The text begins with an overview of concepts from system theory. New results are provided on feedback stabilization and smooth control of non-holonomic systems. Control design moves from open-loop ...steering control of an individual vehicle to cooperative control of multiple vehicles, a progression culminating in a decentralized control hierarchy requiring only local feedback information. Novel methods are presented: parameterization for collision avoidance and optimization in path planning, near-optimal control for tracking and regulation of non-holonomic chained systems and matrix-theoretical analysis of cooperativity. These methods generate solutions of guaranteed performance for problems of: optimal and collision-free path planning, near-optimal stabilization of non-holonomic systems, cooperative control of dynamic systems. Examples, simulations and comparative studies add zest to the fundamental issues, illustrate the technical approaches and verify the performance of the final control designs.
In this paper, a new framework based on matrix theory is proposed to analyze and design cooperative controls for a group of individual dynamical systems whose outputs are sensed by or communicated to ...others in an intermittent, dynamically changing, and local manner. In the framework, sensing/communication is described mathematically by a time-varying matrix whose dimension is equal to the number of dynamical systems in the group and whose elements assume piecewise-constant and binary values. Dynamical systems are generally heterogeneous and can be transformed into a canonical form of different, arbitrary, but finite relative degrees. Utilizing a set of new results on augmentation of irreducible matrices and on lower triangulation of reducible matrices, the framework allows a designer to study how a general local-and-output-feedback cooperative control can determine group behaviors of the dynamical systems and to see how changes of sensing/communication would impact the group behaviors over time. A necessary and sufficient condition on convergence of a multiplicative sequence of reducible row-stochastic (diagonally positive) matrices is explicitly derived, and through simple choices of a gain matrix in the cooperative control law, the overall closed-loop system is shown to exhibit cooperative behaviors (such as single group behavior, multiple group behaviors, adaptive cooperative behavior for the group, and cooperative formation including individual behaviors). Examples, including formation control of nonholonomic systems in the chained form, are used to illustrate the proposed framework.
This study proposes a secondary voltage and frequency control scheme based on the distributed cooperative control of multi-agent systems. The proposed secondary control is implemented through a ...communication network with one-way communication links. The required communication network is modelled by a directed graph (digraph). The proposed secondary control is fully distributed such that each distributed generator only requires its own information and the information of its neighbours on the communication digraph. Thus, the requirements for a central controller and complex communication network are obviated, and the system reliability is improved. The simulation results verify the effectiveness of the proposed secondary control for a microgrid test system.
This paper presents three design techniques for cooperative control of multiagent systems on directed graphs, namely, Lyapunov design, neural adaptive design, and linear quadratic regulator ...(LQR)-based optimal design. Using a carefully constructed Lyapunov equation for digraphs, it is shown that many results of cooperative control on undirected graphs or balanced digraphs can be extended to strongly connected digraphs. Neural adaptive control technique is adopted to solve the cooperative tracking problems of networked nonlinear systems with unknown dynamics and disturbances. Results for both first-order and high-order nonlinear systems are given. Two examples, i.e., cooperative tracking control of coupled Lagrangian systems and modified FitzHugh-Nagumo models, justify the feasibility of the proposed neural adaptive control technique. For cooperative tracking control of the general linear systems, which include integrator dynamics as special cases, it is shown that the control gain design can be decoupled from the topology of the graphs, by using the LQR-based optimal control technique. Moreover, the synchronization region is unbounded, which is a desired property of the controller. The proposed optimal control method is applied to cooperative tracking control of two-mass-spring systems, which are well-known models for vibration in many mechanical systems.
The increasing number of electric vehicles (EVs) on highways calls for the installment of adequate charging infrastructure. Since charging infrastructure has limited capacity, EVs need to wait at a ...charging station to get charged, and their waiting times may differ significantly from one location to another. This paper aims at developing a strategy to coordinate the queues among the charging stations, with only local information about traffic flows and the status of EV charging stations along a bidirectional highway, so that excessively long waiting times can be avoided. Specifically, a distributed algorithm is presented to schedule EV flows into neighboring charging stations, so that EVs are all appropriately served along the highway and that all the charging resources are uniformly utilized. In addition, a distributed decision making policy is developed to influence the aggregate number of EVs entering any given service station, so that each EV makes an appropriate decision (i.e., whether or not it should enter the next charging station) by contributing positively to meeting the desired queue length at service stations and by considering its own battery constraint. Performance improvement of the proposed strategy is illustrated via one of the highways in the United States, namely the Florida Turnpike.
Conventionally, power system has a hierarchical control structure including primary, secondary, and tertiary controls. The drawbacks of this hierarchical scheme are manifest: 1) it lacks flexibility ...and scalability, which is against the trend toward an open-access power system; 2) load forecast as the basis of tertiary control could be inaccurate and infeasible, especially in microgrid for example; 3) as the penetration of renewable energy increases, the relatively long time-scales of secondary and tertiary controls cannot accommodate to more severe power fluctuation within the system. To avoid these drawbacks, a distributed real-time optimal power flow control strategy is introduced in this paper. With the aid of up-to-date smart grid technologies such as two-way communication and distributed sensor, the proposed approach can avoid the need of load forecast and achieve the same objective as hierarchical control with a feedback mechanism in real time, that is to recover the nominal system frequency and maintain the active power of the generators close to the optimal operational condition in the presence of any disturbance. Convergence of the proposed approach is analytically proved. Simulation results in a 34-bus islanded microgrid and the IEEE 118-bus bulk power grid validate the effectiveness and efficiency of the proposed approach.
In this paper, the finite time consensus problem of distributed nonlinear systems is studied under the general setting of directed and switching topologies. Specifically, a contraction mapping ...argument is used to investigate performance of networked control systems, two classes of varying topologies are considered, and distributive control designs are presented to guarantee finite time consensus. The proposed control scheme employs a distributed observer to estimate the first left eigenvector of graph Laplacian and, by exploiting this knowledge of network connectivity, it can handle switching topologies. The proposed methodology ensures finite time convergence to consensus under varying topologies of either having a globally reachable node or being jointly strongly connected, and the topological requirements are less restrictive than those in the existing results. Numerical examples are provided to illustrate the effectiveness of the proposed scheme.
Distributed generators (DGs) have been developing rapidly in power systems. Motivated by their intrinsic distributed nature, distributed cooperative control based upon local communication recently ...emerge as a preferred strategy. For instance, a cooperative power control strategy can regulate the active power from a cluster of DGs at a certain ratio of its maximal available power according to a dispatch command. However, such a networked control system is susceptible to both communication failure and cyber-attack, e.g., denial-of-service attack and deceptive attack. To address this potential problem, an attack-resilient cooperative control strategy is proposed in this paper. With a properly designed observation network, each DG can monitor the behaviors of all its in-neighbors, and gradually isolate the misbehaving DGs (when present) from the network as long as they do not collude with each other. Consequently, even certain DGs misbehave, the rest of them can together accomplish the control objective provided that the remaining communication network is still connected. Simulations of the IEEE standard 34-bus test feeder demonstrate effectiveness of the proposed strategy.
The focus of this paper is to develop a distributed control algorithm that will regulate the power output of multiple photovoltaic generators (PVs) in a distribution network. To this end, the ...cooperative control methodology from network control theory is used to make a group of PV generators converge and operate at certain (or the same) ratio of available power, which is determined by the status of the distribution network and the PV generators. The proposed control only requires asynchronous information intermittently from neighboring PV generators, making a communication network among the PV units both simple and necessary. The minimum requirement on communication topologies is also prescribed for the proposed control. It is shown that the proposed analysis and design methodology has the advantages that the corresponding communication networks are local, their topology can be time varying, and their bandwidth may be limited. These features enable PV generators to have both self-organizing and adaptive coordination properties even under adverse conditions. The proposed method is simulated using the IEEE standard 34-bus distribution network.
This letter considers the problem of estimating all the eigenvalues and eigenvectors of an irreducible matrix, corresponding to a strongly connected digraph, in the absence of knowledge on the global ...network topology. To this end, we propose a unified distributed strategy performed by each node in the network and relies only on the local information. The key idea is to transform the nonlinear problem of computing both the eigenvalues and eigenvectors of an irreducible matrix into a linear one. Specifically, we first transform distributively the irreducible matrix into a nonsingular irreducible matrix. Each node in the network then estimates in a distributed fashion the inverse of the nonsingular matrix by solving a set of linear equations based on a consensus-type algorithm. The eigenvalues and the corresponding eigenvectors are finally computed by exploiting the relations between the eigenvalues and eigenvectors of both the inverse and the original irreducible matrices. A numerical example is provided to demonstrate the effectiveness of the proposed distributed strategy.
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