Fig 8 - uploaded by Zhiyun Lin
Content may be subject to copyright.
Source publication
Similar publications
We work with a symmetric scalar theory with quartic coupling in 4-dimensions. Using a 2PI effective theory and working at 4 loop order, we renormalize with a renormalization group method. All divergences are absorbed by one bare coupling constant and one bare mass which are introduced at the level of the Lagrangian. The method is much simpler than...
EGU 2017: Oral Presentation: Biogeosciences
Citations
... Consensus, agreement, rendezvous, flocking, swarming, and synchronization problems for multi-agent systems have been extensively studied for over two decades. See textbooks and research monographs (Bullo, 2019;Bullo, Cortés, & Martínez, 2009;Lewis, Zhang, Hengster-Movric, & Das, 2014;Lin, 2008;Mesbahi & Egerstedt, 2010;Ren & Beard, 2008). These problems can be unified, more or less, into an output synchronization problem where a number of dynamical agents are connected by a network protocol so that the agents' behaviors are coordinated, e.g., made to converge to a common trajectory. ...
In this paper, the synchronization of heterogeneous agents interacting over a dynamical network is studied. The edge dynamics can model the inter-agent communications which are often heterogeneous by nature. They can also model the controllers of the agents which may be different for each agent or uniform for all the agents. Novel synchronization conditions are obtained for both cases from a phase perspective by exploiting a recently developed small phase theorem. The conditions scale well with the network and reveal the trade-off between the phases of node dynamics and edge dynamics. We also study the synchronizability problem which aims to characterize the allowable diversity of the agents for which controllers can be designed so as to achieve synchronization. The allowable diversity is captured in terms of phase conditions engaging the residue matrices of the agents at their persistent modes. Controller design algorithms are provided for the cases of agent-dependent and uniform controllers, respectively.
... A digraph G is said to be quasi-strongly connected, if for every two nodes i and j there is a node k from which i and j are reachable. For detailed discussion on graph theory, the readers are referred to [26]. ...
This paper presents finite-and fixed-time protocols, which solve the consensus problem in multi-agent systems with time-varying directed topologies. We show that the proposed distributed protocols solve the consensus problem under switching topologies, which are jointly strongly connected. These distributed protocols homogenize the multi-agent networks, which make the overall system robust against disturbances. We employ the homogeneity property of the vector fields, graph theory, Lyapunov stability theory and convex analysis to show the finite-and fixed-time stability of the multi-agent systems. Numerical examples are presented to demonstrate the effectiveness of the proposed control methods.
... In [13], jointly communication graphs are used to derive a sufficient condition for achieving consensus using first-order integrator dynamics. Many of the researchers came up with monographs on co-operative control for multi-agent systems [14][15][16][17]. After 2013, researchers started testing and validating the consensus algorithms on robotics platforms. ...
... Equation (14) gives the position at each time t. The position of each robot at particular time is given by t i+1 = Figure 3: Undirected graph t i + t, i = 1, 2, 3 · · · where t 0 = 0 and t is the sampling time. ...
This paper explains mathematical framework of physical phenomenon happening in nature and social opinion dynamics. It is divided into two parts. The first part deals with design of the trajectory tracking algorithm for multiple mobile robots and in the second part rendezvous algorithm is described. Trajectory tracking algorithm is designed using leader–follower approach in which each follower robot tracks the reference trajectory generated by the leader. Rendezvous algorithm is designed by deriving consensus equation using algebraic graph theory. Condition for achieving rendezvous point is also derived. Simulation shows the effectiveness of proposed algorithm
... Remark 1 (23). Consider a group of n agents in a planar world with a global coordinate system, ∑ . ...
In this article, we consider the optimal topology design and distributed formation control problem of multiagent systems (MAS) with complex‐weighted directed topology. First, a framework is proposed to associate optimal topology of MAS to a constrained optimization problem with a complex Laplacian matrix, which is independent of the agent dynamics. The main contribution of the proposed approach compared with existing results is that the proposed approach does not require the calculation of the stabilizing matrix such that the closed‐loop system is asymptotically stable, and a unique set of complex weights that satisfy associated cooperative conditions can be chosen. Then, a distributed formation control protocol is proposed to enable all agents to achieve the control goal. Finally, some numerical example results are provided to demonstrate the effectiveness of the proposed scheme.
... Nevertheless, the proposed method in [15] is performed in a centralized manner laking of adaptability and scalability. Decentralized or distributed control algorithms are deemed as a desirable alternative [16][17]. Motivated by this consideration, a non-cooperative game approach is applied in [18] to maximize individual utility function independently for a group of EVs in a vehicleto-building scenario, in which the valley filling and peak shifting are achieved as well. ...
... Now we present a hierarchical optimal algorithm to solve the decomposed optimization problems (15)- (18). Specifically, the iterative water-filling-based algorithm is applied to solve the optimal load shifting problems (15) and (16), and the consensus-based optimization method is utilized to solve the total costs minimization problems (17) and (18). ...
... Step 5: Due to the nonlinear projection, the estimated power state may not be a feasible solution to (17) and (18). To overcome this issue, let each EV i at time k associate with a surplus variable to temporarily store the resulting deviation. ...
Cyber-physical-social system (CPSS), an integration of cyberspace, physical space, and social space, has revolutionized the relationship between human, computers and physical environments. Electrical cyber-physical system integrating human behaviors and interactions is a typical CPSS, and the study of electric vehicles (EVs) charging and discharging in the CPSS has become a research hotspot due to its environmental advantages and social benefits. This paper focuses on simultaneously optimizing the power load stability and the total cost of vehicle owners in the CPSS. First, the optimal scheduling problem is formulated as a multi-objective optimization problem with system’s technical constraints, and then a hierarchical optimal algorithm is proposed to solve the problem. The convergence analysis of the proposed algorithm is presented to ensure its optimal performance. Further, this paper combines the proposed algorithm with a moving horizon method to deal with the EV owners random arrival and departure case based on the owners’ convenience and preferences. It shows that the proposed algorithm not only enhances stable performance of the power load but also improves satisfaction of the vehicle owners in the CPSS framework integrating power grids, energy consumption areas, and social components. Numerical simulations are presented to demonstrate the effectiveness of the proposed algorithm.
... IEEE57-bus system contains seven generators units located on buses {1, 2, 3, 6, 8, 9, 12}. Besides, we selected the buses with load power as the load buses, which are all buses except for buses {4, 7,11,21,22,24,26,34,36,37,39,40,45,46, 48} in the IEEE57-bus system. By analyzing the load power data of IEEE57-bus, the summation of the power load could be calculated as P 0 = 1250.8 ...
The economic dispatch problem (EDP) is a significant class of optimization issues in the power system, which works on minimizing the total cost when generating a certain amount of power. A novel distributed approach for EDP is proposed in this paper. The presented approach consists of two steps. The first step, named absorption search, is to simplify the network structure through absorption searching. A flooding-based consensus approach is applied in the first step, which can be used to achieve consensus information among nodes. After the first step, only the generation nodes are kept in the network. The data collection can be completed by local computation and communication between neighbors. The first step can be considered as the stage of gathering information. In the second step, a distributed half-search algorithm makes the nodes obtain the final optimal solution in a distributed way. The results on three case studies demonstrate that the proposed approach is highly effective for solving the EDP.
... There exists a diagonal positive definite matrix P such that Q := PL 22 + L 22 T P > 0 [32]. Then the control law in [22] can be given as follows, Overall, the trajectories of the five agents generated by the two control schemes are, respectively, shown in Figs. 4 and 5, from which, it can be seen that the five agents achieve and maintain the formation during their motions with both control schemes. ...
In this study, a distributed adaptive control strategy for distance-based formation and flocking control of multi-agent system with parametric uncertainty is proposed. A 3-agent leader–first-follower system is considered first. The agents are supposed to have non-identical dynamics, whereas with similar structure. By introducing two new variables that involve distance error and velocity error and utilising them in the controller design, global convergence of all agents to the desired formation and to the velocity of the leader is established. Finally, the three-agent case is inductively extended to N-agent case. The stability and the effectiveness of the proposed control strategy are analysed in theory and demonstrated through simulation results, respectively.
... This is the symbol, ψ G (e) = (u, v), where e is said to join u to v; u is the tail of e, and v is the head. An undirected graph [42], G, can be treated as a bidirectional diagraph by replacing each line or edge (u, v) of G with the pair of arcs (u, v) and (v, u). ...
The cooperative, reliable and responsive characteristics make smart grid more popular than traditional power grid. However, with the extensive employment of smart grid concepts, the traditional centralized control methods expose a lot of shortcomings, such as communication congestion, computing complexity in central management systems, and so on. The distributed control method with flexible characteristics can meet the timeliness and effectiveness of information management in smart grid and ensure the information collection timely and the power dispatch economically. This article presents a decentralized approach based on multi agent system (MAS) for solving data collection and economic dispatch problem of smart grid. First, considering the generators and loads are distributed on many nodes in the space, a flooding-based consensus algorithm is proposed to achieve generator and load information for each agent. Then, a suitable distributed algorithm called λ-consensus is used for solving the economic dispatch problem, eventually, all generators can automatically minimize the total cost in a collective sense. Simulation results in standard test cases are presented to demonstrate the effectiveness of the proposed control strategy.
... We first introduce a lemma on non-negative matrices and then present the consensus-like algorithm. Lemma 1 [21]: A non-negative matrix A ∈ ℝ n × n is primitive, if and only if its associated graph is strongly connected and aperiodic. ...
... The remaining constraints are local and only lead to the temporal correlations of local variables. • The variables directly coupled by the system-wide constraints (21) and (27) include P, S and R. Besides, the objective function does not involve any other variables except P. Therefore, the remaining variables can be viewed as auxiliary variables for defining the feasible region of P, S and R. ...
The dynamic economic dispatch problem with energy storage in a smart grid scenario is studied, which aims at minimising the aggregate generation costs over multiple periods on condition that the time-varying demand is met, while physical constraints on generation and storage as well as system spinning reserve requirement are satisfied. In our model, energy storage devices are incorporated for not only inter-temporal energy arbitrage to reduce total generation cost, but also providing spinning reserve to share generators' burden. To solve this problem, we assume that the communication networks are strongly connected directed graphs and propose a fully distributed algorithm based on the 'consensus-like' iterative algorithm and the alternating direction method of multipliers. Our algorithm is distributed in the sense that no leader or master nodes are needed, while all the nodes conduct local computation and communicate merely with their neighbours. Numerical simulation is included to show the effectiveness of the proposed algorithm.
... Following the terminology used for coupled cell systems, see e.g. [29], we describe a nearest-neighbor interaction system (NNIS) as a network of interacting systems -so-called cells. These cells can represent highly diverse physical or biological systems, e.g. ...
Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods anymore due to the so-called curse of dimensionality. This requires techniques to handle linear operators defined on extremely large state spaces and to solve the resulting systems of linear equations or eigenvalue problems. In this paper, we present a systematic tensor train decomposition for nearest neighbor interaction systems which is applicable to a host of different problems. With the aid of this decomposition, it is possible to reduce the memory consumption as well as the computational costs significantly. Furthermore, it can be shown that in some cases the rank of the tensor decomposition does not depend on the network size. The format is thus feasible even for high-dimensional systems. We will illustrate the results with several guiding examples such as the Ising model, a system of coupled oscillators, and a CO oxidation model.
