Transition-aware DVS algorithm for real-time systems using tree structure analysis

Dynamic voltage scaling (DVS) is a key technique for embedded real-time systems to reduce energy consumption by lowering the supply voltage and operating frequency. Many existing DVS algorithms have to generate the canonical schedules or estimate the lengths of slack time in advance for generating the voltage scaling decisions. Therefore, these methods have to compute the schedules with exponential time complexities in general. In this paper, we consider a set of jitter-controlled, independent, periodic, hard real-time tasks scheduled according to preemptive pinwheel model. Our approach constructs a tree structure corresponding to a schedule and maintains the data structure at each early-completion point. Our approach consists of off-line and on-line algorithms which consider the effects of transition time and energy. The off-line and on-line algorithm takes O(k + n log n) and O(k + (p_max/p_min)) time complexity, respectively, where n, k, p_max and p_min denotes the number of tasks, jobs, longest and shortest task period, respectively. Experimental results show that the proposed approach is effective in reducing computational complexity, transition time and energy overhead.     

Stability and l2‐gain of discrete‐time switched systems with unstable modes

This paper addresses stability and l₂‐gain for discrete‐time switched systems with unstable modes based on slow/fast mode‐dependent average dwell time (MDADT) switching strategies. Firstly, by employing a class of multiple discontinuous Lyapunov functions (MDLFs) and developing a kind of alternative switching signals, the sufficient conditions on stability are established for the system without external disturbances under a slow/fast MDADT switching scheme with a tighter bounds on the dwell time. Furthermore, by defining indicator functions and exploring the features of slow/fast MDADT switching, the weighted l₂‐gain conditions are achieved for the system with external disturbances. Particularly, the criteria of stability and l₂‐gain are also established for the corresponding discrete‐time switched linear systems with unstable modes via the MDLFs method and the slow/fast MDADT switching strategy. Finally, two numerical examples are presented to illustrate the advantages of the proposed methods.     

Evolution of simple sequence repeats

Simple Sequence Repeats (SSRs) are common and frequently polymorphic in eukaryote DNA. Many are subject to high rates of length mutation in which a gain or loss of one repeat unit is most often observed. Can the observed abundances and their length distributions be explained as the result of an unbiased random walk, starting from some initial repeat length? In order to address this question, we have considered two models for an unbiased random walk on the integers, n (n₀ ⩽ n). The first is a continuous time process (Birth and Death Model or BDM) in which the probability of a transition to n + 1 or n − 1 is λk, with k = n − n₀ + 1 per unit time. The second is a discrete time model (Random Walk Model or RWM), in which a transition is made at each time step, either to n − 1 or to n + 1. In each case the walks start at length n₀, with new walks being generated at a steady rate, S, the source rate, determined by a base substitution rate of mutation from neighboring sequences. Each walk terminates whenever n reaches n₀ − 1 or at some time, T, which reflects the contamination of pure repeat sequences by other mutations that remove them from consideration, either because they fail to satisfy the criteria for repeat selection from some database or because they can no longer undergo efficient length mutations. For infinite T, the results are particularly simple for N(k), the expected number of repeats of length n = k + n₀ − 1, being, for BDM, N(k) = S/kλ, and for RWM, N(k) = 2S. In each case, there is a cut-off value of k for finite T, namely k = Tλ ln2 for BDM and k = 0.57√T for RWM; for larger values of k, N(k) becomes rapidly smaller than the infinite time limit. We argue that these results may be compared with SSR length distributions averaged over many loci, but not for a particular locus, for which founder effects are important. For the data of Beckmann & Weber [(1992), Genomics 12, 627] on GT·AC repeats in the human, each model gives a reasonable fit to the data, with the source at two repeat units (n₀ = 2). Both the absolute number of loci and their length distribution are well represented.     

Simulation of a thermonuclear target drive at the 1 MJ laser energy level

The objective of this study was by use of mathematical simulation methods to create an opportunity of a thermonuclear target (k _f ) gain of the order of 1 at the 1 MJ laser energy level. The calculations were performed in two codes with a comparison of their results. It is shown that in the direct drive mode it is possible to obtain a neuron yield an order higher than that obtained in experiments on the NIF (LLNL, the United States) installation in the indirect drive target.     

Predictive switching supervisory control of persistently disturbed input-saturated plants

Predictive switching logic schemes are considered whereby a feedback-gain is switched-on at any time from a family of candidate feedback-gains so as to control a discrete-time input-saturated LTI system possibly subject to persistent bounded disturbances of unknown arbitrary magnitude. It is constructively shown that such schemes do exist which ensure, along with good tracking performance, global asymptotic and semi-global exponential stability in the noiseless case, as well as finite l_∞-induced gain to the disturbance-to-state map, whenever the structure of the disturbed plant can make such properties conceptually achievable, viz., the disturbance which enters an Asymptotically Null-Controllable with Bounded Input (ANCBI) system acts directly only on the stable modes, while the critically unstable ones are indirectly affected by the disturbance only via the feedback controls. More generally, in ANCBI systems general disturbances of suitably bounded magnitude can also be handled by the scheme, provided that the switching logic be equipped with an appropriate hysteresis facility.     

Independent tracking and regulation adaptive control with forgetting factor

This paper considers a discrete-time adaptive control algorithm with a forgetting factor applicable to minimum phase plants. The tracking and regulation objectives are independently specified. The relevance of the eigenvalues of the gain matrix (F_k) used in the updating equation for the adaptive parameters ($\text{}\text{?}\text{gq(k)}$) is shown. It is proved that if the maximum eigenvalue of the inverse of the gain matrix F_k has an upper bound and a non-zero lower bound then the global convergence of the control algorithm is insured. The result of the design is a simple control scheme using a linear constant feedforward controller and a nonlinear feedback controller. The performance of the control structure in tracking and regulation are evaluated by simulations.     

Introducing k-point parallelism into VASP

For many years ab initio electronic structure calculations based upon density functional theory have been one of the main application areas in high performance computing (HPC). Typically, the Kohn–Sham equations are solved by minimisation of the total energy functional, using a plane wave basis set for valence electrons and pseudopotentials to obviate the representation of core states. One of the best known and widely used software for performing this type of calculation is the Vienna Ab initio Simulation Package, VASP, which currently offers a parallelisation strategy based on the distribution of bands and plane wave coefficients over the machine processors. We report here an improved parallelisation strategy that also distributes the k-point sampling workload over different processors, allowing much better scalability for massively parallel computers. As a result, some difficult problems requiring large k-point sampling become tractable in current computing facilities. We showcase three important applications: dielectric function of epitaxially strained indium oxide, solution energies of tetravalent dopants in metallic VO₂, and hydrogen on graphene.     

Finite-gain L p consensus of multi-agent systems

This paper studies consensus problems for multi-agent systems modeled by linear time-invariant systems with external disturbances under a fixed directed communication topology. It is shown that consensus can be achieved if each agent with the same disturbance signals. But the result is different for each agent with different disturbances. In this case, the finite-gain L _p consensus is introduced to describe the effects of the external disturbance on the consensus performance. A necessary and sufficient condition for reaching finite-gain L _p consensus is presented, and analytic estimation of the L _p gain is given. A distributed algorithm is proposed to ensure that the finite-gain L ₂ consensus can be reached with a desired L ₂ gain. Numerical examples are given to illustrate the given results.     

Coordinated control of a satellite-mounted manipulator with consideration of payload flexibility

When a space robot performs tasks, disturbances caused by payload motion downgrade the attitude control's accuracy. Thus, the payload should be controlled so as not to generate large disturbances. In this paper, payload motion planning based on angular momentum constraints (AMC) is proposed. In this method, disturbances are reduced by controlling the payload's redundant motions. Remaining disturbances caused by payload flexibility are compensated for by a robust feedback controller consisting of a variable gain and a H_∞ controller. The usefulness of this approach is verified through numerical simulations and hardware experiments.     

Database-friendly random projections: Johnson-Lindenstrauss with binary coins

A classic result of Johnson and Lindenstrauss asserts that any set of n points in d-dimensional Euclidean space can be embedded into k-dimensional Euclidean space—where k is logarithmic in n and independent of d—so that all pairwise distances are maintained within an arbitrarily small factor. All known constructions of such embeddings involve projecting the n points onto a spherically random k-dimensional hyperplane through the origin. We give two constructions of such embeddings with the property that all elements of the projection matrix belong in {−1,0,+1}. Such constructions are particularly well suited for database environments, as the computation of the embedding reduces to evaluating a single aggregate over k random partitions of the attributes.     

A Mixed DG Method for Linearized Incompressible Magnetohydrodynamics

We introduce and analyze a discontinuous Galerkin method for the numerical discretization of a stationary incompressible magnetohydrodynamics model problem. The fluid unknowns are discretized with inf-sup stable discontinuous ? _k ³ ?? _k?1 elements whereas the magnetic part of the equations is approximated by discontinuous ? _k ³ ?? _k+1 elements. We carry out a complete a-priori error analysis of the method and prove that the energy norm error is convergent of order k in the mesh size. These results are verified in a series of numerical experiments.     

Thresholds for Extreme Orientability

Multiple-choice load balancing has been a topic of intense study since the seminal paper of Azar, Broder, Karlin, and Upfal. Questions in this area can be phrased in terms of orientations of a graph, or more generally a k-uniform random hypergraph. A (d,b)-orientation is an assignment of each edge to d of its vertices, such that no vertex has more than b edges assigned to it. Conditions for the existence of such orientations have been completely documented except for the “extreme” case of (k?1,1)-orientations. We consider this remaining case, and establish:

• The density threshold below which an orientation exists with high probability, and above which it does not exist with high probability.
• An algorithm for finding an orientation that runs in linear time with high probability, with explicit polynomial bounds on the failure probability.

Previously, no closed-form expression for the threshold was known. The only known algorithms for constructing (k?1,1)-orientations worked for k≤3, and were only shown to have expected linear running time.     

Upper signed k-domination in a general graph

Let k be a positive integer, and let G=(V,E) be a graph with minimum degree at least k−1. A function f:V→{−1,1} is said to be a signed k-dominating function (SkDF) if _∑u∈N[v]f(u)?k for every v∈V. An SkDF f of a graph G is minimal if there exists no SkDF g such that g≠f and g(v)?f(v) for every v∈V. The maximum of the values of _∑v∈Vf(v), taken over all minimal SkDFs f, is called the upper signed k-domination numberΓkS(G). In this paper, we present a sharp upper bound on this number for a general graph.     

A geometric approach to multivariable control system design of a distillation column

A multivariable control problem of a distillation column is considered, where the object is to maintain two output variables, the compositions of the distillate and the bottom product at some desired values by manipulating the reflux flow rate and the boil-up rate.Based on a linearized model, a geometric approach is applied to the design problem of disturbance rejection control. In other words, a feedback control strategy is desired which enables the complete rejection of the effect of disturbances on both output variables.In obtaining the feedback control, the problem of how many and what state variables are to be measured and fed back has been made clear. In this control strategy, only five state variables are fed back. Thus, only five columns of the feedback gain matrix have non-zero values. Furthermore, two out of these five columns are uniquely determined, and the other three columns can be assigned arbitrary values and used for pole assignment of the controlled system.For the disturbances in composition and flow rate of the feed stream, Δx_F and ΔL_F, the effect of the disturbance Δx_F is completely rejected by the feedback controller, but the effect of the disturbance ΔL_F can only be eliminated from the output Δx_D.A digital simulation of a distillation column composed of nine plates, a condenser and a reboiler was carried out to confirm these results and to show that the linearized model used in this paper is valid for fairly large step changes.     

Analysis of flow patterns in a patient-specific thoracic aortic aneurysm model

In this study, a newly developed two-equation transitional model was employed for the prediction of blood flow patterns in a thoracic aortic aneurysm (TAA) where the growth and progression are closely linked to low and oscillating wall shear stresses. Laminar–turbulent transition in the dilated vessel can alter the flow structure, shear stress and pressure distribution within the aneurysm. A patient-specific TAA model was reconstructed from magnetic-resonance (MR) images and measured velocity waveform was used as the inflow condition. Laminar flow and a correlation-based transitional version of Menter’s hybrid k ? ?/k ? ω Shear Stress Transport (SST Tran) model were implemented in pulsatile simulations from which WSS distribution was obtained throughout a cardiac cycle and velocity profiles were compared with MR measurements. The correlation-based transitional model was found to produce results in closer agreement with the MR data than the laminar flow simulation.     

Anelastic Stokes Eigenmodes in Infinite Channel

The anelastic Stokes eigenmodes are computed for a fluid confined, in presence of gravity, between two horizontally infinite plates. These eigenmodes are described by one horizontal wave number k. The eigenvalues λ(k ²) are proved to be all negative. They depend monotonically upon k, behaving like k ² for very large k. Two particular values of k are considered, i.e., k=2?π and k=0, and the stratification parameter of the equilibrium state is taken between 0 (incompressible approximation) and 10 (upper limit of the anelastic configuration). The k=2?π eigenvalue problem is solved numerically while the k=0 is solved both numerically and analytically. Two physical configurations are analyzed, one with no-slip boundary conditions imposed on both horizontal walls, and one with no-stress, while imposing no flow through these boundaries in both cases. The main results are: (i) the smaller the stratification, the larger the decay rate, (ii) the eigenmodes are localized in the lower part of the channel, their vertical extension increasing with the eigenmode spatial frequency, (iii) the Neumann eigenmode decay rates are smaller than their Dirichlet counterparts, except for k=0, where it is just the reverse, (iv) a general trend seems to emerge from the present study, regarding the way the numerical eigenvalues of an elliptic operator compare with the analytical ones, viz., the numerical spectrum overestimates (in absolute value) the analytical spectrum, slightly in the low frequency part of the spectrum and more and more strongly in the upper part.     

Performance enhancement for a class of hysteresis nonlinearities using disturbance observers

This paper addresses performance enhancement using disturbance observers (DOBs) for a class of hysteresis nonlinearities characterized by the Prandtl-Ishlinskii model. The proposed approach makes use of internal model-based estimation of exogenous disturbances. The synthesis of the DOB is formulated as an H _∞ weighted-sensitivity optimization for static output feedback (SOF) gain of a Luenberger observer. A linearization approach is then implemented to solve the rank-constrained (nonconvex) constrained semi-definite program (SDP) for the (sub) optimal static gain. Simulation results indicate that the closed-loop tracking performance is indeed enhanced using the DOB for reference inputs at different excitation frequencies.     

Modified nonlinearly dispersive mK(m,n,k) equations: I. New compacton solutions and solitary pattern solutions

In this paper exact solutions of the modified nonlinearly dispersive KdV equations (simply called mK(m,n,k) equations), u^m−1u_t+a(uⁿ)_x+b(u^k)_xxx=0, are investigated by using some direct ansatze. As a result, abundant new compacton solutions: solitons with the absence of infinite wings, solitary pattern solutions having infinite slopes or cups, solitary wave solutions and periodic wave solutions are obtained.     

Vibration and local instability of thermally stressed plates

The vibration and buckling of a double wedge square cantilever plate has been investigated. It is shown that the free vibration modes, which occur at ΔT_ref = 0, transition into the buckled modes which occur at ΔT_ref = ΔT_refcr for the respective mode. ΔT_refcr for a particular mode is defined as the magnitude of thermal load at which the frequency of the particular mode vanishes. The analysis, in which no assumption whatsoever is made about the shape of the vibration modes, about the vibration frequencies, about the shape of the buckled modes, or about the magnitude of the critical loads, yields the same number of buckling eigenvalues and buckling modes as there are vibration eigenvalues and vibration modes. Gradual application of the load in the analysis permits the change in each vibration frequency of interest and its associated mode to be followed up to the load at which the frequency of the mode becomes zero. This constitutes the limit of linear theory. Only linear theory is used in this paper; thus, no post buckled behavior is considered. As the load is increased, the thin edges of the plate begin to duform during vibration. This local deformation, which begins in the vibration mode, is shown to transition into the phenomena of local edge buckling at ΔT_refcr for the mode.