Relative State Information Research Articles

Distributed robust adaptive control of high order nonlinear multi agent systems

In this paper, a robust adaptive neural network based controller is presented for multi agent high order nonlinear systems with unknown nonlinear functions, unknown control gains and unknown actuator failures. At first, Neural Network (NN) is used to approximate the nonlinear uncertainty terms derived from the controller design procedure for the followers. Then, a novel distributed robust adaptive controller is developed by combining the backstepping method and the Dynamic Surface Control (DSC) approach. The proposed controllers are distributed in the sense that the designed controller for each follower agent only requires relative state information between itself and its neighbors. By using the Young's inequality, only few parameters need to be tuned regardless of NN nodes number. Accordingly, the problems of dimensionality curse and explosion of complexity are counteracted, simultaneously. New adaptive laws are designed by choosing the appropriate Lyapunov-Krasovskii functionals. The proposed approach proves the boundedness of all the closed-loop signals in addition to the convergence of the distributed tracking errors to a small neighborhood of the origin. Simulation results indicate that the proposed controller is effective and robust.

Fully Distributed Fault-Tolerant Consensus Protocols for Lipschitz Nonlinear Multi-Agent Systems

In this paper, we investigate the fault-tolerant consensus problems for multi-agent systems with actuator faults. Based on the relative state information, fully distributed adaptive protocols are designed for these agents described by Lipschitz nonlinear dynamics under leaderless and leader-follower communication structures. As the special case, for linear multi-agent systems, fault-tolerant consensus problems are also solved with the proposed protocols. First, for the leaderless multi-agent systems, all agents reach an agreement on a common value with undirected connected communication graphs. Second, for the leader-follower multi-agent systems, in which the state of the leader is only available to a subset of the followers, the state of each follower converges to the state of the leader, asymptotically. A distinctive feature of this paper is that the adaptive protocols here are independent of the eigenvalues of the Laplacian matrix associated with the whole communication graph, which means the protocols can be implemented by each agent in a fully distributed fashion. Simulation examples are provided to illustrate the theoretical results.

Consensus of Discrete-Time Multiagent Systems With Input Delays by Truncated Pseudo-Predictor Feedback

The consensus problem for multiagent systems (MASs) described by discrete-time linear systems with multiple input delays is investigated. Under two reasonable assumptions, a truncated pseudo-predictor feedback (TPPF) approach is established to solve the consensus problem. The proposed TPPF protocols allow arbitrarily large yet bounded delays and are easy to implement in practice since they are finite dimensional and only use the relative current state information of neighboring agents. Moreover, the proposed protocols can also achieve semi-global consensus of MASs if the actuators are subject to saturations. A numerical example is given to illustrate the effectiveness of the proposed approaches.

Leader-Following Consensus Control of General Linear Multi-Agent Systems With Diverse Time-Varying Input Delays

This paper addresses the problem of leader-following consensus control of general linear multi-agent systems (MASs) with diverse time-varying input delays under the integral quadratic constraint (IQC) framework. A novel exact-memory distributed output-feedback delay controller structure is proposed, which utilizes not only relative estimation state information from neighboring agents but also local real-time information of time delays and the associated dynamic IQC-induced states from the agent itself for feedback control. As a result, the distributed consensus problem can be decomposed into H∞ stabilization subproblems for a set of independent linear fractional transformation (LFT) systems, whose dimensions are equal to that of a single agent plant plus the associated local IQC dynamics. New delay control synthesis conditions for each subproblem are fully characterized as linear matrix inequalities (LMIs). A numerical example is used to demonstrate the proposed approach.

Distributed Adaptive Consensus Disturbance Rejection for Multi-Agent Systems on Directed Graphs

This paper considers the distributed consensus disturbance rejection problem for general linear multiagent systems with deterministic disturbances under directed communication graphs. Based on the relative state information of the neighboring agents, the consensus protocols, which consist of two observers, including a state observer and a separate disturbance observer, are designed to guarantee that the consensus error goes to zero with complete disturbance rejection. Furthermore, the state observer is designed in a fully distributed fashion with adaptive coupling gain, which has the advantage that the consensus controller design is independent of the Laplacian matrix associated with the communication network. The distributed observer-based consensus disturbance rejection protocols are further extended to containment control. Finally, an example is provided to demonstrate the effectiveness of the proposed strategies.

Observer‐based event‐triggered control for consensus of general linear MASs

This study investigates the consensus problem for general linear multi-agent systems (MAS) via observer-based dynamic output feedback event-triggered control. Assume that the relative state information is unknown for each agent and only the relative output feedback between neighbouring agents can be measured. To solve the consensus problem, the authors develop a novel observer-based event-triggered approach to design a dynamic relative output feedback control. Two event-triggering time sequences are constructed. One is the relative output to the observer and another is the observer error to the controller. One can prove that under the proposed control strategies, the consensus problem can be solved via linear matrix inequalities as well as Riccati inequality if the communication graph of the MAS is connected. Furthermore, the Zeno-behaviour of triggering time sequences can be avoided. Finally, the effectiveness of the proposed strategies is illustrated by a numerical example.

On the Stability Margin of Networked Dynamical Systems

This paper is concerned with the stability (gain and phase) margin of networked dynamical systems, e.g., vehicles in formation, each of which has access to the state of its neighbors and subsequently uses a state feedback gain $F$ for a certain global objective such as attitude synchronization. Here, the network topology is directed and described by a generalized Laplacian matrix $L$ . An individual dynamical system can adopt its own state feedback control law such as a linear-quadratic-regulator controller for an ample stability margin, but it may lose the stability margin to a great extent when the same control strategy utilizing relative state information is used after being interconnected with other dynamical systems. This paper reveals and elaborates upon the following four facts: First, the stability margin after interconnection is quantified via the minimum singular value of a frequency-dependent matrix made up of $F$ and $L$ ; Second, the stability margin of a networked dynamical system having a pole at the origin is at most the inverse of the zero-eigenvalue sensitivity of $L$ ; Third, there exists an upper bound of the stability margin that has a computational merit, and asymptotically converges to the exact margin with respect to network size, probability of link existence, and control gain in a random network setting; and finally, $L$ can be designed to maximize the stability margin. Numerical examples are provided to demonstrate the elaboration.

Distributed adaptive consensus for linear multi-agent systems with quantised information

ABSTRACTThis paper considers the distributed adaptive consensus problem for linear multi-agent systems with quantised relative information. By using a lemma in algebraic graph theory and introducing a projection operator in adaptive law, a novel distributed adaptive state feedback controller is designed with quantised relative state information. It is shown that the practical consensus for multi-agent systems with a uniform quantiser is achieved via the Lyapunov theory and the non-smooth analysis. In contrast with the existing quantised controllers, which rely on the minimum nonzero eigenvalue of the Laplacian matrix, the developed controller is only dependent on the number of nodes. Furthermore, a dynamic output feedback controller based on quantised relative output information is proposed. Finally, a simulation example is given to illustrate the effectiveness of the proposed control scheme.

Consensus for multi-agent systems with time-varying input delays

ABSTRACTThis paper addresses the consensus control problem for linear multi-agent systems subject to uniform time-varying input delays and external disturbance. A novel state-feedback consensus protocol is proposed under the integral quadratic constraint (IQC) framework, which utilises not only the relative state information from neighbouring agents but also the real-time information of delays by means of the dynamic IQC system states for feedback control. Based on this new consensus protocol, the associated IQC-based control synthesis conditions are established and fully characterised as linear matrix inequalities (LMIs), such that the consensus control solution with optimal disturbance attenuation performance can be synthesised efficiently via convex optimisation. A numerical example is used to demonstrate the proposed approach.

Improvement of coordination performance of fractional-order systems based on weighted state and relative state information

The weighted state and relative state information feedback is introduced into the existing coordination control protocol aiming to improve the robustness of fractional-order multi-agent systems against fractional-order [Formula: see text]. By applying frequency-domain method and Nyquist stability theorem, a sufficient condition is given to ensure the fractional-order coordination. It is shown that the proposed coordination control protocol can improve the robustness of fractional-order multi-agent systems against fractional-order under directed communication topology. Two numerical examples are given and the corresponding simulation results show that compared with the existed coordination control protocols, the proposed weighted state and relative state information feedback control protocol is feasible and effective for improving the robustness performance.

An open benchmark for distributed formation flight control of Fixed-Wing Unmanned Aircraft Systems

The capability of autonomous formation flight has the potential to significantly enhance the utility and efficiency of small low-cost Unmanned Aerial Systems (UAS). Formations of small, inexpensive fixed-wing UAS allow for the sharing of remote sensing functionality, mission-level redundancy and range enhancements due to aerodynamic interactions widely exploited by migratory birds. This article presents a benchmark problem for scalable distributed flight control of formations of UAS with only local relative state information, one of the open problems in this field as of today. The benchmark is openly available and comprises a nonlinear six degrees of freedom dynamics model of an electric glider UAS. In this article we furthermore introduce a nominal guidance frame that does not require state information of other UAS and point out a fundamental issue related to wake vortex tracking during formation maneuvers. A set of LQ baseline controllers that are part of the benchmark is presented along with simulation results.

Robust Semi-global Coordinated Tracking of Saturated Networked Systems

This paper focuses on the robust semi-global coordinated tracking of general linear systems subject to input saturation together with input additive disturbance and dead zone. A fully distributed algorithm which relating only with the number of the following agents and the relative state information of its neighbors is first constructed, and then sufficient conditions guaranteeing the robust semi-global consensus tracking and the robust semi-global swarm tracking are provided, respectively, on the basis of the low-and-high feedback technique. Finally, numerical simulations are performed to illustrate the effectiveness of the theoretical results.

Formation Control for Multi-Agent Systems with Connectivity Preservation and Event-Triggered Controllers

In this paper, event-triggered controllers and corresponding algorithms are proposed to establish the formation with connectivity preservation for multi-agent systems. Each agent needs to update its control input and to broadcast this control input together with the relative state information to its neighbors at its own triggering times, and to receive information at its neighbors’ triggering times. Two types of system dynamics, single integrators and double integrators, are considered. As a result, all agents converge to the formation exponentially with connectivity preservation, and Zeno behavior can be excluded. Numerical simulations show the effectiveness of the theoretical results.

Distributed tracking control of mobile sensor networks with intermittent communications

This paper investigates the distributed tracking control problem of mobile sensor networks (MSNs) with intermittent communications. The MSNs are assumed to operate in a leader-following structure. When the communication network is accessible, the input of the leader is nonzero and unknown to the followers. When the communication is unavailable, the leader input is assumed to be zero. Based on intermittently available relative state information of neighboring sensors, a distributed tracking control method is proposed for the MSNs. A sufficient condition under which all follower sensors can track the leader under a fixed topology is derived using graph theory, non-smooth analysis and the switching system approach. Furthermore, an interesting design algorithm is proposed by which the tracking controller and the minimum admissible communication rate can be calculated simultaneously. The effectiveness of the results is demonstrated by numerical simulations.

Robust consensus of Lur'e networks with uncertain communications

This study addresses the robust consensus problem of a network of Lur'e systems coordinating over uncertain communication channels. The authors model each communication channel of the network as an ideal transmission system with the unitary transfer function perturbed by a norm-bounded uncertainty, which is particularly susceptible to describe quantisation errors and communication noises. Based on the uncertain relative state information among neighbouring agents, a distributed consensus protocol is proposed and designed in terms of linear matrix inequalities to ensure robust consensus for both undirected connected graphs and leader-follower graphs containing a directed spanning tree.

Asynchronous Periodic Edge-Event Triggered Control for Double-Integrator Networks With Communication Time Delays.

This paper focuses on the average consensus of double-integrator networked systems based on the asynchronous periodic edge-event triggered control. The asynchronous property lies in the edge event-detecting procedure. For different edges, their event detections are performed at different times and the corresponding events occur independently of each other. When an event is activated, the two adjacent agents connected by the corresponding link sample their relative state information and update their controllers. The application of incidence matrix facilitates the transformation of control objects from the agent-based to the edge-based. Practically, due to the constraints of network bandwidth and communication distance, agents usually cannot receive the instantaneous information of some others, which has an impact on the system performance. Hence, it is necessary to investigate the presence of communication time delays. For double-integrator multiagent systems with and without communication time delays, the average state consensus can be asynchronously achieved by designing appropriate parameters under the proposed event-detecting rules. The presented results specify the relationship among the maximum allowable time delays, interaction topologies, and event-detecting periods. Furthermore, the proposed protocols have the advantages of reduced communication costs and controller-updating costs. Simulation examples are given to illustrate the proposed theoretical results.

Decentralized Robust Synchronization of Unknown High Order Nonlinear Multi-Agent Systems With Prescribed Transient and Steady State Performance

In this paper, we consider the synchronization control problem for uncertain high-order nonlinear multi-agent systems in a leader-follower scheme, under a directed communication protocol. A robust decentralized control law of minimal complexity is proposed that achieves prescribed, arbitrarily fast and accurate synchronization of the following agents with the leader. The control protocol is decentralized in the sense that the control signal of each agent is calculated based solely on local relative state information from its neighborhood set. Additionally, no information regarding the agents' dynamic model is employed in the design procedure. Moreover, provided that the communication graph is connected and contrary to the related works on multi-agent systems, the controller-imposed transient and steady state performance bounds are fully decoupled from: 1) the underlying graph topology, 2) the control gains selection, and 3) the agents' model uncertainties, and are solely prescribed by certain designer-specified performance functions. Extensive simulation results clarify and verify the approach.

Fully distributed containment control of high-order multi-agent systems with nonlinear dynamics

In this paper, distributed containment control problems for high-order multi-agent systems with nonlinear dynamics are investigated under directed communication topology. The states of the leaders are only available to a subset of the followers and the inputs of the leaders are possibly nonzero and time varying. Distributed adaptive nonlinear protocol is proposed based only on the relative state information, under which the states of the followers converge to the dynamic convex hull spanned by those of the leaders. As the special case with only one dynamic leader, leader–follower consensus problem is also solved with the proposed protocol. The adaptive protocol here is independent of the eigenvalues of the Laplacian matrix, which means the protocol can be implemented by each agent in a fully distributed fashion. A simulation example is provided to illustrate the theoretical results.

Formation tracking control for time-delayed multi-agent systems with second-order dynamics

In this paper, formation tracking control problems for second-order multi-agent systems (MASs) with time-varying delays are studied, specifically those where the position and velocity of followers are designed to form a time-varying formation while tracking those of the leader. A neighboring relative state information based formation tracking protocol with an unknown gain matrix and time-varying delays is presented. The formation tracking problems are then transformed into asymptotically stable problems. Based on the Lyapunov-Krasovskii functional approach, conditions sufficient for second-order MASs with time-varying delays to realize formation tracking are examined. An approach to obtain the unknown gain matrix is given and, since neighboring relative velocity information is difficult to measure in practical applications, a formation tracking protocol with time-varying delays using only neighboring relative position information is introduced. The proposed results can be used on target enclosing problems for MASs with second-order dynamics and time-varying delays. An application for target enclosing by multiple unmanned aerial vehicles (UAVs) is given to demonstrate the feasibility of theoretical results.

Consensus disturbance rejection for Lipschitz nonlinear multi-agent systems with input delay: A DOBC approach

In this paper, a new predictor-based consensus disturbance rejection method is proposed for high-order multi-agent systems with Lipschitz nonlinearity and input delay. First, a distributed disturbance observer for consensus control is developed for each agent to estimate the disturbance under the delay constraint. Based on the conventional predictor feedback approach, a non-ideal predictor based control scheme is constructed for each agent by utilizing the estimate of the disturbance and the prediction of the relative state information. Then, rigorous analysis is carried out to ensure that the extra terms associated with disturbances and nonlinear functions are properly considered. Sufficient conditions for the consensus of the multi-agent systems with disturbance rejection are derived based on the analysis in the framework of Lyapunov–Krasovskii functionals. A simulation example is included to demonstrate the performance of the proposed control scheme.