Distributed Feedback Control Research Articles

Containment control of heterogeneous multi-agent systems subject to Markovian randomly switching topologies and unbounded delays

This paper addresses the problem of containment control for heterogeneous multi-agent systems subject to Markovian randomly switching topologies and unbounded communication delays. The objective is to design a distributed control strategy that ensures the output of each follower converges to the convex hull formed by the outputs of a group of leaders in mean square sense. A novel distributed observer is proposed by tackling both Markovian randomly switching topologies and unbounded delays. Then, a distributed state feedback controller and a distributed output feedback controller are developed based on the distributed observer, respectively. Finally, simulation results are provided to demonstrate the effectiveness of the proposed controllers.

Consensus of linear multi‐agent systems under switching topology by sampled‐data output feedback control

AbstractThis paper studies both synchronous and asynchronous consensus problems for linear multi‐agent systems under switching topology. A novel distributed continuous‐discrete observer is established by solely using the relative sampled output messages, which needs neither to store messages from neighboring agents nor estimate the information of itself and all neighbors. Based on the estimation provided by the distributed observer, a distributed output feedback control with digital form is synthesized, which allows each agent to update the value of its controller at the synchronous/asynchronous sampling instants. It is of interest to see that, for the class of chain‐integrator multi‐agent systems, the proposed control approach allows the sampling periods to be chosen freely and thus would be more practical in some situations from the perspective of energy saving. The theoretical results are illustrated by formation flying of spacecraft and synchronization of multiple double‐integrators.

Parameter variational based adaptive bipartite formation control of second-order multi-agent systems with antagonistic interactions

This article mainly concentrates on researching the leader-following bipartite formation of second-order nonlinear multi-agent systems (MASs) with antagonistic interactions and time-varying delay. A novel distributed feedback control and impulsive control strategy is proposed for realizing the bipartite formation. By establishing an error system, the bipartite formation issue of the MASs is transformed into the stability issue of the error systems. Sufficient conditions for achieving the bipartite formation of second-order nonlinear MASs are obtained by jointly employing the extended parameters variation formula, the comparison principle and the definition of average impulsive interval. In addition, in order to obtain the optimal control gains and control effects, an adaptive control strategy is taken into account by designing the adaptive updating laws. Ultimately, the effectiveness of the theoretical results is demonstrated by two numerical simulations.

Event‐triggered cooperative robust output regulation of minimum‐phase linear uncertain multi‐agent systems

AbstractIn this article, we investigate the event‐triggered cooperative robust output regulation problem of a class of minimum‐phase linear uncertain multi‐agent systems. In particular, we first propose a dynamic event‐triggered mechanism and an event‐triggered distributed output feedback control law. Then, by the internal model, the event‐triggered cooperative robust output regulation problem is converted into the event‐triggered cooperative robust stabilization problem of an augmented system composed of the distributed internal model and the original multi‐agent system. Next, we show that the event‐triggered cooperative robust stabilization problem can be solved by the proposed event‐triggered distributed output feedback control law together with a dynamic event‐triggered mechanism, and thus the event‐triggered cooperative robust output regulation problem is solved exactly in the sense that the tracking error of each subsystem converges to zero asymptotically while preventing the Zeno behavior from happening. Finally, we provide an example to illustrate the proposed control approach.

Optimal time-invariant distributed formation tracking for second-order multi-agent systems

This paper addresses the optimal time-invariant formation tracking problem with the aim of providing a distributed solution for multi-agent systems with second-order integrator dynamics. In the literature, most of the results related to multi-agent formation tracking do not consider energy issues while investigating distributed feedback control laws. In order to account for this crucial design aspect, we contribute by formalizing and proposing a solution to an optimization problem that encapsulates trajectory tracking, distance-based formation control and input energy minimization, through a specific and key choice of potential functions in the optimization cost. To this end, we show how to compute the inverse dynamics in a centralized fashion by means of the Projector-Operator-based Newton’s method for Trajectory Optimization (PRONTO) and, more importantly, we exploit such an offline solution as a general reference to devise a stabilizing online distributed control law. Finally, numerical examples involving a cubic formation following a chicane-like path in the 3D space are provided to validate the proposed control strategies.

Distributed Leader-Following Consensus of Feedforward Nonlinear Delayed Multiagent Systems via General Switched Compensation Control.

This work examines the distributed leader-following consensus problem of feedforward nonlinear delayed multiagent systems involving directed switching topologies. In contrast to the existing studies, we focus on time delays acting on the outputs of feedforward nonlinear systems, and we permit that the partial topology dissatisfy the directed spanning tree condition. In the cases, we present a novel output feedback-based general switched cascade compensation control method that addresses the above-mentioned problem. First, we put forward a distributed switched cascade compensator by introducing multiple equations, and we design the delay-dependent distributed output feedback controller with the compensator. Subsequently, when the control parameters-dependent linear matrix inequality is met and the switching signal of the topologies obeys a general switching law, we prove that the established controller can render that the follower's state asymptotically tracks the leader's state by employing an appropriate Lyapunov-Krasovskii functional. The given algorithm allows output delays to be arbitrarily large and increases the switching frequency of the topologies. A numerical simulation is presented to demonstrate the practicability of our proposed strategy.

Leader-following consensus control for nonlinear multiagent systems with unknown time-varying measurement sensitivity and infinite communication delays

This paper investigates the consensus problem for nonlinear multiagent systems (MASs) with unknown time-varying measurement sensitivity and infinite communication delays. Unlike existing works, the output measurement sensitivity is described as time-varying, and an infinite communication delay is considered between the agents. Under this condition, a novel output feedback control algorithm is developed. First, based on the hierarchical technique and Lyapunov-based time-domain method, the high-gain compensator and observer are constructed to tolerate the effect of infinite communication delays and accurately estimate the state of the leader. Subsequently, a new distributed k-filter and output feedback controller are proposed, which not only further relax the traditional Lipschitz conditional conservatism but also greatly simplify the design process. It is proved that the closed-loop system is globally stable and all agents can achieve consensus. Finally, the effectiveness of the proposed method is verified through the simulation of the single-link manipulators.

An intelligent hybridised distributed feedback control approach for the JIT open-shop scheduling problem

An intelligent hybridised distributed feedback control approach for the JIT open-shop scheduling problem

Distributed Feedback Control of Multichannel Linear Systems

In this paper it is established that any jointly controllable, jointly observable, multi-channel, discrete or continuous time linear system with a strongly connected neighbor communication graph can be exponentially stabilized with any pre-specified convergence rate using a time-invariant distributed linear control. As an illustration of how this finding can be used to deal with certain distributed tracking problems, a solution is given to a distributed set-point control problem for a continuous-time, multi-channel linear system in which each and every agent with access to the system is able to independently adjust its scalar-valued, controlled output to any desired set-point value. To better understand the constraints on controller design, the distributed control problem is recast as a classical decentralized control problem. Armed with the tools of decentralized control, including the notion of a “fixed spectrum”, it is possible to show quite surprisingly that if the only information each agent is allowed to share with its neighbors is its measured output, then distributed stabilization in some cases is impossible. Using well-known decentralized control concepts, lower bounds are derived on the dimensions of the shared sub-states of local controllers which, if satisfied, guarantee that there will be no fixed closed-loop system eigenvalues to contend with. The decentralized control perspective also enables one to assert definitively that without imposing a partitioning constraint, the closed-loop spectrum of any jointly controllable, jointly observable multi-channel linear system with a strongly connected neighbor graph, can be freely assigned with distributed feedback control. The paper then turns to the important and often overlooked design problem of dealing with the effects of transmission delays across a network. It is explained why in the face of finite delays, exponential stabilization at any prescribed convergence rate can still be achieved with distributed control, at least for discrete-time multi-channel linear systems.

Discrete-time adaptive distributed output observer for time-varying formation tracking of heterogeneous multi-agent systems

This paper presents discrete-time distributed algorithms to achieve time-varying output formation tracking of heterogeneous linear multi-agent systems subject to time-varying faults and directed graphs. To overcome the impacts caused by unknown faults and directed graphs, a discrete-time adaptive distributed output observer-based control architecture is established to guarantee time-varying output formation tracking exponentially. In particular, several distributed leader observers are firstly given to estimate and reconstruct the leader’s state over a directed graph. The new discrete-time adaptive distributed output observer is presented to remove the need of having fully access to the leader’s system matrices and to reduce the dimension and information exchange in the developed distributed observers. In terms of this estimated information from the adaptive distributed output observer, a distributed output feedback controller integrated with an observer-based scheme is developed to compensate for the impact of unknown faults such that time-varying output formation tracking is achieved with a global exponential convergence. Two examples and simulation results are provided to validate the effectiveness of the proposed designs.

Adaptive mean‐square consensus of heterogeneous multiagent systems with stochastic switching topologies

AbstractThe leader–following consensus of linear heterogeneous multiagent systems is investigated in this paper. To comply with the most practical scenario, the communicating topologies among agents are assumed to switch stochastically and driven by a continuous‐time discrete‐state Markov process, whose state space corresponds to all the possible topologies. A novel distributed adaptive compensator is designed for the followers to reconstruct the exogenous signals without knowing the Laplacian matrix who is regarded as a global information, and sufficient conditions are given to ensure the compensator converges to the dynamic of the leader asymptotically in the mean square sense. Then, based on the compensator, we solved the consensus problem both by distributed state and measurement output feedback control schemes under output regulation framework, which allow followers to have nonidentical state dimensions. Finally, the theoretical results are demonstrated by a numerical example.

Krasovskii and shifted passivity based output consensus

Motivated by current sharing in power networks, we consider a class of output consensus (also called agreement) problems for nonlinear systems, where the consensus value is determined by external disturbances, e.g., power demand. This output consensus problem is solved by a simple distributed output feedback controller if a system is either Krasovskii or shifted passive, which is the only essential requirement. The effectiveness of the proposed controller is shown in simulation on an islanded DC power network.

Reimagining Automotive Service-Oriented Communication: A Case Study on Programmable Data Planes

Automotive electrical and electronic (E/E) engineering architectures are being radically overhauled to satisfy the needs of the current automotive trends ranging from electrification to connected vehicles and autonomous driving. Novel networking technologies are being explored for future-proofing in-vehicular networks and making them ready for applications emerging from these trends. Programmable data plane technologies based on reconfigurable match-action tables have been successfully used in data center networking for handling data center-specific applications. In this article, we seek to explore programmable data planes for their utility in in-vehicular networks. To this end, we briefly discuss programmable data plane technologies and present a case study on implementing a distributed feedback control loop using SOME/IP, an automotive service-oriented communication middleware. We outline the parts of the SOME/IP stack that can be moved from the end systems to the network devices for achieving a better workload split using these technologies, thus improving system utilization.

Distributed Adaptive Consensus Tracking Control for Second-Order Nonlinear Heterogeneous Multi-Agent Systems with Input Quantization

In this paper, the problem of distributed adaptive consensus tracking control for second-order nonlinear heterogeneous multi-agent systems (MASs) with input quantization is considered. A distributed output feedback control scheme based on a K-filter is developed to suppress the influences of unknown disturbances and input quantization. In contrast to existing approaches, an additional design parameter is introduced into the controller design to ensure that the subsystem tracking error converges to an arbitrarily small residual set. Through Lyapunov stability analysis, it can be proved that the proposed control scheme can achieve distributed consensus tracking control of second-order nonlinear heterogeneous MASs. In addition, all signals in the closed-loop system are shown to be globally uniformly bounded. Finally, a practical example demonstrates the effectiveness of the proposed control method.

A New Approach for Stabilization Criteria of n-Order Function Differential Equation by Distributed Control Function

In the current paper, we demonstrate a new approach for an stabilization criteria for n-order functional-differential equation with distributed feedback control in the integral form. We present a correlation between the order of the functional-differential equation and degree of freedom of the distributed control function. We present two cases of distributed control function in the integral form. Such a case of stabilization control functions plays a very important role in physics, aeronautics, aerospace, ship navigation and traffic network control management. Structure of functional-differential equations is based on the symmetry properties.

Event-Based Output Feedback Consensus Control for Multiagent Systems With Unknown Non-Identical Control Directions

This article studies the event-triggered output feedback consensus problem for a class of high-order uncertain nonlinear multiagent systems with totally unknown non-identical control directions. Firstly, the reduced-order filters are constructed by utilizing the dynamic gain technique to compensate the system uncertainties and unmeasurable states of the followers. Based on the filter states and output information, the asymptotic output consensus result is guaranteed with the developed distributed adaptive output feedback control protocol, while the inherent issue “complexity explosion” in backstepping design is avoided. Then, to solve the interaction of multiple Nussbaum functions in a single inequality, the Nussbaum functions with different frequencies are adopted, with which the unknown directions of multiagent system are no longer limited in identical. In addition, we propose a dynamic triggering strategy with time-varying threshold parameters to reduce the updates of controller without Zeno phenomenon. Finally, simulation results are provided to illustrate the effectiveness of theoretical algorithm.

Distributed H∞ consensus of multiagent systems with nonuniform time-varying communication delays

This article addresses the distributed H∞ consensus control problem of general linear multiagent systems with time-varying communication delays and external disturbances. The communication network is subject to arbitrarily bounded and nonuniform time-varying communication delays. Based on the leader-following control mode, a novel distributed state feedback control protocol is proposed to achieve state consensus over undirected fixed topology while guaranteeing a prescribed disturbance rejection objective. By means of Lyapunov analysis and some inequality techniques, admissible upper bounds of nonuniform time-varying delays and H∞ consensus criteria are acquired. As opposed to the existing result for the similar problem, our result has its distinct advantages in that it can accommodate arbitrarily bounded nonuniform time-varying communication delays, and has greater delay margin and better consensus performance. Moreover, the consensus problem for the multiagent systems over connected undirected switching topology is discussed. Finally, a numerical example is provided to show the effectiveness and superiority of these obtained results.

Resilient time‐varying output formation tracking of heterogeneous linear multiagent systems under malicious false data injection attacks and denial‐of‐service attacks over digraphs

AbstractA distributed control fashion of cooperative formation tracking may be vulnerable to malicious attacks on sensors and communications that deteriorate the formation tracking performance or even destabilize the entire multiagent system. This article addresses a resilient time‐varying output formation tracking problem of linear heterogeneous multiagent systems, where an attacker can adversely inject false data injection (FDI) attacks on sensors and Denial‐of‐Service (DoS) attacks on communications. Both characteristics will not only enhance the practical relevance of the studied issue, but also bring nontrivial design challenges of distributed control algorithms and convergence analysis. A novel resilient distributed control architecture is developed to guarantee a global exponential time‐varying output formation tracking. In particular, the design includes features: (1) a resilient distributed leader estimator is developed to estimate the leader's state for each follower under DoS attacks over digraphs; (2) a distributed output feedback controller integrated with an observer‐based resilient mechanism is developed to achieve the time‐varying output formation tracking under attacks; (3) unlike existing related works to handle attacks as bounded disturbances or faults, the proposed design is resilient to enable exponential convergence, whereas many related works obtain uniformly ultimately boundedness (UUB) convergence. Simulation results are presented to validate the design's effectiveness.

Synchronization and balancing around simple closed polar curves with bounded trajectories

The problem of synchronization and balancing around simple closed polar curves is addressed for unicycle-type multi-agent systems. Leveraging the concept of barrier Lyapunov function in conjunction with bounded Lyapunov-like curve-phase potential functions, we propose distributed feedback control laws and show that the agents asymptotically stabilize to the desired closed curve in synchronized and balanced curve-phase patterns, and their trajectories remain bounded within a compact set. Our control design methodology is based on the proposition of two models, namely the parametric-phase control model and the curve-phase control model. We also characterize the trajectory-constraining set based on the magnitude of the safe distance of the exterior boundary from the desired curve. We further establish a connection between the perimeters and areas of the trajectory-constraining set with the perimeter and area of the desired curve. We obtain bounds on different quantities of interest in the post-design analysis and provide simulation results to illustrate the theoretical findings.

Exponential stability for magnetic effected piezoelectric beams with time-varying delay and time-dependent weights

<p style='text-indent:20px;'>In this paper, we consider a system of magnetic effected piezoelectric beams with interior time-varying delay and time-dependent weights, in which the beam is clamped at the two side points subject to a single distributed state feedback controller with a time-varying delay. By combining the semigroup theory with Kato's variable norm technique, we obtain the existence and uniqueness of solution. By imposing appropriate assumptions on the time-varying delay term and time-dependent weights, we introduce suitable perturbed Lyapunov functional to obtain exponential stability estimates.</p>