Control Of Heterogeneous Multi-agent Systems Research Articles

Controllability of heterogeneous multiagent systems with two-time-scale feature.

In this paper, we investigate the controllability problems for heterogeneous multiagent systems (MASs) with two-time-scale feature under fixed topology. Firstly, the heterogeneous two-time-scale MASs are modeled by singular perturbation system with a singular perturbation parameter, which distinguishes fast and slow subsystems evolving on two different time scales. Due to the ill-posedness problems caused by the singular perturbation parameter, we analyze the two-time-scale MASs via the singular perturbation method, instead of the general methods. Then, we split the heterogeneous two-time-scale MASs into slow and fast subsystems to eliminate the singular perturbation parameter. Subsequently, according to the matrix theory and the graph theory, we propose some necessary/sufficient criteria for the controllability of the heterogeneous two-time-scale MASs. Lastly, we give some simulation and numerical examples to demonstrate the effectiveness of the proposed theoretical results.

Event‐triggered tracking control of heterogeneous multiagent systems based on two kinds of observers with asymmetric delay

SummaryIn this paper, we consider the output tracking problem of a multiagent system with asymmetric delays and a switching topology. The multiagent system contains a leader and some followers, the dynamics of which are heterogeneous, and the output of the leader is available to only a subset of followers. We propose two types of observers to estimate states of the leader and reduce communication cost. For the informed followers that can directly obtain information of the leader, a common observer is given to reduce the complexity of observer design. Meanwhile, for the rest of the followers, a distributed observer with asymmetric communication delays for each follower is designed. The observer error system is transformed into a switched system. Through designing the average dwell‐time switching law and constructing multiple Lyapunov functionals, some sufficient conditions for stability of the observer error system are obtained. Furthermore, a distributed controller for followers based on the relative information is developed to track the output of the leader. Finally, an example is given to validate the effectiveness of the proposed results.

Output containment control of heterogeneous multi-agent systems with leaders of bounded inputs: An adaptive finite-time observer approach

In this paper, we address the problem of output containment control of general linear multi-agent systems (MASs). The MAS under consideration is comprised by multiple followers and multiple leaders, all with heterogeneous dynamics. In particular, the leaders’ dynamics are subject to heterogeneous non-zero (possibly persistent) but bounded inputs, which are not measurable for any follower agent, making the associated distributed control design problem rather challenging. A new distributed observer-based containment control protocol is proposed to overcome associated challenges. It consists of two hierarchical layers including (i) the first layer of adaptive finite-time cooperative observer responsible for estimating the convex-hull signals formed by multiple leaders’ states through inter-agent collaboration; and (ii) the second layer of distributed state-feedback controller responsible for local tracking control through a modified output regulation technique. Important novelties of the proposed protocol are that (i) it deals with MASs with not only heterogeneous followers but also heterogeneous leaders; (ii) exact output containment control performance can be achieved in the presence of unmeasurable leaders’ inputs and unknown connectivity of communication network; and (iii) associated solvability conditions are formulated as linear matrix inequalities plus linear algebraic equations, which can be tested and solved effectively via efficient semi-definite programming. The developed theoretical results are demonstrated both rigorously using Lyapunov methods and through numerical simulations.

Average-Consensus Tracking of Sensor Network via Distributed Coordination Control of Heterogeneous Multi-Agent Systems

Average-consensus tracking problem is investigated for sensor network, in which the computing units are modeled by heterogeneous multi-agent systems composed of first-order agents and second-order agents. To track the average value of sensors’ measured values, the proportional-integral consensus tracking algorithms are proposed for first-order and second-order agents, respectively. By using generalized Nyquist stability criterion, sufficient conditions of average-consensus convergence are obtained for the heterogeneous multi-agent systems under a fixed, symmetric and connected topology. Furthermore, delay-dependent convergence conditions are obtained for the multi-agent systems with identical communication delay. Numerical simulations illustrate the correctness of our results.

Affine formation control for heterogeneous multi-agent systems with directed interaction networks

In this paper, affine formation control problems of heterogeneous multi-agent systems with linear dynamics are studied. As a novel method, the affine formation control has the ability to handle various movement constraints based on the affine transformation. A proportional-integral (PI)-type control scheme is proposed to ensure the effective affine formation control of the leader-following group with directed interaction graphs and successfully eliminate the steady-state errors. Sufficient conditions for the selection of control parameters are given and proved. Considering that the followers are subjected to the external bounded time-varying disturbances, the designed protocol shows good robustness and can guarantee uniformly ultimate boundedness of affine formation errors. Numerical simulations are carried out to verify the theoretical results.

Formula omitted] output containment control of heterogeneous multi-agent systems via distributed dynamic output feedback

This paper addresses the problem of output containment control of heterogeneous multi-agent systems (MASs), which aims to drive the outputs of all followers to a dynamic convex hull spanned by the outputs of multiple leaders. The considered MAS consists of heterogeneous linear agent dynamics with possibly non-identical state dimensions and subject to unknown external disturbances. New distributed control protocols via dynamic output feedback are proposed, such that the output containment control problem can be decomposed into independent H∞ stabilization subproblems for the follower agents. The resulting distributed control synthesis conditions are formulated as linear matrix equations plus linear matrix inequalities, which can be solved efficiently via convex optimization. Both continuous-time and discrete-time output containment control problems are addressed under a unifying framework. Two examples have been used to demonstrate the effectiveness of the proposed approaches.

Adaptive output containment control of heterogeneous multi-agent systems with unknown leaders

This paper investigates the adaptive output containment control of general linear heterogeneous multi-agent systems with multiple unknown leaders whose dynamics are only known to the neighboring followers. The output containment control objective is to assure the convergence of each follower’s output to the dynamic convex hull spanned by the leaders’ outputs. Compared with the situation where the leaders’ dynamics are known to each follower exactly, local adaptive observers are presented at each follower to estimate the leaders’ dynamics. Then, an adaptive tuning law is proposed to solve the associated output regulator equations without knowing leaders’ dynamics. Two distributed control protocols, using state-feedback and dynamic output-feedback are locally designed, using the estimated leaders’ dynamics and adaptive solutions to the output regulator equations. Both proposed control protocols are verified using numerical simulations.

Distributed LQR Consensus Control for Heterogeneous Multiagent Systems: Theory and Experiments

Controlling heterogeneous multiagent systems (MASs) to cooperatively accomplish tasks is currently an emerging topic in the application-oriented research of robotics. This paper investigates the consensus problem of a MAS consisting of quadrotors and two-wheeled mobile robots (2WMRs). Directed and switching interaction topologies over the network are considered. We propose a distributed linear quadratic regulation (LQR) consensus protocol for the quadrotors and design an LQR-based Rotate&Run Consensus Scheme for the 2WMRs to update the states. We use the algebraic graph theory and stochastic matrix analysis to conduct the convergence analysis of consensus. The underactuation characteristic of the 2WMR dynamics is considered in the controller design. The effectiveness of the control methods is verified by simulations and experiments.

Containment Control of Heterogeneous Systems With Non-Autonomous Leaders: A Distributed Optimal Model Reference Approach

This paper presents a distributed optimal model reference adaptive control approach for solving containment control of heterogeneous multi-agent systems (MASs) with non-autonomous leaders. First, a fully distributed adaptive observer is designed to provide for each agent the desired reference trajectory by estimating the convex hull spanned by leaders. The distributed observer dynamics serves as a reference model for each follower to synchronize. The global communication graph information or the leader dynamics is not required to design the observer. In contrast to existing model reference adaptive controllers (MRAC) for single-agent systems and containment control solutions for MASs, the proposed MRAC approach imposes optimality and presents a distributed adaptive optimal solution to the containment control problem. To impose optimality, a performance function is defined based on the adaptive observers’ states as well as the followers’ local measurements. It is shown that considering non-autonomous leaders in this optimal control problem leads to solving inhomogeneous algebraic Riccati equations (AREs), instead of normal AREs in standard optimal control problems. To obviate the requirement of knowing the agents’ dynamics, an off-policy reinforcement learning approach implemented on an actor-critic structure is utilized for solving the inhomogeneous ARE. A simulation example is conducted to illustrate the effectiveness of the presented method.

Containment control for heterogeneous multi-agent systems with asynchronous updates

This paper is concerned with the asynchronous containment control problem for heterogeneous multi-agent systems with time-varying delays. Here, asynchrony means that each agent updates the state information by its own clock that is independent of the other agents’ update times, and the update intervals of each agent are not necessarily equispaced. It is assumed that the leaders are stationary, and the followers can be classified into two generic categories: the followers with the first-order dynamics and the followers with second-order dynamics. For different kinds of followers, two distributed containment control protocols are presented to guarantee that all the followers can asymptotically converge into the convex hull formed by the leaders. The properties of the product of infinite nonnegative matrices are explored to arrive at that the asynchronous containment control can be achieved under the proposed protocols if and only if the communication topology among the agents contains a directed spanning forest rooted at the leaders. At last, simulation results are given to demonstrate the validity of the theoretical findings.

Distributed adaptive switching consensus control of heterogeneous multi-agent systems with switched leader dynamics

In this paper, the leader-following distributed consensus control problem is addressed for general linear multi-agent systems with heterogeneous uncertain agent dynamics and switched leader dynamics. Different from most existing results with a single linear time-invariant (LTI) leader dynamics, the leader dynamics under consideration is composed by a family of LTI models and a switching logic governing the switches among them, which is capable of generating more diverse and sophisticated reference signals to accommodate more complicated consensus control design tasks. A novel distributed adaptive switching consensus protocol is developed by incorporating the model reference adaptive control mechanism and arbitrary switching control technique, which can be synthesized by following a two-layer hierarchical design scheme. A numerical example has been used to demonstrate the effectiveness of the proposed approach.

Distributed Optimal Output Feedback Control of Heterogeneous Multi-agent Systems under a Directed Graph

In this paper, we consider distributed optimal feedback control design problem for a network of heterogeneous systems. The agents are coupled through their linear quadratic cost function and their interaction (communication) topology is given by a strongly connected directed graph. The goal is to design a distributed optimal feedback control which minimizes the total cost function in a distributed manner by only relying on the neighboring information of each agent. Moreover, the design of the optimal feedback control gain is also performed in a distributed manner by only relying on the neighboring information of each agent. To this end, firstly the necessary conditions are derived for the noninferior solution to the overall performance index. Then, by utilizing the idea of finite-time consensus algorithm, it is shown that the optimal feedback gain can also be computed in a distributed manner by the agents. Finally, we demonstrate the effectiveness of the proposed control law via a simulation on a group of heterogeneous dynamical systems.

Multi‐tracking control of heterogeneous multi‐agent systems with single‐input– single‐output based on complex frequency domain analysis

This paper studies the multi-tracking control for high-order heterogeneous multi-agent systems under a directed acyclic graph. The authors first convert the multi-tracking control problem for multi-agent systems into the zero steady-state error control problem of some independent subsystems. Based on final-value theorem and Mason's rule, a sufficient condition for achieving the multi-tracking control is proposed. It explicitly reveals how the system dynamic and desired object dynamic jointly affect the multi-tracking control of heterogeneous multi-agent systems. Meanwhile, a new result on the steady-state error for multi-subnetworks is established. Moreover, the multi-tracking control for heterogeneous multi-agent systems with time delay is discussed. Some simulations are performed to illustrate the effectiveness of the theoretical results.

Event-triggered control for heterogeneous multi-agent systems with time-varying delays when using the second-order neighbours' information

This paper mainly investigates the event-triggered control for heterogeneous multi-agent systems with time-varying delays when both the first-order and the second-order neighbours' information are used. First, the heterogeneous multi-agent systems are composed of two kinds of agents differed by their dynamics. Then, event-triggered control laws are adopted so as to reduce the frequency of individual actuation updating under the sampled-data framework for discrete-time agent dynamics. By applying the Lyapunov functional method and the Kronecker product technique, two sufficient conditions for consensus are established in terms of linear matrix inequalities (LMIs) when the communication topologies are undirected connected graphs and switching networks. Finally, simulation examples are given to demonstrate the effectiveness of the proposed methods.

Consensus Control for Heterogeneous Multiagent Systems

We study distributed output feedback control for a heterogeneous multi-agent system (MAS), consisting of N different continuous-time linear dynamical systems. For achieving output consensus, a virtual reference model is assumed to generate the desired trajectory that the MAS is required to track and synchronize. A distinct feature of our results lies in the local optimality and robustness achieved by our proposed consensus control algorithm. In addition our study is focused on the case when the available output measurements contain only relative information from the neighboring agents and reference signal. Indeed by exploiting properties of strictly positive real (SPR) transfer matrices, conditions are derived for the existence of distributed output feedback control protocols, and solutions are proposed to synthesize the stabilizing and consensus control protocol over a given connected digraph. It is shown that design techniques based on the LQG, LQG/LTR and H-infinity loop shaping can all be directly applied to synthesize the consensus output feedback control protocol, thereby ensuring the local optimality and stability robustness. Finally the reference trajectory is required to be transmitted to only one or a few agents and no local reference models are employed in the feedback controllers thereby eliminating synchronization of the local reference models. Our results complement the existing ones, and are illustrated by a numerical example.

Controllability of heterogeneous multi-agent systems under directed and weighted topology

ABSTRACTThis paper considers the controllability problem for both continuous- and discrete-time linear heterogeneous multi-agent systems with directed and weighted communication topology. First, two kinds of neighbour-based control protocols based on the distributed protocol of first-order and second-order multi-agent systems are proposed, under which it is shown that a heterogeneous multi-agent system is controllable if the underlying communication topology is controllable. Then, under special leader selection, the result shows that the controllability of a heterogeneous multi-agent system is solely decided by its communication topology graph. Furthermore, some necessary and/or sufficient conditions are derived for controllability of communication topology from algebraic and graphical perspectives. Finally, simulation examples are presented to demonstrate the effectiveness of the theoretical results.

Group consensus control for heterogeneous multi-agent systems with fixed and switching topologies

ABSTRACTIn this paper, the group consensus problems of heterogeneous multi-agent systems with fixed and switching topologies are investigated. First, a class of distributed group consensus protocol is proposed for achieving the group consensus of heterogeneous multi-agent systems by using the neighbours’ information. Then, some corresponding sufficient conditions are obtained to guarantee the achievement of group consensus. Rigorous proofs are given by using graph theory, matrix theory and Lyapunov theory. Finally, numerical simulations are also given to verify the theoretical analysis.

On Controllability Problems of High-Order Dynamical Multi-Agent Systems

Controllability problems of dynamical high-order multi-agent systems are concerned. A methodology on graph topology transformation is proposed, which can help to analyze the controllability. According to this methodology, a path can be regarded as controllability canonical form of graph, and any controllable graph can be transformed into an equivalent path. Besides, controllability of heterogeneous multi-agent systems is also discussed.

Containment control of heterogeneous multi-agent systems

In this paper, we consider the containment control problem for a group of autonomous agents modelled by heterogeneous dynamics. The communication networks among the leaders and the followers are directed graphs. When the leaders are first-order integrator agents, we present a linear protocol for heterogeneous multi-agent systems such that the second-order integrator agents converge to the convex hull spanned by the first-order integrator agents if and only if the directed graph contains a directed spanning forest. If the leaders are second-order integrator agents, we propose a nonlinear protocol and obtain a necessary and sufficient condition that the heterogeneous multi-agent system solves the containment control problem in finite time. Simulation examples are also provided to illustrate the effectiveness of the theoretical results.

Event-triggered tracking control for heterogeneous multi-agent systems with Markov communication delays

In this paper, we investigate the consensus problem of a set of discrete-time heterogeneous multi-agent systems with random communication delays represented by a Markov chain, where the multi-agent systems are composed of two kinds of agents differed by their dynamics. First, distributed consensus control is designed by employing the event-triggered communication technique, which can lead to a significant reduction of the information communication burden in the multi-agent network. Then, the mean square stability of the closed loop multi-agent systems is analyzed based on the Lyapunov functional method and the Kronecker product technique. Sufficient conditions are obtained to guarantee the consensus in terms of linear matrix inequalities (LMIs). Finally, a simulation example is given to illustrate the effectiveness of the developed theory.