Multiple Stationary Leaders Research Articles

Prescribed time attitude containment control for satellite cluster with bounded disturbances

The paper investigates the problem of prescribed time attitude containment control for satellite cluster with bounded disturbances. Two novel prescribed time sliding modes are initially designed, where the prescribed time is a predefined constant. Subsequently, based on the prescribed time sliding mode, two prescribed time attitude containment controllers are presented. Under the first controller, the followers’ states could converge to the stationary convex hull surrounded by multiple stationary leaders within the prescribed time. Under the action of the second controller, the follower can track the dynamic convex hull formed by multiple dynamic leaders within the prescribed time. Finally, simulations and a comparative study are conducted to illustrate the effectiveness of the proposed control schemes.

Distributed Containment Control of Continuous-Time Multiagent Systems With Nonconvex Control Input Constraints

In this paper, we investigate the distributed constrained containment control problem for continuous-time multiagent systems with nonconvex control input constraints. A nonlinear projection containment control algorithm for followers with double-integrator continuous-time dynamics is proposed. We show that each follower finally stays in the convex hull formed by multiple stationary leaders, provided that for each follower, there exists at least one directed path from leaders to it in the union of the graphs in each bounded time interval. Finally, a simulation example is implemented to illustrate theoretical results.

Containment Problem for Multiagent Systems With Nonconvex Velocity Constraints.

In this paper, the containment problem with nonconvex velocity constraints is studied for second-order discrete-time multiagent systems. A distributed projection-based algorithm is proposed for all followers to be gathered in the convex area formed by multiple stationary leaders. It is revealed that the algorithm can solve the velocity-constrained containment problem with communication delays and switching networks provided that each follower has at least a directed path from some leaders to itself in the union of graphs. The main analysis approaches include model transformation techniques, Lyapunov function, and convexity analysis. A simulation example is also included to elucidate the obtained result.

Containment Control for High-Order Multi-Agent Systems With Nonuniform Communication Delays and Switching Topologies

In this paper, the containment control was studied for high-order discrete-time multi-agent systems. A distributed algorithm is proposed for all followers to be gathered in the convex area formed by multiple stationary leaders. It is revealed that the algorithm can solve the containment problem with communication delays and switching networks provided that each follower has at least a directed path from some leaders to itself in the union of graphs. The main analysis approaches include model transformation techniques, Lyapunov function, and convexity analysis. Finally, a simulation is also given to show the theoretical result.

Distributed containment control for first‐order and second‐order multiagent systems with arbitrarily bounded delays

SummaryThis paper studies containment control with communication delays and switching topologies. Firstly, a containment control algorithm for first‐order discrete‐time followers is proposed. Then, it is extended to handle double‐integrator dynamics. The main approach is to use the convexity of the convex hull spanned by multiple stationary leaders to verify the nonincreasing monotonicity of the largest distance from the followers to the convex hull. It is shown that both algorithms are robust to arbitrarily bounded communication delays as long as each follower jointly has a path from some leaders to itself. Finally, a numerical example is implemented to illustrate the effectiveness of the theoretical results.

Containment Control for Discrete-Time Multiagent Systems With Communication Delays and Switching Topologies.

This paper studies a containment problem with communication delays and switching topologies. A nonlinear projection containment control algorithm for followers with single-integrator discrete-time dynamics is proposed. The main approach is to use the convexity of the convex hull spanned by multiple stationary leaders to show the nonincreasing monotonicity of the largest distance from the agents to the convex hull. It is shown that the nonlinear projection containment control algorithm is robust to arbitrarily bounded communication delays as long as each follower jointly has a path from some leaders to itself. Finally, a numerical example is implemented to show the obtained theoretical results.

Second-Order Containment Control of Multiagent Systems in the Presence of Uncertain Topologies with Time-Varying Delays

This paper considers the containment control problem of second-order multiagent systems in the presence of time-varying delays and uncertainties with dynamically switching communication topologies. Moreover, the control algorithm is proposed for containment control, and the stability of the proposed containment control algorithm is studied with the aid of Lyapunov-Krasovskii function when the communication topology is jointly connected. Some sufficient conditions in terms of linear matrix inequalities (LMIs) are provided for second-order containment control with multiple stationary leaders. Finally, simulations are given to verify the effectiveness of the obtained theoretical results.

Distributed finite-time containment control for double-integrator multiagent systems.

In this paper, the distributed finite-time containment control problem for double-integrator multiagent systems with multiple leaders and external disturbances is discussed. In the presence of multiple dynamic leaders, by utilizing the homogeneous control technique, a distributed finite-time observer is developed for the followers to estimate the weighted average of the leaders' velocities at first. Then, based on the estimates and the generalized adding a power integrator approach, distributed finite-time containment control algorithms are designed to guarantee that the states of the followers converge to the dynamic convex hull spanned by those of the leaders in finite time. Moreover, as a special case of multiple dynamic leaders with zero velocities, the proposed containment control algorithms also work for the case of multiple stationary leaders without using the distributed observer. Simulations demonstrate the effectiveness of the proposed control algorithms.

L 2 – L ∞ containment control of multi‐agent systems with Markovian switching topologies and non‐uniform time‐varying delays

In this study, the authors investigate L 2 − L ∞ containment control problem of multi-agent systems with multiple stationary leaders and external disturbances. Furthermore, the interaction topology is Markovian switching and non-uniform time-varying delays are considered. By using a model transformation, the containment control problem of the multi-agent systems is turned into a normal L 2 − L ∞ control problem. Based on the theory in stochastic stability for time-delays systems, sufficient conditions in terms of a set of linear matrix inequalities are given to ensure that all the followers will move into the convex hull formed by the leaders in mean square sense with a prescribed L 2 − L ∞ performance. Two numerical simulations are provided to show the effectiveness of theoretical results.

Containment control for second-order multi-agent systems with time-varying delays

This paper considers the containment control problem for second-order multi-agent systems with time-varying delays. Both the containment control problem with multiple stationary leaders and the problem with multiple dynamic leaders are investigated. Sufficient conditions on the communication digraph, the feedback gains, and the allowed upper bound of the delays to ensure containment control are given. In the case that the leaders are stationary, the Lyapunov–Razumikhin function method is used. In the case that the leaders are dynamic, the Lyapunov–Krasovskii functional method and the linear matrix inequality (LMI) method are jointly used. A novel discretized Lyapunov functional method is introduced to utilize the upper bound of the derivative of the delays no matter how large it is, which leads to a better result on the allowed upper bound of the delays to ensure containment control. Finally, numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.

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.

Containment Control of Multiagent Systems with Multiple Leaders and Noisy Measurements

We consider the distributed containment control of multiagent systems with multiple stationary leaders and noisy measurements. A stochastic approximation type and consensus‐like algorithm is proposed to solve the containment control problem. We provide conditions under which all the followers can converge both almost surely and in mean square to the stationary convex hull spanned by the leaders. Simulation results are provided to illustrate the theoretical results.

Distributed finite-time attitude containment control for multiple rigid bodies

Distributed finite-time attitude containment control for multiple rigid bodies is addressed in this paper. When there exist multiple stationary leaders, we propose a model-independent control law to guarantee that the attitudes of the followers converge to the stationary convex hull formed by those of the leaders in finite time by using both the one-hop and two-hop neighbors’ information. We also discuss the special case of a single stationary leader and propose a control law using only the one-hop neighbors’ information to guarantee cooperative attitude regulation in finite time. When there exist multiple dynamic leaders, a distributed sliding-mode estimator and a non-singular sliding surface were given to guarantee that the attitudes and angular velocities of the followers converge, respectively, to the dynamic convex hull formed by those of the leaders in finite time. We also explicitly show the finite settling time.