4,788 research outputs found

    Anytime Control using Input Sequences with Markovian Processor Availability

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    We study an anytime control algorithm for situations where the processing resources available for control are time-varying in an a priori unknown fashion. Thus, at times, processing resources are insufficient to calculate control inputs. To address this issue, the algorithm calculates sequences of tentative future control inputs whenever possible, which are then buffered for possible future use. We assume that the processor availability is correlated so that the number of control inputs calculated at any time step is described by a Markov chain. Using a Lyapunov function based approach we derive sufficient conditions for stochastic stability of the closed loop.Comment: IEEE Transactions on Automatic Control, to be publishe

    Zeroth Hochschild homology of preprojective algebras over the integers

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    We determine the Z-module structure of the preprojective algebra and its zeroth Hochschild homology, for any non-Dynkin quiver (and hence the structure working over any base commutative ring, of any characteristic). This answers (and generalizes) a conjecture of Hesselholt and Rains, producing new pp-torsion classes in degrees 2p^l, l >= 1, We relate these classes by p-th power maps and interpret them in terms of the kernel of Verschiebung maps from noncommutative Witt theory. An important tool is a generalization of the Diamond Lemma to modules over commutative rings, which we give in the appendix. In the previous version, additional results are included, such as: the Poisson center of Sym HH0(Π)\text{Sym } HH_0(\Pi) for all quivers, the BV algebra structure on Hochschild cohomology, including how the Lie algebra structure HH0(ΠQ)HH_0(\Pi_Q) naturally arises from it, and the cyclic homology groups of ΠQ\Pi_Q.Comment: 69 pages, 2 figures; final pre-publication version; many corrections and improvements throughout. Note though the first version has additional results (for instance, it computes the higher Hochschild (co)homology and its structures

    On Separation for Multiple Access Channels

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    We examine the issue of separation for multiple access channels. We demonstrate that source-channel separation holds for noisy multiple access channels, when the channel operates over a common finite field. This robustness of separation is predicated on the fact that noise and inputs are independent, and we examine the loss from failure of separation when noise is input dependent