Distributed Finite-time Tracking Research Articles

Distributed finite-time neural network observer-based consensus tracking control of heterogeneous underwater vehicles

This note scrutinizes the distributed finite-time tracking problem of heterogeneous multi-agent systems with uncertain dynamics and environmental disturbances. To estimate the exogenous disturbances, an adaptive neural network-based disturbance observer is developed in which the approximation error of the neural network is compensated using adaptation laws. Based on finite-time stability theory, a distributed finite-time observer is proposed for each follower in order to estimate the leader's position. Moreover, an adaptive dynamic sliding mode-based controller is also developed for each follower, which ensures finite-time convergence of the tracking error between the leader and the follower. Incorporating adaptive control into the developed composite control structure leads to reducing the chattering, as well as enhancing the robustness and accuracy. Stability analysis and finite-time convergence of the tracking error are performed using the Lyapunov theory and multiple time scale principle, respectively. Finally, simulations and comparisons are performed in order to verify the effectiveness of the developed control algorithm for a group of autonomous underwater vehicles (AUVs).

Neural Network-Based Distributed Finite-Time Tracking Control of Uncertain Multi-Agent Systems With Full State Constraints

This paper addresses the distributed tracking control problem of pure-feedback multi-agent systems with full state constraints under a directed graph in finite time. By introducing the nonlinear mapping technique, the system with full state constraints is converted into the form without state constraints. Furthermore, by combining fractional dynamic surface and radial basis function neural networks, a novel finite-time adaptive tracking controller is conducted recursively. In light of Lyapunov stability theory, it is proven that all signals of multi-agent systems are semi-globally uniformly ultimately bounded in finite time and the full states satisfy the constraints. Lastly, numerical simulations are supplied to demonstrate the effectiveness of the proposed control strategy.

Distributed finite-time tracking for multiple uncertain mechanical systems with dead-zone input and external disturbances

This paper addresses the distributed finite-time tracking problem for multiple uncertain mechanical systems with dead-zone input and external disturbances. An observer-based adaptive finite-time consensus protocol is designed, which consists of two steps. Firstly, distributed observers are developed such that all the mechanical systems can obtain the leader’s state in finite settling time. Then, based on backstepping method and adding a power integrator technique, the finite-time consensus protocol and appropriate adaptive laws are designed to track the estimated leader’s state. Rigorous proofs show that the tracking errors between each mechanical system and the leader can converge to a small neighborhood of origin in finite time despite the presence of dead-zone nonlinearity and external disturbances. Finally, simulation example is provided to demonstrate the effectiveness of the proposed scheme.

Distributed finite-time tracking control for multiple uncertain Euler-Lagrange systems with error constraints

ABSTRACT In this paper, the distributed finite-time error constrained tracking control for multiple uncertain Euler-Lagrange systems is investigated under directed topology. We consider that the information of the dynamic leader is available to only a portion of the followers. First, for each follower, the error variable relating to the states of the neighbours is designed. Then, by using backstepping method, a distributed finite-time tracking control algorithm is developed with the neural network being utilizsd to estimate the model uncertainties. A tan-type barrier Lyapunov function is used to guarantee that the error variables will not exceed the prescribed bounds. Finite-time stability of the systems is demonstrated by Lyapunov theory and graph theory. Numerical simulations show the advantages of the proposed control strategy by comparisons with the existing methods.

Distributed finite-time coordinated tracking control for multiple Euler–Lagrange systems with input nonlinearity

In this paper, distributed finite-time coordinated tracking control for multiple Euler–Lagrange systems with input nonlinearity is investigated by using backstepping design technique under directed topology. The controller is designed under the condition that the information of the dynamic leader is available to only a subset of the followers. We first design an auxiliary variable relating to trajectory errors among neighbor agents. Then a distributed finite-time tracking control algorithm is developed where two neural networks are used to approximate the nonlinear model uncertainties and input nonlinearity, respectively. When considering that there exists incomplete known state for each follower, a modified distributed finite-time tracking control strategy is designed by utilizing high-gain observers. Based on backstepping method, finite-time technique, and graph theory, both proposed control strategies guarantee that tracking errors between each follower and the leader could be ultimately bounded in finite time. Numerical simulations show the superiorities of the proposed protocols by comparisons with existing methods.

Distributed finite‐time tracking control for multiple uncertain Euler–Lagrange systems with input saturations and error constraints

This study addresses the distributed finite-time tracking control for multiple uncertain Euler-Lagrange systems with input saturations and error constraints. In order to achieve distributed finite-time tracking control in the model-independent way, neural networks are used to approximate the system unknown terms. Besides, the authors consider that there exists input saturation for each dimension of each follower in the systems. The input saturations are tackled by converting the systems with input saturations to the cases with unknown input gains. Then, based on backstepping technique, the distributed finite-time tracking control law is developed. Tan-type barrier Lyapunov function is utilised to guarantee that the error variables would not exceed the predefined bounds. Lyapunov theory and graph theory demonstrate the finite-time stability of the systems. By choosing a class of two-link manipulators consisting of one leader and four followers, numerical simulations are provided to show the effectiveness of the proposed control algorithm.

Distributed finite‐time tracking of second‐order multi‐agent systems: An edge‐based approach

Distributed finite-time tracking problem of a multi-agent system with second-order non-linear dynamics is studied in this article. Based on measurements of edges, a finite-time tracking protocol is proposed without relying the complete position and velocity measurements. It means that the proposed protocol only requires a binary information between the neighbouring agent. By designing a carefully constructed Lyapunov function, the distributed finite-time tracking problem is solved if the sub-topology among the followers is connected and undirected and the topology of whole systems has a spanning tree with a leader been a root node. Furthermore, it has successfully estimated the finite settling time in theory with the proposed control protocol. The authors provide a numerical example to illustrate the effectiveness of the analytical results.

Distributed finite-time coordinated control for multi-robot systems

In this paper, we study the finite-time coordinated control problems under directed topologies for multi-robot systems with general disturbances. The dynamics model of each robot is described by a Euler–Lagrange equation. When considering that only a subset of the follower robots has access to the leader information, the distributed finite-time tracking algorithm with an active leader robot is proposed. Then, we extend the tracking method to the case of containment control. Some special error functions and terminal sliding variables are defined. The finite-time convergence properties of the closed-loop systems are investigated by using a combination of matrix properties of graph theory and Lyapunov theory. Numerical examples and comparisons with other methods are provided to show the effectiveness and the performance of the proposed control strategies.

Distributed finite-time tracking of multiple non-identical second-order nonlinear systems with settling time estimation

This paper investigates the distributed finite-time consensus tracking problem for a group of autonomous agents modeled by multiple non-identical second-order nonlinear systems. First, a class of distributed finite-time protocols are proposed based on the relative position and relative velocity measurements. By providing a topology-dependent Lyapunov function, it is shown that distributed consensus tracking can be achieved in finite time under the condition that the nonlinear errors between the leader and the followers are bounded. Then, a new class of observer-based algorithms are designed to solve the finite-time consensus tracking problem without using relative velocity measurements. The main contribution of this paper is that, by computing the value of the Lyapunov function at the initial point, the finite settling time can be theoretically estimated for second-order multi-agent systems with the proposed control protocols. Finally, the effectiveness of the analytical results is illustrated by an application in low-Earth-orbit spacecraft formation flying.

Distributed finite-time tracking for a multi-agent system under a leader with bounded unknown acceleration

This paper addresses the distributed finite-time tracking problem for a group of mobile agents modeled by double-integrator dynamics under a leader with bounded unknown acceleration. First, a distributed finite-time tracking protocol is designed based on both the relative position and the relative velocity measurements. This protocol can drive the states of the followers to track the leader in finite time under the constraint that the leader’s acceleration is bounded but unknown to the followers. Then, a novel position-based tracking protocol is designed and analyzed for solving the distributed finite-time tracking problem when both velocity and acceleration measurements are not available for the followers. It is theoretically proved that the followers can move to be with the leader in finite time if the network topology is undirected among the followers but has a directed path from the leader to each follower. In particular, the position-based protocol does not require the relative input information between the agents. Finally, the effectiveness of the algorithms is illustrated by numerical simulations.

Distributed finite-time tracking of multiple Euler-Lagrange systems without velocity measurements

Summary This paper investigates the distributed finite-time tracking problem of networked agents with multiple Euler–Lagrange dynamics. To achieve finite-time tracking, a distributed finite-time protocol is first proposed on the basis of both relative position and relative velocity measurements. By using tools from homogeneous theory, it is theoretically shown that the proposed protocol can guarantee finite-time tracking in the presence of control input constraints. On the basis of the state feedback analysis and with the aid of second-order sliding-mode observer approach, a new class of finite-time tracking protocols based only on the relative position measurements is developed and employed. It is proved that the multiple agents equipped with the designed protocols can track the target location in finite time. Furthermore, a decentralized finite-time protocol based on a distributed estimator is proposed to solve the finite-time tracking problems with a dynamic leader. The effectiveness of the theoretical results is finally illustrated by numerical simulations. Copyright © 2014 John Wiley & Sons, Ltd.

Distributed finite-time tracking control for multi-agent systems: An observer-based approach

This paper addresses the distributed finite-time tracking control problem for second-order multi-agent systems. First, we propose a finite-time tracking protocol for multi-agent systems by using state feedback. Then, a new class of observer-based control algorithms are designed for achieving finite-time consensus tracking in multi-agent systems with a single active leader, where each agent can only share its position states with its neighbors. Within the same context, the present control algorithms are then extended to solve the finite-time containment tracking problem for multi-agent systems in the presence of multiple active leaders. It is theoretically shown that the position states of the followers will converge to that of the leader or a convex hull spanned by those of the leaders, respectively, in finite time. Furthermore, the finite-time formation control problem is discussed. The effectiveness of the results is also illustrated by numerical simulations.

Finite-time tracking control of multiple nonholonomic mobile robots

This paper investigates finite-time tracking control problem of multiple nonholonomic wheeled mobile robots in dynamic model. First of all, the resulting tracking error dynamic is transformed into two subsystems, i.e., a third-order subsystem and a second-order subsystem for each mobile robot. Then, the two subsystems are discussed respectively, continuous distributed finite-time tracking control laws are designed for each mobile robot. Rigorous proof shows that the group of mobile robots can track the desired trajectory in finite time. Simulation example illustrates the effectiveness of our method.