The paper concentrates on the fundamental coordination problem that requires a network of agents to achieve a specific but arbitrary formation shape. A new technique based on complex Laplacian is ...introduced to address the problems of which formation shapes specified by inter-agent relative positions can be formed and how they can be achieved with distributed control ensuring global stability. Concerning the first question, we show that all similar formations subject to only shape constraints are those that lie in the null space of a complex Laplacian satisfying certain rank condition and that a formation shape can be realized almost surely if and only if the graph modeling the inter-agent specification of the formation shape is 2-rooted. Concerning the second question, a distributed and linear control law is developed based on the complex Laplacian specifying the target formation shape, and provable existence conditions of stabilizing gains to assign the eigenvalues of the closed-loop system at desired locations are given. Moreover, we show how the formation shape control law is extended to achieve a rigid formation if a subset of knowledgable agents knowing the desired formation size scales the formation while the rest agents do not need to re-design and change their control laws.
This paper concentrates on the integration of relative localization and the formation control over leader-follower networks. First, we develop a consensus-like relative localization scheme for each ...agent to estimate the real-time relative positions of its neighbors by merely using velocity as well as distance-related measurements and local communications under the assumption that the local frames of all agents share a common orientation. It is shown that the relative position estimate exponentially converges to its true value under a persistent excitation condition on relative velocity between the two agents. Second, an integrated relative localization and a leader-follower formation control are developed by combining the proposed relative localization scheme and a complex Laplacian-based formation control scheme. It is proven that the integrated system globally asymptotically converges to a stationary similar formation in the case of error-free initial relative position estimates while globally uniformly bounds in a neighborhood of the prescribed formation in the case with initial relative position estimation errors. Furthermore, based on the two degrees of freedom of similar formation on translation, the integrated scheme is also generalized to achieve moving similar formation control. Finally, simulations are presented to illustrate the effectiveness of our theoretical results.
This paper introduces a new multi-agent control problem, called an affine formation control problem, with the objective of asymptotically reaching a configuration that preserves collinearity and ...ratios of distances with respect to a target configuration. Suppose each agent updates its own state using a weighted sum of its neighbor's relative states with possibly negative weights. Then the affine control problem can be solved for either undirected or directed interaction graphs. It is shown in this paper that an affine formation is stabilizable over an undirected graph if and only if the undirected graph is universally rigid, while an affine formation is stabilizable over a directed graph in the d-dimensional space if and only if the directed graph is (d + 1)-rooted. Rigorous analysis is provided, mainly relying on Laplacian associated with the interaction graph, which contain both positive and negative weights.
This paper concentrates on coordinate-free formation control for directed networks, for which the dynamic motion of each agent is assumed to be governed only by a local control. We develop a graph ...Laplacian approach to solve the global and exponential formation stabilization problem using merely relative position measurements between neighbors. First, to capture the sensing and control architectures that are needed to maintain the shape of a formation, a necessary and sufficient topological condition is proposed. Second, a Laplacian-based control law is developed for the stabilization problem of a group of mobile agents to a desired formation shape under both fixed and switching topologies due to temporal node failures. Simulation results are provided to demonstrate that our Laplacian-based formation control strategy is inherently fault-tolerant and robust to node failures.
In this paper, we present a fully distributed bisection algorithm for the economic dispatch problem (EDP) in a smart grid scenario, with the goal to minimize the aggregated cost of a network of ...generators, which cooperatively furnish a given amount of power within their individual capacity constraints. Our distributed algorithm adopts the method of bisection, and is based on a consensus-like iterative method, with no need for a central decision maker or a leader node. Under strong connectivity conditions and allowance for local communications, we show that the iterative solution converges to the globally optimal solution. Furthermore, two stopping criteria are presented for the practical implementation of the proposed algorithm, for which sign consensus is defined. Finally, numerical simulations based on the IEEE 14-bus and 118-bus systems are given to illustrate the performance of the algorithm.
This paper focuses on the procurement of load shifting service by optimally scheduling the charging and discharging of PEVs in a decentralized fashion. We assume that the energy flow between PEVs and ...the grid is bidirectional, i.e., PEVs can also release energy back into the grid as distributed generation, which is known as vehicle-to-grid (V2G). The optimal scheduling problem is then formulated as a mixed discrete programming (MDP) problem, which is NP-hard and extremely difficult to solve directly. To get over this difficulty, we propose a solvable approximation of the MDP problem by exploiting the shape feature of the base demand curve during the night, and develop a decentralized algorithm based on iterative water-filling. Our algorithm is decentralized in the sense that the PEVs compute locally and communicate with an aggregator. The advantages of our algorithm include reduction in computational burden and privacy preserving. Simulation results are given to show the performance of our algorithm.
We consider the control of formations of a leader-follower network, where the objective is to steer a team of multiple mobile agents into a formation of variable size. We assume that the shape ...description of the formation is known to all the agents, which is captured by a complex-valued Laplacian associated with the sensing graph, but the size scaling of the formation is not known or only known to two agents, called the leaders in the network. A distributed linear control strategy is developed in this paper such that the agents converge to the desired formation shape, for which the size of the formation is determined by the two leaders. Moreover, in order to make all agents in a formation move with a common velocity, the distributed control law also incorporates a velocity consensus component, which is implemented with the help of a communication network that may, in general, be of different topology from the sensing graph. Both the setup of single-integrator kinematics and the one of double-integrator dynamics are addressed in the same framework except that the acceleration control in the double-integrator setup has an extra damping term.
Plug-in hybrid electric vehicles (PHEV) are expected to become widespread in the near future. However, high penetration of PHEVs can overload the distribution system. In smart grid, the charging of ...PHEVs can be controlled to reduce the peak load, known as demand-side management (DSM). In this paper, we focus on the DSM for PHEV charging at low-voltage transformers (LVTs). The objective is to flatten the load curve of LVTs, while satisfying each consumer's requirement for their PHEV to be charged to the required level by the specified time. We first formulate this problem as a convex optimization problem and then propose a decentralized water-filling-based algorithm to solve it. A moving horizon approach is utilized to handle the random arrival of PHEVs and the inaccuracy of the forecast nonPHEV load. We focus on decentralized solutions so that computational load can be shared by individual PHEV chargers and the algorithm is scalable. Numerical simulations are given to demonstrate the effectiveness of our algorithm.
The paper introduces complex-valued Laplacians for graphs whose edges are attributed with complex weights and studies the leader–follower formation problem based on complex Laplacians. The main goal ...is to control the shape of a planar formation of point agents in the plane using simple and linear interaction rules related to complex Laplacians. We present a characterization of complex Laplacians that preserve a specific planar formation as an equilibrium solution for both single integrator kinematics and double integrator dynamics. Planar formations under study are subject to translation, rotation, and scaling in the plane, but can be determined by two co-leaders in leader–follower networks. Furthermore, when a complex Laplacian does not result in an asymptotically stable behavior of the multi-agent system, we show that a stabilizing matrix, which updates the complex weights, exists to asymptotically stabilize the system while preserving the equilibrium formation. Also, algorithms are provided to find stabilizing matrices. Finally, simulations are presented to illustrate our results.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
This paper studies the problem of determining the sensor locations in a large sensor network using only relative distance (range) measurements. Based on a generalized barycentric coordinate ...representation, our work generalizes the DILOC algorithm to the localization problem under arbitrary deployments of sensor nodes and anchor nodes. First, a criterion and algorithm are developed to determine a generalized barycentric coordinate of a node with respect to its neighboring nodes, which do not require the node to be inside the convex hull of its neighbors. Next, for the localization problem based on the generalized barycentric coordinate representation, a necessary and sufficient condition for the localizability of a sensor network with a generic configuration is obtained. Finally, a new linear iterative algorithm is proposed to ensure distributed implementation as well as global convergence to the true coordinates.
