Mixed-order Multi-agent Systems Research Articles

Distributed consensus tracking control based on state and disturbance observations for mixed-order multi-agent mechanical systems

In this paper, we study the cooperative consensus control problem of mixed-order (also called hybrid-order) multi-agent mechanical systems (MMSs) under the condition of unmeasurable state, unknown disturbance and constrained control input. Here, the controlled mixed-order MMSs are consisted of the mechanical agents having heterogeneous nonlinear dynamics and even non-identical orders, which means that the agents can be of different types and their states to be synchronized can be not exactly the same. In order to achieve the ultimate synchronization of all mixed-order followers, we present a novel distributed adaptive tracking control protocol based on the state and disturbance observations. Wherein, a distributed state observer is used to estimate the followers’ and their neighbors’ unmeasurable states. And, a novel estimated-state-based disturbance observer (DOB) is proposed to reduce the effect of unknown lumped disturbance for the mixed-order MMSs. The proposed control protocol and observers are fully distributed and can be calculated for each follower locally. Lyapunov theory is used for proving the stability of the proposed control algorithm and the convergence of the cooperative tracking errors. A practical cooperative longitudinal landing control example of unmanned aerial vehicles (UAVs) is given to illustrate the effectiveness of the presented control protocol.

Consensus Control of Mixed-Order Nonlinear Multiagent Systems: Framework and Case Study.

This article investigates the consensus problem of mixed-order nonlinear multiagent systems (MASs). First, a new research framework of consensus control for MASs with hybrid-order dynamics is established. In this framework, the order of low-order dynamic subsystems is increased to higher-order dynamic subsystems by means of increasing order technology, so that the mixed-order MASs can be changed into the same-order MASs. Thus, the distributed controller of hybrid-order MASs can be designed by using the consensus control method of the same-order MASs. Second, through a case study of a stochastic mixed first- and second-order nonlinear MASs, this article further expounds the design idea of the framework structure and gives the concrete design form of the distributed controller and the stability analysis of the closed-loop system. Finally, simulations are given to verify the effectiveness of the distributed control protocol in this case.

Adaptive neural control of nonlinear periodic time-varying parameterized mixed-order multi-agent systems with unknown control coefficients

Adaptive neural control of nonlinear periodic time-varying parameterized mixed-order multi-agent systems with unknown control coefficients

A novel modularized formation tracking control for mixed-order discrete-time multi-agent systems

A modularized output formation tracking control for mixed-order multi-agent systems is investigated. The multi-agent systems are composed of first-order and second-order integrators. The stability and formation tracking performance are analysed theoretically by the mathematical induction method. Finally, the effectiveness of the proposed modularized output control protocol is verified by simulation examples.

Finite-time consensus control for heterogeneous mixed-order nonlinear stochastic multi-agent systems

This study investigates the finite-time consensus control problem for a class of mixed-order multi-agent systems (MASs) with both stochastic noises and nonlinear dynamics. The sub-systems of the MASs under consideration are heterogenous that are described by a series of differential equations with different orders. The purpose of the addressed problem is to design a control protocol ensuring that the agents' states can achieve the desired consensus in finite time in probability 1. By using the so-called adding a power integrator technique in combination with Lyapunov stability theory, the required distributed consensus control protocol is developed and the corresponding settling time is estimated. Finally, a simulation example is given to demonstrate the correctness and usefulness of the proposed theoretical results.

Cooperative Tracking Control of Heterogeneous Mixed-Order Multiagent Systems With Higher-Order Nonlinear Dynamics

This article investigates a class of finite-time cooperative tracking problems of heterogeneous mixed-order multiagent systems (MASs) with higher-order dynamics. Different from the previous works of heterogeneous MASs, the agents in this study are considered to have different first-, second-, or even higher-order nonlinear dynamics. It means that, according to different tasks and situations, the following agents can have nonidentical orders or different numbers of states to be synchronized, which is more general for the practical cooperative applications. The leader is a higher-order nonautonomous system and contains full state information to be synchronized for all agents with mixed-order dynamics. Accordingly, the spanning tree is defined based on the specific state rather than on the agent to guarantee that each following agent can receive adequate state information. Distributed control protocols are designed for all agents to achieve the ultimate state synchronization to the leader in finite time. The Lyapunov approach is used for the stability analysis and a practical example of mixed-order mechanical MASs verifies the effectiveness and performance of the proposed distributed control protocols.

Group Consensus of Mixed-Order Multi-Agent Systems With Fixed and Directed Interactive Topology

This paper studies the group consensus of discrete-time mixed-order multi-agent systems with fixed and directed interactive topology. First, group consensus protocols are designed for all agents to investigate the group consensus of mixed-order multi-agent systems without time delays. Under some assumptions on the interactive topology, sufficient conditions for group consensus are obtained based on matrix theory and graph theory, which are dependent on the sampling period and the control gains. Then, group consensus protocols are proposed for a case where communication delays exist. Sufficient conditions are also established for group consensus using Nyquist stability criterion. Finally, several simulation examples are given to verify the validity of the theoretical results.

Optimally distributed formation control with obstacle avoidance for mixed‐order multi‐agent systems under switching topologies

In this study, an optimally distributed formation control approach is proposed for mixed-order multi-agent systems to achieve formation consistency with obstacle avoidance. The systems consist of unmanned aerial vehicles and ground robots. The authors present a formation consistency control for a mixed-order system under switching topologies. An optimally distributed method is developed by matrix transformation method and linear quadratic regulator theory, which leads to an optimisation on both horizontal and vertical control. For obstacle avoidance, a non-quadratic cost function is introduced based on optimal control. The resulting closed-loop mixed-order system is validated to be stable with an optimal performance. The formation consensus and obstacle avoidance are verified by simulations to show the effectiveness and potentials.

A Novel Leader-following Consensus of Multi-agent Systems with Smart Leader

This article studies the leader-following consensus problem for mixed-order multi-agent systems with a leader. Different from the traditional leader which is independent of all the other agents, the leader, called smart leader, can obtain and utilize the feedback information from its neighbors at some disconnected time intervals. A new distributed consensus control protocol based on intermittent control is developed for leader-following consensus with a smart leader. Moreover, the smart leader can adjust the control protocol based on the feedback information from its neighbors. With the aid of Lyapunov function, some sufficient conditions are derived for leader-following consensus of multi-agent systems with mixed-order dynamics under fixed directed topology. In addition, the similar results are obtained under switching directed topology. Finally, simulation results are provided to verify the correctness and effectiveness of theoretical results.

Collective behavior of mixed-order linear multi-agent systems under output-coupled consensus algorithm

Output consensus problem is investigated for mixed-order linear multi-agent systems composed of two-type agents with one and two poles at the origin respectively, and usual output-coupled consensus algorithm is adopted. According to generalized Nyquist stability criterion, consensus conditions are gained for the mixed-order multi-agent systems to achieve an asymptotic stationary consensus without and with communication delay respectively. Besides, output consensus is also discussed for a simple mixed-order multi-agent system, which consists of single and double integrators. Numerical examples show the correctness of theoretical results.

Consensus analysis for a class of mixed-order multi-agent systems with nonlinear consensus protocols

The consensus problem for a class of mixed-order multi-agent systems is investigated in this paper, where the multi-agent system is composed of first- and second-order dynamic agents. Firstly, consensus protocols are proposed for solving the finite-time consensus problem for mixed-order multi-agent systems. By employing the finite-time stability theory and LaSalle’s invariance principle, some sufficient conditions for finite-time consensus are given for multi-agent systems with directed communication topologies. Then, a class of nonlinear consensus protocols are given to solve the asymptotic consensus problem for mixed-order multi-agent systems. In addition, an invariant quantity is introduced to specify the expressions of the final consensus states when asymptotic consensus is reached. Finally, a simulation example is provided to demonstrate the effectiveness of the theoretical results.