Semi-global Containment Research Articles

Semi-Global Bipartite Fault-Tolerant Containment Control for Heterogeneous Multiagent Systems With Antagonistic Communication Networks and Input Saturation.

Semi-global bipartite fault-tolerant containment control framework on antagonistic communication networks is proposed in this article for heterogeneous multiagent systems (MASs) under the influence of input saturation and actuator faults. An observer is constructed to estimate the leaders' states on signed digraph, where the communication networks are antagonistic. A fully distributed virtual control approach is developed to acquire the containment trajectory. Based on the observer, a semi-global containment control method is developed to compensate for the detrimental impacts of both input saturation and actuator faults. Besides, the dynamics and state-space dimensions of the agents can be different. The proposed framework overcomes two drawbacks of the conventional containment control: 1) the containment trajectory is obtained under general antagonistic communication networks, which is more general in engineering applications and 2) both actuator faults and input saturation are solved for heterogeneous agents, which relaxes the limitation of homogeneous dynamics. Finally, a simulation example is conducted to test and verify the feasibility of the proposed method framework.

Observer-based semi-global containment of saturated multi-agent systems with uncertainties

In this article, the robust semi-global containment control for multi-agent systems affected by uncertainties, such as input additive disturbance, input saturation and dead zone is addressed. An observer-based control algorithm is designed by combining the high-gain observer approach and the low-and-high gain feedback technique. Under the assumption that all agents are asymptotically null controllable with bounded controls and each follower can access the information of at least one leader through a directed path, sufficient conditions for the semi-global output feedback containment control are provided. Finally, numerical simulations are proposed to verify the main theoretical results.

Model-Free Algorithms for Containment Control of Saturated Discrete-Time Multiagent Systems via Q-Learning Method

In this article, we propose two model-free algorithms using state or output feedback for saturated discrete-time multiagent systems (SDTMASs) to attain global containment control. In most previous works, the control input can avoid saturation by utilizing the low gain feedback (LGF) method whereas requiring the knowledge of agent dynamics, and SDTMASs just can attain semi-global containment control. Distinct with the previous works, first, based on the <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula>-learning (QL) technique, this article defines a <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula>-function and deduces the corresponding QL Bellman equation, which is the most important part of the QL algorithm. Then, in order to solve the QL Bellman equation, we propose two iterative model-free algorithms using state and output feedback, and the LGF matrix can be acquired from that solution directly. Furthermore, under the state and output feedback control protocols with the feedback matrices obtained from the proposed model-free algorithms, the SDTMASs can achieve global containment control instead of semi-global containment control. Finally, we present some simulations to confirm the validity of the proposed algorithms.

Semi‐global containment of discrete‐time high‐order multi‐agent systems with input saturation via intermittent control

This study investigates the intermittent semi-global containment of discrete-time high-order multi-agent systems with input saturation. The intermittent semi-global containment protocol is proposed based on discrete-time low-gain state feedback control. Some containment conditions are obtained, and the convergence analysis is given. It is turned out that all the followers beginning from a bounded initial set will asymptotically enter into the convex hull spanned by the leaders under the proposed protocol. Moveover, intermittent semi-global leader-following consensus with input saturation is considered as a special case, and the corresponding result is introduced. Finally, numerical simulations are presented to illustrate the theoretical findings.

Semi-global containment control of discrete-time linear systems with actuator position and rate saturation

In this paper, we study semi-global containment control problem for a multi-agent system in the presence of multiple leader agents. We describe the dynamics of each follower agent in multi-agent system by a general discrete-time linear system subject to both actuator position and rate saturation. By using low gain approach, we construct both a linear state feedback control law and an observer-based output feedback control law for each follower agent. Under some standard assumptions, we provide a sufficient condition to guarantee that the states of follower agents converge to the convex hull formed by the leader agents asymptotically. Finally, we illustrate the theoretical results by numerical simulation results.

Semi-global leader-following coordination of multi-agent systems with input saturation and aperiodic intermittent communications

This paper addresses the semi-global leader-following coordination problem of general linear multi-agent systems, in which the control input of each agent is steered by aperiodically intermittent saturated actuator. Both the case with only one virtual leader and the case with multiple virtual leaders are discussed. By using multiple Lyapunov stability theory and applying algebraic Riccati equation-based low-gain feedback technique, sufficient conditions guaranteeing semi-global consensus tracking and semi-global containment tracking are provided. Numerical simulations finally verify the theoretical analysis.

Robust Semi-Global Leaderless Consensus and Containment Control of Identical Linear Systems with Imperfect Actuators

This paper investigates both the robust semi-global leaderless consensus problem and the robust semi-global containment control problem for a group of identical linear systems with imperfect actuators. The imperfect actuators are characterized by nonlinearities such as saturation and dead zone and there input output relationships are not precisely known. The dynamics of follower agents are also affected by the input additive disturbances. Low-and-high gain feedback consensus protocols are constructed to solve these problems. More specifically, it is shown that robust semi-global leaderless consensus can be achieved over a connected undirected graph and robust semi-global containment control can be achieved when each follower agent has access to the information of at least one leader agent. Numerical simulation illustrates the theoretical results.

Semi-global and global containment control of multi-agent systems with second-order dynamics and input saturation

This paper considers both semi-global and global containment control for a second-order multi-agent system that is composed by a network of identical harmonic oscillators or double integrators with multiple leaders and input saturation. A distributed low gain feedback algorithm is proposed to solve the semi-global containment control problem for the network whose topology is directed and initial condition is taken from any a priori given bounded set. In particular, by using a parametric Lyapunov equation approach, M-matrix properties and algebraic graph theory, an upper bound of the low gain parameter is estimated such that the low gain feedback matrix can be analytically determined without involving numerical computation. Furthermore, under the assumption that the induced subgraph formed by the followers is strongly connected and detail balanced, two linear feedback protocols are designed for coupled harmonic oscillators and coupled double integrators, respectively, to asymptotically achieve the global containment control of the network with any initial condition. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results

Semi-global containment control of multi-agent systems with intermittent input saturation

This paper investigates containment control of multi-agent systems with intermittent communications and input saturation on fixed undirected networks. Under the assumption that each agent is asymptotically null controllable with bounded controls and there exists at least one leader that has directed path to each followers, both state feedback and output feedback control protocols are designed by utilizing the algebraic Riccati equation. For any a priori given bounded set, semi-global state feedback and output feedback containment control of multi-agent systems with intermittent communication can be attained. Numerical simulations are provided to ensure the effectiveness of results.