We study a new variant of consensus problems, termed `local average consensus, in networks of agents. We consider the task of using sensor networks to perform distributed measurement of a parameter which has both spatial (in this paper 1D) and tempor
al variations. Our idea is to maintain potentially useful local information regarding spatial variation, as contrasted with reaching a single, global consensus, as well as to mitigate the effect of measurement errors. We employ two schemes for computation of local average consensus: exponential weighting and uniform finite window. In both schemes, we design local average consensus algorithms to address first the case where the measured parameter has spatial variation but is constant in time, and then the case where the measured parameter has both spatial and temporal variations. Our designed algorithms are distributed, in that information is exchanged only among neighbors. Moreover, we analyze both spatial and temporal frequency responses and noise propagation associated with the algorithms. The tradeoffs of using local consensus, as compared to standard global consensus, include higher memory requirement and degraded noise performance. Arbitrary updating weights and random spacing between sensors are analyzed in the proposed algorithms.
Recently we developed supervisor localization, a top-down approach to distributed control of discrete-event systems in the Ramadge-Wonham supervisory control framework. Its essence is the decomposition of monolithic (global) control action into local
control strategies for the individual agents. In this paper, we establish a counterpart supervisor localization theory in the framework of State Tree Structures, known to be efficient for control design of very large systems. In the new framework, we introduce the new concepts of local state tracker, local control function, and state-based local-global control equivalence. As before, we prove that the collective localized control behavior is identical to the monolithic optimal (i.e. maximally permissive) and nonblocking controlled behavior. In addition, we propose a new and more efficient localization algorithm which exploits BDD computation. Finally we demonstrate our localization approach on a model for a complex semiconductor manufacturing system.
We identify a new observability concept, called relative observability, in supervisory control of discrete-event systems under partial observation. A fixed, ambient language is given, relative to which observability is tested. Relative observability
is stronger than observability, but enjoys the important property that it is preserved under set union; hence there exists the supremal relatively observable sublanguage of a given language. Relative observability is weaker than normality, and thus yields, when combined with controllability, a generally larger controlled behavior; in particular, no constraint is imposed that only observable controllable events may be disabled. We design algorithms which compute the supremal relatively observable (and controllable) sublanguage of a given language, which is generally larger than the normal counterparts. We demonstrate the new observability concept and algorithms with a Guideway and an AGV example.
We have recently proposed a surplus-based algorithm which solves the multi-agent average consensus problem on general strongly connected and static digraphs. The essence of that algorithm is to employ an additional variable to keep track of the state
changes of each agent, thereby achieving averaging even though the state sum is not preserved. In this note, we extend this approach to the more interesting and challenging case of time-varying topologies: An extended surplus-based averaging algorithm is designed, under which a necessary and sufficient graphical condition is derived that guarantees state averaging. The derived condition requires only that the digraphs be arbitrary strongly connected in a emph{joint} sense, and does not impose balanced or symmetric properties on the network topology, which is therefore more general than those previously reported in the literature.
It is generally thought that protoplanetary disks embedded in envelopes are more massive and thus more susceptible to gravitational instabilities (GIs) than exposed disks. We present three-dimensional radiative hydrodynamics simulations of protoplane
tary disks with the presence of envelope irradiation. For a disk with a radius of 40 AU and a mass of 0.07 Msun around a young star of 0.5 Msun, envelope irradiation tends to weaken and even suppress GIs as the irradiating flux is increased. The global mass transport induced by GIs is dominated by lower-order modes, and irradiation preferentially suppresses higher-order modes. As a result, gravitational torques and mass inflow rates are actually increased by mild irradiation. None of the simulations produce dense clumps or rapid cooling by convection, arguing against direct formation of giant planets by disk instability, at least in irradiated disks. However, dense gas rings and radial mass concentrations are produced, and these might be conducive to accelerated planetary core formation. Preliminary results from a simulation of a massive embedded disk with physical characteristics similar to one of the disks in the embedded source L1551 IRS5 indicate a long radiative cooling time and no fragmentation. The GIs in this disk are dominated by global two and three-armed modes.
