Guangfu Ma

Brief paper: Distributed containment control for Lagrangian networks with parametric uncertainties under a directed graph

In this paper, we study the distributed containment control problem for networked Lagrangian systems with multiple dynamic leaders in the presence of parametric uncertainties under a directed graph that characterizes the interaction among the leaders and the followers. We propose a distributed adaptive control algorithm combined with distributed sliding-mode estimators. A necessary and sufficient condition on the directed graph is presented such that all followers converge to the dynamic convex hull spanned by the dynamic leaders asymptotically. As a byproduct, we show a necessary and sufficient condition on leaderless consensus for networked Lagrangian systems under a directed graph. Numerical simulation results are given to show the effectiveness of the proposed control algorithms.

Distributed Coordinated Tracking With a Dynamic Leader for Multiple Euler-Lagrange Systems

In this note, we study a distributed coordinated tracking problem for multiple networked Euler-Lagrange systems. The objective is for a team of followers modeled by full-actuated Euler-Lagrange equations to track a dynamic leader whose vector of generalized coordinates is time varying under the constraints that the leader is a neighbor of only a subset of the followers and the followers have only local interaction. We consider two cases: i) The leader has a constant vector of generalized coordinate derivatives, and ii) The leader has a varying vector of generalized coordinate derivatives. In the first case, we propose a distributed continuous estimator and an adaptive control law to account for parametric uncertainties. In the second case, we propose a model-independent sliding mode control algorithm. Simulation results on multiple networked two-link revolute joint arms are provided to show the effectiveness of the proposed control algorithms.

Distributed coordination for second-order multi-agent systems with nonlinear dynamics using only relative position measurements

In this paper, we study the distributed coordination for second-order multi-agent systems with intrinsic nonlinear dynamics under an undirected graph that characterizes the interaction among the agents or followers. Both the leaderless consensus problem and the coordinated tracking problem with a dynamic leader are considered. By introducing a distributed filter for each agent or follower, the proposed control algorithms use only relative position measurements in the absence of communication. In the special case without the intrinsic nonlinear dynamics, i.e., for multi-agent systems with double-integrator dynamics, we further derive a necessary and sufficient condition for the leaderless consensus problem under a general directed graph. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.

Distributed adaptive coordination for multiple Lagrangian systems under a directed graph without using neighbors' velocity information

In this paper, we study the distributed coordination problem for multiple Lagrangian systems in the presence of parametric uncertainties under a directed graph without using neighbors velocity information in the absence of communication. We consider two cases, namely, the distributed containment control problem with multiple stationary leaders and the leaderless synchronization problem. In both cases, distributed adaptive control algorithms without using neighbors velocity information are proposed. The control gains in the algorithms are varying with distributed updating laws. Furthermore, necessary and sufficient conditions on the directed graph are presented, respectively, such that all followers converge to the stationary convex hull spanned by the stationary leaders asymptotically in the containment control problem and the systems synchronize asymptotically in the leaderless synchronization problem. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.

Distributed Containment Control for Multiple Unknown Second-Order Nonlinear Systems With Application to Networked Lagrangian Systems

In this paper, we consider the distributed containment control problem for multiagent systems with unknown nonlinear dynamics. More specifically, we focus on multiple second-order nonlinear systems and networked Lagrangian systems. We first study the distributed containment control problem for multiple second-order nonlinear systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a general directed graph that characterizes the interaction among the leaders and the followers. A distributed adaptive control algorithm with an adaptive gain design based on the approximation capability of neural networks is proposed. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, the leaderless consensus problem is solved with asymptotical convergence. Because relative velocity measurements between neighbors are generally more difficult to obtain than relative position measurements, we then propose a distributed containment control algorithm without using neighbors velocity information. A two-step Lyapunov-based method is used to study the convergence of the closed-loop system. Next, we apply the ideas to deal with the containment control problem for networked unknown Lagrangian systems under a general directed graph. All the proposed algorithms are distributed and can be implemented using only local measurements in the absence of communication. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.

Containment control for multiple euler-lagrange systems with parametric uncertainties in directed networks

In this paper, we study the distributed containment control problem for networked Lagrangian systems with multiple stationary or dynamic leaders in the presence of parametric uncertainties under a directed graph that characterizes the interaction among the leaders and the followers. When the leaders are stationary, a distributed adaptive control algorithm is proposed. We present a necessary and sufficient condition on the directed graph such that all followers converge to the stationary convex hull spanned by the stationary leaders asymptotically. As a byproduct, we show a necessary and sufficient condition on leaderless consensus for networked Lagrangian systems under a directed graph. When the leaders are dynamic, two cases are considered: i) The leaders have constant vectors of generalized coordinate derivatives; ii) The leaders have varying vectors of generalized coordinate derivatives. In the first case, we propose a distributed continuous estimator and a distributed adaptive control algorithm. In the second case, we propose a distributed adaptive control algorithm combined with distributed sliding-mode estimators. In both cases, a necessary and sufficient condition on the directed graph is presented such that all followers converge to the dynamic convex hull spanned by the dynamic leaders asymptotically.

Distributed finite-time configuration containment control for satellite formation

This paper investigates the distributed finite-time configuration containment control problem for satellite formation with multiple leader satellites under directed communication topology. We consider that only a portion of follower satellites can receive leaders’ information and unknown perturbations and model uncertainties exist in the dynamics models of satellites. By defining the relative configuration error functions and selecting suitable nonsingular terminal sliding mode variables, a fully distributed finite-time configuration containment control scheme is proposed using the matrix properties of graph theory. The Lyapunov method is used to demonstrate the finite-time convergence property of the closed-loop systems. Numerical examples and comparisons with other methods are provided to show the effectiveness and the performance of the proposed control strategy.

Containment control for networked unknown Lagrangian systems with multiple dynamic leaders under a directed graph

In this paper, we address the containment control problem for multiple Lagrangian systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a directed graph. A distributed adaptive control algorithm with an adaptive gain design using both relative position and velocity feedback is proposed based on the approximation capability of neural networks. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, we show a necessary and sufficient condition on leaderless consensus for networked Lagrangian systems under a directed graph with unknown nonlinearities and external disturbances, in which the systems achieve consensus asymptotically. We then propose a distributed containment control algorithm without using neighbors velocity information.

Distributed coordinated tracking for multiple Euler-Lagrange systems

In this paper we study a distributed coordinated tracking problem for networked Euler-Lagrange systems. The objective is for a team of followers modeled by Euler-Lagrange equations to track a leader under the constraints that the leader is a neighbor of only a subset of the followers and the followers have only local interaction. We consider two cases: i) The leader has a constant vector of generalized coordinate derivatives, and ii) The leader has a varying vector of generalized coordinate derivatives. In the first case, we propose a distributed continuous estimator and an adaptive control law to account for parametric uncertainties. In the second case, we propose a model-independent sliding mode control algorithm.

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.