we investigate distributed adaptive consensus tracking control without such requirements for nonlinear high-order multi-agent systems subjected to mismatched unknown parameters and uncertain external disturbances. By introducing compensating terms in a smooth function form of consensus errors and certain positive integrable functions in each step of virtual control design, a new backstepping based distributed adaptive control protocol is proposed. An extra estimator is designed in each subsystem to handle the parametric uncertainties involved in its neighbors’ dynamics, which avoids information exchange of local neighborhood consensus errors among connected subsystems. It is shown that global uniform boundedness of all the closed-loop signals and asymptotically output consensus tracking can be achieved. Simulation results are provided to verify the effectiveness of our scheme.

Fuzzy Observed-Based Adaptive Consensus Tracking Control for Second-Order Multiagent Systems With Heterogeneous Nonlinear Dynamics

In this paper, the consensus tracking control problem of second-order multiagent systems with unknown nonlinear dynamics, immeasurable states, and disturbances is investigated. The nonlinear dynamics in multiagent systems do not satisfy the matched condition. In this paper, fuzzy logic system is introduced to approximate the unknown nonlinear dynamics, and adaptive high-gain observer is designed to estimate the unmeasured states. Based on backstepping approach and Lyapunov theory, a new adaptive fuzzy distributed controller is proposed for each agent only using the information of itself and its neighbors. Then the consensus tracking is achieved under the designed distributed controller. Moreover, it is proved that all the signals in the multiagent systems are semiglobally uniformly ultimately bounded, and the consensus tracking error converges to a small neighborhood of the origin that can be designed as small as possible. Finally, the simulation result illustrates the effectiveness of the designed controller.

Adaptive consensus tracking for linear multi-agent systems with input saturation

This paper addresses the consensus protocol design problem for linear multi-agent systems with input saturation. Existing consensus protocols usually contain certain global information, such as network size or the spectrum of the Laplacian matrix, and this global knowledge is often unavailable to all agents. In this paper, based on only the agent dynamics and the relative states of neighbouring agents, a novel adaptive consensus protocol is designed by assigning a time-varying coupling weight to each node. This protocol has two advantages: it is independent of any global information, and hence is fully distributed; and it is implemented by actuators with input saturation constraints. By combining the low-gain feedback method and appropriate Lyapunov techniques, it is shown that our protocol can achieve the semi-global consensus tracking in a fully distributed fashion, under the mild assumptions on agent dynamics and the topology graph. The results are illustrated by numerical simulations

Distributed adaptive consensus tracking control of higher-order nonlinear strict-feedback multi-agent systems using neural networks

This paper considers the output consensus problem of tracking a desired trajectory for a group of higher-order nonlinear strict-feedback multi-agent systems over directed communication topologies. Only a subset of the agents is given direct access to the desired trajectory information. A distributed adaptive consensus protocol driving all agents to track the trajectory is presented using the backstepping technique and neural networks. The Lyapunov theory is applied to guarantee that all signals in the closed-loop system are uniformly ultimately bounded and that all agents' outputs synchronize to the desired trajectory with bounded residual errors. Compared with prior work, the dynamics of each agent discussed here is more general and does not require the assumption “linearity in the unknown parameters” or the matching condition. Moreover, the bounded residual errors can be reduced as small as desired by appropriately choosing design parameters. Simulation results are included to demonstrate the effectiveness of the proposed methods.

Distributed adaptive neural network control for a class of heterogeneous nonlinear multi-agent systems subject to actuation failures

ABSTRACTIn this paper, the cooperative adaptive consensus tracking problem for heterogeneous nonlinear multi-agent systems on directed graph is addressed. Each follower is modelled as a general nonlinear system with the unknown and nonidentical nonlinear dynamics, disturbances and actuator failures. Cooperative fault tolerant neural network tracking controllers with online adaptive learning features are proposed to guarantee that all agents synchronise to the trajectory of one leader with bounded adjustable synchronisation errors. With the help of linear quadratic regulator-based optimal design, a graph-dependent Lyapunov proof provides error bounds that depend on the graph topology, one virtual matrix and some design parameters. Of particular interest is that if the control gain is selected appropriately, the proposed control scheme can be implemented in a unified framework no matter whether there are faults or not. Furthermore, the fault detection and isolation are not needed to implement. Finally, a simulation is given to verify the effectiveness of the proposed method.

Adaptive output feedback consensus tracking for heterogeneous multi-agent systems with unknown dynamics under directed graphs

This paper considers the distributed consensus tracking problem for the linear multi-agent systems with unknown dynamics under general directed graphs. Based on the output information among the agents, distributed adaptive consensus tracking protocols together with two observers, consisting of a local observer and an adaptive estimator, are designed to guarantee that all the signals in the closed-loop dynamics are uniformly ultimately bounded and the tracking errors converge to a small neighborhood around the origin. Moreover, the consensus protocols are in fully distributed fashion in the sense that the coupling gains in the controllers are independent without requiring the global knowledge that the eigenvalues of the Laplacian matrix associated with the whole communication graph. Finally, a simulation example is provided to verify the theoretical results.

Distributed adaptive consensus tracking for a class of multi-agent systems via output feedback approach under switching topologies

The consensus tracking problem is discussed for a class of multi-agent systems (MASs) in non-affine pure-feedback form via output feedback approach under switching directed topologies. Observers are employed to reconstruct state information of the system, and then a consensus tracking control scheme is presented by the backstepping method combining with dynamic surface control (DSC) technique, neural networks (NNs), and graph theory. The main advantage of the proposed strategy is that it only relies on the output signals of individual agents in communication graph and it removes the requirement for exact priori knowledge about parameters of agents. Moreover, by introducing DSC technology, it avoids the well known problem of ‘explosion of complexity’ that conventional backstepping method suffers from along with the increasement of the degree of individual agents. It is proven that the designed output feedback control scheme guarantees consensus errors are cooperatively semiglobally uniformly ultimately bounded and converge to neighborhood of the origin by suitable choice of design parameters. Simulation results are presented to demonstrate the effectiveness of the proposed control approach.