Information flow and cooperative control of vehicle formations

We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. Tools from algebraic graph theory prove useful in modeling the communication network and relating its topology to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability. We also propose a method for decentralized information exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle with a common reference to be used for cooperative motion. We prove a separation principle that decomposes formation stability into two components: Stability of this is achieved information flow for the given graph and stability of an individual vehicle for the given controller. The information flow can thus be rendered highly robust to changes in the graph, enabling tight formation control despite limitations in intervehicle communication capability

Graph Laplacians and Stabilization of Vehicle Formations

Control of vehicle formations has emerged as a topic of significant interest to the controls community. In this paper, we merge tools from graph theory and control theory to derive stability criteria for formation stabilization. The interconnection between vehicles (i.e., which vehicles are sensed by other vehicles) is modeled as a graph, and the eigenvalues of the Laplacian matrix of the graph are used in stating a Nyquist-like stability criterion for vehicle formations. The location of the Laplacian eigenvalues can be correlated to the graph structure, and therefore used to identify desirable and undesirable formation interconnection topologies

Reply to “Comments on “Consensus and Cooperation in Networked Multi-Agent Systems””

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A Distributed Scalable Approach to Formation Control in Multi-Robot Systems

A new algorithm for the control of formations of mobile robots is presented. Formations with a triangular lattice structure are created using distributed control rules, using only local information on each robot. The overall direction of movement of the formation is not pre-established but rather results from local interactions, giving all the robots a common, self-organized heading. Experiments were done to test the algorithm, yielding results in which robots behaved as expected, moving at a reasonable speed and maintaining the desired distances among themselves. Up to seven robots were used in real experiments and up to forty in simulation

Diffusion on networked systems is a question of time or structure

Network science investigates the architecture of complex systems to understand their functional and dynamical properties. Structural patterns such as communities shape diffusive processes on networks. However, these results hold under the strong assumption that networks are static entities where temporal aspects can be neglected. Here we propose a generalized formalism for linear dynamics on complex networks, able to incorporate statistical properties of the timings at which events occur. We show that the diffusion dynamics is affected by the network community structure and by the temporal properties of waiting times between events. We identify the main mechanism—network structure, burstiness or fat tails of waiting times—determining the relaxation times of stochastic processes on temporal networks, in the absence of temporal–structure correlations. We identify situations when fine-scale structure can be discarded from the description of the dynamics or, conversely, when a fully detailed model is required due to temporal heterogeneities

Two Cellular Protein Kinases, DNA-PK and PKA, Phosphorylate the Adenoviral L4-33K Protein and Have Opposite Effects on L1 Alternative RNA Splicing

Accumulation of the complex set of alternatively processed mRNA from the adenovirus major late transcription unit (MLTU) is subjected to a temporal regulation involving both changes in poly (A) site choice and alternative 3′ splice site usage. We have previously shown that the adenovirus L4-33K protein functions as an alternative splicing factor involved in activating the shift from L1-52,55K to L1-IIIa mRNA. Here we show that L4-33K specifically associates with the catalytic subunit of the DNA-dependent protein kinase (DNA-PK) in uninfected and adenovirus-infected nuclear extracts. Further, we show that L4-33K is highly phosphorylated by DNA-PK in vitro in a double stranded DNA-independent manner. Importantly, DNA-PK deficient cells show an enhanced production of the L1-IIIa mRNA suggesting an inhibitory role of DNA-PK on the temporal switch in L1 alternative RNA splicing. Moreover, we show that L4-33K also is phosphorylated by protein kinase A (PKA), and that PKA has an enhancer effect on L4-33K-stimulated L1-IIIa splicing. Hence, we demonstrate that these kinases have opposite effects on L4-33K function; DNA-PK as an inhibitor and PKA as an activator of L1-IIIa mRNA splicing. Taken together, this is the first report identifying protein kinases that phosphorylate L4-33K and to suggest novel regulatory roles for DNA-PK and PKA in adenovirus alternative RNA splicing