Distributed Feedback Control Research Articles

Adaptive Cooperative Output Regulation of Discrete-Time Linear Multi-Agent Systems by a Distributed Feedback Control Law

An adaptive distributed observer was recently proposed to solve the cooperative output regulation problem for discrete-time linear multi-agent systems. The validity of this approach relies on the assumptions that all the eigenvalues of the leader's system matrix are inside or on the unit circle and the solution to the regulator equations is unique. Besides, the range of the observer gains of the adaptive distributed observer is determined by the spectrum of a graph matrix of the communication network, which is not desirable in applications. To overcome these drawbacks, in this paper, we will first propose a new type of the discrete-time adaptive distributed observer for the leader system, whose observer gains are fixed and hence are independent of the communication network, and moreover, this observer allows the eigenvalues of the leader's system matrix to be inside a circle with radius strictly greater than one. Then, we will strengthen the existing adaptive control approach so that it can handle the case where the solution to the regulator equations is not unique. These improvements have not only made our approach more practical, but also enlarged the systems that can be handled by the existing approach.

Distributed feedback control of a fractional diffusion process

In this paper, a control law that enforces an output tracking of a fractional diffusion process is developed. The dynamical behavior of the process is described by a space-fractional parabolic equation. The objective is to force a spatial weighted average output to track its specified output by manipulating a control variable assumed to be distributed in the spatial domain. The state feedback is designed in the framework of geometric control using the notion of the characteristic index. Then, under the assumption that the fractional diffusion process is a minimum phase system, it is shown that the developed control law guarantees exponential stability in $$L_2$$-norm for the resulting closed loop system. Numerical simulations are performed to show the tracking and disturbance rejection capabilities of the developed controller.

Cooperative output regulation problem of multi-agent systems with stochastic packet dropout and time-varying communication delay

In this paper, we deal with the cooperative output regulation problem of linear multi-agent systems on a directed network topology subject to both stochastic packet dropout and time-varying communication delay. On the basis of introducing a queuing mechanism, a distributed state feedback control algorithm is proposed. Then the continuous-time multi-agent systems with piece-wise constant control are converted into discrete-time systems. Under some standard assumptions, the necessary and sufficient conditions under which the tracking errors of followers approach to the origin asymptotically are proposed for different exosystems. Finally, the proposed results are verified via two examples.

Cooperative Output Regulation of Singular Multi-Agent Systems Under Switching Network by Standard Reduction

The cooperative output regulation problem for singular multi-agent systems subject to static networks was studied recently under the assumption that each follower system satisfies the standard assumption. In this paper, we further study the same problem for singular multi-agent systems subject to jointly connected switching networks. First, by introducing a static output feedback control, we remove the unnecessary standard assumption on the singular system in the existing result. Then, we derive a reduced-order normal multi-agent system and obtain a distributed output measurement feedback control law based on the existing result on the normal multi-agent system. Finally, we show that the composition of the static output feedback control law and the distributed output measurement feedback control law solves the cooperative output regulation problem for the original singular multi-agent system. Our result enlarges the class of systems whose cooperative output regulation problem is solvable.

Cooperative global robust group output regulation for multi-agent systems with heterogeneous uncertain second-order nonlinear dynamics

In this paper, we study the global robust group output regulation problem for multi-agent systems with heterogeneous uncertain second-order nonlinear dynamics. The intelligence factor is introduced to construct a designed graph matrix which overcomes the communication influence between multiple coupled subnetworks with different exosystems. In terms of internal model principle, the global robust group output regulation problem is converted into the global robust dynamic stability problem of the so-called augmented multi-agent system. Further, the augmented multi-agent system is globally stabilized via a distributed state feedback control law. A special case of the main result of this paper leads to the solution of the global robust multi-tracking control problem for nonlinear multi-agent networks. A simulation is performed to illustrate the effectiveness of the theoretical results.

Optimal Power Flow Pursuit

This paper considers distribution networks featuring inverter-interfaced distributed energy resources, and develops distributed feedback controllers that continuously drive the inverter output powers to solutions of ac optimal power flow (OPF) problems. Particularly, the controllers update the power setpoints based on voltage measurements as well as given (time-varying) OPF targets, and entail elementary operations implementable onto low-cost microcontrollers that accompany power-electronics interfaces of gateways and inverters. The design of the control framework is based on suitable linear approximations of the ac power-flow equations as well as Lagrangian regularization methods. Convergence and OPF-target tracking capabilities of the controllers are analytically established. Overall, the proposed method allows to bypass traditional hierarchical setups where feedback control and optimization operate at distinct time scales, and to enable real-time optimization of distribution systems.

Prescribed Performance for Bipartite Tracking Control of Nonlinear Multiagent Systems With Hysteresis Input Uncertainties.

This paper studies bipartite tracking problem of nonlinear multiagent systems over signed directed graphs. Each following agent is modeled by a higher-order nonlinear system in strict-feedback form with unknown dynamics and hysteresis input uncertainty. Both distributed state feedback and output feedback control laws are proposed to achieve bipartite tracking confined by the prescribed performance bounds. The proposed approximation-free distributed controllers only utilize error variables incorporating with performance bound functions, which lead to a low-complexity control algorithm. Moreover, the proposed control laws guarantee that all signals of the closed-loop system are uniformly ultimately bounded.

Distributed finite‐time output feedback synchronisation control for six DOF spacecraft formation subject to input saturation

This study is devoted to the distributed finite-time output feedback synchronisation control problem for six degree-of-freedom (DOF) spacecraft formation flying (SFF) with coupled attitude and position motions subject to input saturation. On the basis of a new velocity filter, a bounded distributed output feedback control protocol is proposed, whose upper bound is independent on the number and edge weights of the neighbours in the formation. Moreover, a straightforward relationship between the magnitude of the limited control and the control parameters is established, which can be regarded as the guideline to tune the control parameters such that the input saturation can be satisfied. By applying the homogenous theory and Lyapunov approach, it is proved that the closed-loop system is globally finite-time stable and six DOF synchronisation control for SFF can be achieved. With mild modification of the proposed control scheme, the aforementioned results can be successfully extended to the containment control problem for SFF. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed control protocols.

Cloud-assisted Distributed Nonlinear Optimal Control for Dynamics over Graph

Abstract Dynamics over graph are large-scale systems in which the dynamic coupling among subsystems is modeled by a graph. Examples arise in spatially distributed systems (as discretized PDEs), multi-agent control systems or social dynamics. In this paper, we propose a cloud-assisted distributed algorithm to solve optimal control problems for nonlinear dynamics over graph. Inspired by the centralized Hauser’s projection operator approach for optimal control, our main contribution is the design of a descent method in which at each step agents of a network compute a local descent direction, and then obtain a new system trajectory through a distributed feedback controller. Such a controller, iteratively designed by a cloud, allows agents of the network to use only information from neighboring agents, thus resulting into a distributed projection operator over graph. The main advantages of our globally convergent algorithm are dynamic feasibility at each iteration and numerical robustness (thanks to the closed-loop updates) even for unstable dynamics. In order to show the effectiveness of our strategy, we present numerical computations on a discretized model of the Burgers’ nonlinear partial differential equation.

Low‐Complexity Decentralized Active Damping of One‐Dimensional Structures

In the paper, we propose distributed feedback control laws for active damping of one‐dimensional mechanical structures equipped with dense arrays of force actuators and position and velocity sensors. We consider proportional position and velocity feedback from the neighboring nodes with symmetric gains. Achievable control performance with respect to stability margin and damping ratio is discussed. Compared to full‐featured complex controllers obtained by modern design methods like LQG, H‐infinity, or mu‐synthesis, these simplistic controllers are more suitable for experimental fine tuning and are less case‐dependent, and they shall be easier to implement on the target future smart‐material platforms.

Distributed Assistive Control of Power Buffers in DC Microgrids

Low generational inertia and lack of damping elements cause stability concerns in dc microgrids. Power buffers have been introduced to damp volatile load demands and improve microgrid's stability. Power buffer is a power electronics converter with large storage components (e.g., capacitors), which can decouple dynamics of a power distribution network and electronic loads by adjusting its input impedance and stored energy. Typically, power buffers are controlled individually to serve local loads. Alternatively, collective operation of power buffers is considered here to extend their damping effect to neighboring loads. Additionally, the group operation allows buffer designs with smaller storage components. A supervisory control to manage energy-impedance profiles of power buffers across a grid would require a complex communication network. Alternatively, distributed control lays a reliable ground to link power buffers with a minimal communication. This work offers a fully distributed feedback control algorithm to collectively manage the power buffers, using a sparse communication network. The controller enables the buffers to collectively respond to any load transient. Hardware-in-the-Loop simulation of a dc microgrid is used to show the controller's efficacy; it successfully groups power buffers in the neighborhood of the affected load and manages their energy reservoirs to shape the power supplied by the grid.

Cooperative robust output regulation problem for discrete‐time linear time‐delay multi‐agent systems

SummaryIn this paper, we study the cooperative robust output regulation problem for discrete‐time linear multi‐agent systems with both communication and input delays by a distributed internal model approach. We first introduce the distributed internal model for discrete‐time multi‐agent systems with both communication and input delays. Then, we define the so‐called auxiliary system and auxiliary augmented system. Finally, we solve our problem by showing, under some standard assumptions, that if a distributed state feedback control or a distributed output feedback control solves the robust output regulation problem of the auxiliary system, then the same control law solves the cooperative robust output regulation problem of the original multi‐agent systems.

Cooperative adaptive output regulation for linear multi‐agent systems with actuator faults

This paper considers the cooperative fault-tolerant output regulation problem for linear multi-agent systems with actuator faults. It is assumed that the actuator faults are loss of effectiveness faults. A new lemma is introduced to ensure the transmission zero condition for the systems with actuator faults. Based on this lemma, the unique solution of the output regulation equations is achieved. Moreover, a distributed adaptive observer and a distributed state feedback controller with time-varying gains are designed to compensate the actuator faults. In addition, it is shown that the cooperative fault-tolerant output regulation problem can be solved under the proposed controller. Finally, a simulation example is presented to show the validity of the proposed controller.

The Consensus for Discrete-Time Linear Multi-Agent Systems Under Directed Switching Networks

The existing results on the leaderless and leader-following consensus problems for discrete-time linear multi-agent systems subject to jointly connected switching networks are limited to undirected networks. This note will first study the stability property for a class of discrete-time linear switched systems. This stability result will then be applied to the two consensus problems for discrete-time linear multi-agent systems subject to directed jointly connected switching networks. It is shown that, in some interesting cases, the two problems are solvable by the distributed state feedback control law even if the switching networks are directed and every time disconnected.

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.

Distributed Feedforward Approach to Cooperative Output Regulation Subject to Communication Delays and Switching Networks

In this technical note, we consider the cooperative output regulation problem for linear multi-agent systems subject to communication delays and switching networks by a distributed feedforward approach. Both distributed dynamic state feedback controller and distributed dynamic measurement output feedback controller are proposed to solve the problem. In comparison with the existing result for the similar problem, our result can handle the cooperative output regulation problem subject to nonuniform time-varying communication delays and jointly connected switching communication networks. As an application of cooperative output regulation, it is shown that our main result can solve the leader-following consensus problem and includes some existing results as its special cases.

Control methods for localization of nonlinear waves.

A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions.This article is part of the themed issue 'Horizons of cybernetical physics'.

Cooperative Adaptive Output Regulation for Second-Order Nonlinear Multiagent Systems With Jointly Connected Switching Networks.

This paper studies the cooperative global robust output regulation problem for a class of heterogeneous second-order nonlinear uncertain multiagent systems with jointly connected switching networks. The main contributions consist of the following three aspects. First, we generalize the result of the adaptive distributed observer from undirected jointly connected switching networks to directed jointly connected switching networks. Second, by performing a new coordinate and input transformation, we convert our problem into the cooperative global robust stabilization problem of a more complex augmented system via the distributed internal model principle. Third, we solve the stabilization problem by a distributed state feedback control law. Our result is illustrated by the leader-following consensus problem for a group of Van der Pol oscillators.

Stabilization by delay distributed feedback control

In this paper, a new approach to stability of integro-differential equations x′′t+β 1 ∫ t-τ1tte-α1t-sxsds+β 2 ∫ t-τ2tte-α2t-sxsds=0 and x′′t+β 1 ∫ 0t-τ1te-α1t-sxsds +β 2 ∫ 0t-τ2te-α2t-sxsds=0 is proposed. Under corresponding conditions on the coefficients α 1 , α 2 , β 1 and β 2 the first equation is exponentially stable if the delays τ 1 (t ) and τ 2 (t ) are large enough and the second equation is exponentially stable if these delays are small enough. On the basis of these results, assertions on stabilization by distributed input control are proven. It should be stressed that stabilization of this sort, according to common belief, requires a damping term in the second order differential equation. Results obtained in this paper demonstrate that this is not the case.

Control of localized non-linear strain waves in complex crystalline lattices

The distributed feedback control is developed to support propagation of localized non-linear waves for the double sine-Gordon equation and the dispersive sine-Gordon equation previously obtained for the description of dynamic processes in complex crystalline lattices. The control allows the propagation of both bell-shaped and kink-shaped waves with permanent shape and velocity, with a functional form which does not correspond to the known analytical solutions of the equations. The results might be used for choosing external loading providing desired strain localization or variations in the internal structure of the lattice.