Dynamic Output Feedback Protocol Research Articles

A hybrid time/event-triggered interaction framework for multi-agent consensus with relative measurements

This paper is concerned with the output-feedback consensus problem of linear multi-agent systems on undirected graphs. Our focus is on reducing sensing and communication burdens between agents. Based on relative output measurements, a dynamic output-feedback (DOF) protocol is proposed, which, by leveraging the structure of the closed-loop dynamics, integrates a hybrid time/event-triggered sampling mechanism such that only intermittent interaction between agents is needed. Consensus conditions are established by the Lyapunov method and numerical simulations are provided for illustrating the effectiveness of the protocol. Compared with the existing results, the proposed DOF protocol has the following merits: (1) they rely on relative output measurements but do not need absolute measurements about agents; (2) they only require agents to intermittently interact with neighbors and thus can greatly reduce sensing and communication burdens between agents; and (3) the designed event-triggering conditions do not need to perform extra reconstruction operations that are computationally demanding.

LMI-based consensus of linear multi-agent systems by reduced-order dynamic output feedback

This work proposes new conditions for consensus of homogeneous multi-agent systems subjected to exogenous disturbances in directed communication graphs by dynamic output feedback protocols. The agents under investigation are described as linear dynamics, and the communication network is such that each agent receives as information only the output of neighbor agents. The synchronization problem is rewritten as an output feedback stabilization without requiring the Laplacian matrix to be diagonalizable. As the main appeal, we propose new necessary and sufficient conditions for the design of dynamic output feedback controllers of arbitrary order – including static output feedback as a particular case – and sufficient Linear Matrix Inequalities (LMIs) for H∞ consensus. Numerical experiments illustrate the effectiveness of the proposed approach.

Energy-constraint output formation for swarm systems with dynamic output feedback control protocols

This paper studies the energy-constraint output formation control for swarm systems with leaderless and leader-following topology structures. Most existing results on output formation with the dynamic output feedback protocols focus on the swarm systems without the energy constraint, but it is well known that the energy constraint is critically important for practical applications. In order to analyze the impacts of the energy constraint, a new energy-constraint output formation protocol is proposed. First, by the observable decomposition approach, a dynamic output formation protocol is presented, which contains an energy-constraint term to restrict the whole consumption. Then, sufficient conditions for leaderless energy-constraint output formation are presented via establishing the relationship of the energy constraint and the matrix variables, where it is found that the designed gain matrices of the output formation protocol can ensure that the actual energy consumption is lower than the total energy supply. Especially, a partition checking algorithm is proposed to check those conditions, which can ensure the scalability and solvability of a swarm system. Moreover, the output formation center function is derived to depict the whole macroscopic movement of a swarm system. A nonsingular transformation approach is presented to unify leaderless energy-constraint output formation and energy-constraint output formation tracking into the same framework, which are usually discussed in different theoretical frameworks. Finally, two simulation examples are illustrated to show that the theoretical results about leaderless energy-constraint output formation and energy-constraint output formation tracking are correct.

A suboptimality approach to distributed [formula omitted] control by dynamic output feedback

This paper deals with suboptimal distributed H2 control by dynamic output feedback for homogeneous linear multi-agent systems. Given a linear multi-agent system, together with an associated H2 cost functional, the objective is to design dynamic output feedback protocols that guarantee the associated cost to be smaller than an a priori given upper bound while synchronizing the controlled network. A design method is provided to compute such protocols. The computation of the two local gains in these protocols involves two Riccati inequalities, each of dimension equal to the dimension of the state space of the agents. The largest and smallest nonzero eigenvalue of the Laplacian matrix of the network graph are also used in the computation of one of the two local gains. A simulation example is provided to illustrate the performance of the proposed protocols.

A Novel Reduced-Order Protocol for Consensus Control of Linear Multiagent Systems

This paper deals with output-feedback-based state consensus of homogeneous linear multiagent systems. A novel reduced-order dynamic output-feedback protocol is proposed, which does not need the absolute output information of neighboring agents. Necessary and sufficient conditions for the solvability of the consensus problem under the proposed protocol are derived, and it is shown that the protocol state is convergent if consensus is reached. A design algorithm is then constructed for computing the protocol gains. Furthermore, the protocol specialized for leader–follower consensus is addressed. In addition, the solvability of a truncated version of the proposed protocol without controller interaction is discussed from a low-gain perspective. A numerical example is finally presented to demonstrate the effectiveness of the proposed protocol and design method.

Robust consensus for linear multi-agent systems with structured uncertainties

ABSTRACT This paper addresses a robust consensus problem for linear multi-agent systems subject to structured uncertainty and external disturbances under the leaderless framework. A distributed dynamic output-feedback protocol is proposed, which utilises not only relative output information of neighbouring agents but also relative state information of neighbouring controllers. Through model transformations, the robust consensus control problem of multi-agents network is reduced to a set of independent stabilisation problems for single linear subsystems. For robust consensus, it is shown that the analysis and full state-feedback synthesis conditions for such subsystems can be formulated as linear matrix inequality (LMI) optimisation problems. On the other hand, the synthesis condition for dynamic output-feedback protocol is formulated as non-convex bilinear matrix inequality (BMI) optimisation problem. An iterative LMI algorithm is then presented to solve the resulting BMI optimisation problem. An example of multiple mass-spring-damper systems has been used to demonstrate theoretical results.

Robust consensus of uncertain linear multi-agent systems via dynamic output feedback

This paper systematically deals with robust consensus of uncertain linear multi-agent systems via dynamic output-feedback protocols. Agents are assumed to have identical nominal linear time-invariant dynamics but are subject to heterogeneous additive stable perturbations. Dynamic output-feedback protocols with or without controller state information exchange between neighboring controllers are studied in a unified framework. Two methods are proposed for protocol design, which need to solve an algebraic Riccati equation and some scalar/matrix inequalities. The first method characterizes some key parameters by scalar inequalities related to the nonzero eigenvalues of the Laplacian, which requires the diagonalizability of the Laplacian, while the second method characterizes the parameters by linear matrix inequalities, which circumvents the requirement of the diagonalizability of the Laplacian. Compared with existing results, the proposed approach can simultaneously cope with heterogeneous uncertainties and directed communication graphs. Numerical results verify the advantages of the proposed design methods.

Formula omitted] consensus for nonlinear stochastic multi-agent systems with time delay

This paper is concerned with the problem of H∞ consensus for nonlinear stochastic multi-agent systems with time-delay. The objective is to design a dynamic output feedback protocol such that the multi-agent system reaches consensus in mean square and has a prescribed H∞ performance level. First, by transforming models, the H∞ consensus problem is converted to a standard H∞ control problem. Then, by using the Lyapunov–Krasovskii functional method and the generalized Itô’s formula, both delay-independent and delay-dependent stochastic bounded real lemmas are developed. Based on these, sufficient conditions on the existence of the desired dynamic output feedback protocol are presented in the form of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed results.

Given-time consensus for stochastic Markov jump networks by dynamic output feedback

This paper focuses on the given-time consensus of stochastic Markov jump networks with disturbances based on dynamic output feedback control. By exploring the relative output information, a distributed dynamic output feedback protocol is designed to guarantee that the disagreement dynamics of networks keeps within the prescribed bound in a fixed time interval. With the new model transformation approach, the obtained results are more general and lead to less conservativeness. An example of industrial material heating unit verifies the engineering application of the proposed algorithm for networks in the presence of both Markov jump topologies and external disturbances.

Distributed adaptive containment control of heterogeneous linear multi‐agent systems: an output regulation approach

Output regulation is a general framework, for it not only can achieve closed-loop stability, but also can realise asymptotic tracking and disturbance rejection. Within this framework, the authors consider the containment problem of heterogeneous linear multi-agent systems with directed graphs. Via dynamic compensator techniques, the containment problem can be converted into cooperative output regulation problem. Moreover, they artfully construct regulation equations, whose solutions are also given. Adaptive protocols are proposed here by assigning a time-varying coupling weight to each node. Unlike most existing protocols that depend on certain global information, protocols presented in this paper are independent of any global information, and hence are fully distributed. By combining the compensator technique with adaptive control, they propose the distributed dynamic adaptive state feedback and adaptive output feedback protocols for driving followers into the moving convex hull spanned by leaders. The obtained results are applied to the containment control of a network of heterogeneous agents, where the followers are described by mass-damper spring systems, and the leaders are specified by harmonic oscillators.

H ∞ Dynamic Output Feedback Consensus Control for Discrete-Time Multi-Agent Systems with Switching Topology

In this paper, we consider distributed H∞ consensus problem for multi-agent systems with discrete-time high-dimensional linear coupling dynamics subjected to external disturbances. The interaction topology among the agents is assumed to be switching and undirected. To achieve consensus, a neighbor-based dynamic output feedback protocol is proposed for each agent. By using Schur orthogonal transformation, the considered multi-agent H∞ consensus control problem is converted into H∞ control problem of a discrete-time switching subsystem. Based on graph theory and common Lyapunov function method, a sufficient condition in terms of linear matrix inequalities is established to solve H∞ consensus problem of the considered multi-agent systems. Moreover, the feedback gain matrix can be obtained from the feasible solution to the linear matrix inequalities. Finally, a simulation example is given to illustrate our established theoretical result.

Distributed RobustH∞Consensus Control of Multiagent Systems with Communication Errors Using Dynamic Output Feedback Protocol

This paper studies robust consensus problem for multiagent systems modeled by an identical linear time-invariant system under a fixed communication topology. Communication errors in the transferred data are considered, and only the relative output information between each agent and its neighbors is available. A distributed dynamic output feedback protocol is proposed, and sufficient conditions for reaching consensus with a prescribedH∞performance are presented. Numerical examples are given to illustrate the theoretical results.

Allowable sampling period for consensus control of multiple general linear dynamical agents in random networks

This article studies the consensus problem for a group of sampled-data general linear dynamical agents over random communication networks. Dynamic output feedback protocols are applied to solve the consensus problem. When the sampling period is sufficiently small, it is shown that as long as the mean topology has globally reachable nodes, the mean square consensus can be achieved by selecting protocol parameters so that n − 1 specified subsystems are simultaneously stabilised. However, when the sampling period is comparatively large, it is revealed that differing from low-order integrator multi-agent systems the consensus problem may be unsolvable. By using the hybrid dynamical system theory, an allowable upper bound of sampling period is further proposed. Two approaches to designing protocols are also provided. Simulations are given to illustrate the validity of the proposed approaches.

H ∞ consensus control of multi-agent systems with switching topology: a dynamic output feedback protocol

This article is devoted to the consensus control for switching networks of multiple agents with linear coupling dynamics and subject to external disturbances, which is transformed into an H ∞ control problem by defining an appropriate controlled output. On this basis, a distributed dynamic output feedback protocol is proposed with an undetermined system matrix, and a condition in terms of linear matrix inequalities (LMIs) is derived to ensure consensus of the multi-agent system with a prescribed H ∞ level. Furthermore, system matrix of the protocol is designed by solving two LMIs. A numerical example is included to illustrate the effectiveness of the proposed consensus protocol.

Quadratic stabilization of linear networked control systems via simultaneous protocol and controller design

We derive conditions for quadratic stabilizability of linear networked control systems by dynamic output feedback and communication protocols. These conditions are used to develop a simultaneous design of controllers and protocols in terms of matrix inequalities. The obtained protocols do not require knowledge of controller and plant states but only of the discrepancies between current and the most recently transmitted values of nodes’ signals, and are implementable on controller area networks. We demonstrate on a batch reactor example that our design guarantees quadratic stability with a significantly smaller network throughput than previously available designs.