Examining the impact of domain and cognitive complexity on query formulation and reformulation

The purpose of this analysis was to evaluate an existing set of search tasks in terms of their effectiveness as part of a “shared infrastructure” for conducting interactive IR research. Twenty search tasks that varied in their cognitive complexity and domain were assigned to 47 study participants; the 3,101 moves used to complete those tasks were then analyzed in terms of frequency of each type of move and the sequential patterns they formed. The cognitive complexity of the tasks influenced the number of moves used to complete the tasks, with the most complex (i.e., Create) tasks requiring more moves than tasks at other levels of complexity. Across the four domains, the Commerce tasks elicited more search moves per search. When sequences of moves were analyzed, seven patterns were identified; some of these patterns were associated with particular task characteristics. The findings suggest that search tasks can be designed to elicit particular types of search behaviors and, thus, allow researchers to focus attention on particular aspects of IR interactions.     

On the approximate discrete KLT of fractional Brownian motion and applications

This paper establishes connection between discrete cosine transform (DCT) and the discrete-time fractional Brownian motion process (dfBm). It is proved that the eigenvectors of the auto-covariance matrix of a dfBm can be approximated by DCT basis vectors in the asymptotic sense. This shows that DCT basis acts as discrete Karhunen–Loève transform (DKLT) for these processes in the approximate sense. Analytic perturbation theory of linear operators is used to prove this result. This result will be of great practical significance in applications where one is looking for an appropriate basis to work with signals that can perhaps be modeled as belonging to fBm processes. The utility of the proposed work has been illustrated with two real-life data (a) on compressive sampling based reconstruction of financial time-series and (b) in denoising gravitational wave event GW150914 data obtained from a binary black hole merger.     

Impulsive effects on the stability and stabilization of positive systems with delays

This study addresses the exponential stability and positive stabilization problems of impulsive positive systems (IPSs) with time delay. Specially, three types of impulses, namely, disturbance, “neutral”, and stabilizing impulses, are considered. For each type of impulsive effect, the exponential stability criterion is established utilizing the Lyapunov–Razumikhin techniques. Moreover, on the basis of the obtained stability results, the state-feedback controller design problem is investigated to positively stabilize the IPSs with time delay under different types of impulsive effects. Finally, numerical examples are provided to illustrate the effectiveness of the theoretical results.     

Lattices sampling and sampling rate conversion of multidimensional bandlimited signals in the linear canonical transform domain

The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. Many theories for this transform are already known, but the uniform sampling theorem, as well as the sampling rate conversion theory about arbitrary lattices sampling in the LCT domain are still to be determined. Focusing on these issues, this paper carefully investigates arbitrary lattices sampling, the sampling with separable matrices and nonseparable matrices, to obtain uniform sampling theorem and the sampling rate conversion theory in the LCT domain. Firstly, the spectral expression of the discrete-time signal sampled via arbitrary lattice is deduced in the LCT domain. Based on it we propose the alias-free sampling relationship between two matrices and present the perfect reconstruction expressions for bandlimited signals in the LCT domain. Secondly, for further research on discrete signals to obtain sampling rate conversion theory, we define the multidimensional discrete time linear canonical transform (MDTLCT), as well as the convolution for the MDTLCT. Thirdly, the formulas of multidimensional interpolation and decimation via integer matrices in the LCT domain are derived. Then, based on the results of interpolation and decimation, we make analyses of the sampling rate conversion via rational matrices in the LCT domain, including spectral analyses and the formulas in time domain. Finally, simulation results and the potential applications of the theories are also presented.     

Anti-oscillation and chaos control of the fractional-order brushless DC motor system via adaptive echo state networks

This paper proposes anti-oscillation and chaos control scheme for the fractional-order brushless DC motor system wherein there exist unknown dynamics, immeasurable states and chaotic oscillation. Aimed at immeasurable states, the high-gain observers with fast convergence are presented to obtain the information of system states. To compensate uncertainties existing in the dynamic system, a finite-time echo state network with a weight is proposed to approximate uncertain dynamics while its weight is tuned by a fractional-order adaptive law online. Meanwhile a fractional-order filter is introduced to deal with the repeated derivative of the backstepping. Based on the fractional-order Lyapunov stability criterion, the anti-oscillation and chaos control scheme integrated with a high-gain observer, an echo state network and a filter are proposed by using recursive steps of backstepping. The proposed scheme guarantees the boundedness of all signals of the closed-loop system in the sense of global asymptotic stability, and also suppresses chaotic oscillation. Finally, the effectiveness of our scheme is demonstrated by simulation results.     

Parametric delta operator Riccati equation and applications to semi-global stabilization in the presence of actuator saturation

In this paper, a parametric delta operator Riccati equation is established for low gain feedbacks of linear delta operator systems. Some properties for the parametric delta operator Riccati equation are given based on a parameter-dependent cost function. An explicit solution is also given for the delta operator parametric Riccati equation. Semi-global stabilization is described for a linear delta operator system with actuator saturation via low gain state and output feedback control laws. A numerical example is given to illustrate the effectiveness and potential for the developed techniques.     

Stabilization of periodic orbits of discrete-time dynamical systems using the Prediction-Based Control: New control law and practical aspects

This paper tackles in the stabilization of periodic orbits of nonlinear discrete-time dynamical systems with chaotic sets. The problem is approximated locally to the stabilization of linear time-periodic systems and the theory of modern control is applied to the Prediction-Based Control, resulting in a new control law. This control law sets all the Floquet multipliers of the stabilized orbit to zero, resulting in fast convergence of trajectories in its vicinity. Another important characteristic of the control law is that no previous knowledge about the periodic orbit is required for stabilization. Using numerical simulations, this control law was analysed and compared to an optimal Delayed Feedback Control evidencing its advantages in theoretical and practical aspects.     

Nonlinear stochastic position and attitude filter on the Special Euclidean Group 3

This paper formulates the pose (attitude and position) estimation problem as nonlinear stochastic filter kinematics evolved directly on the Special Euclidean Group 3 ($\mathbb{SE}\left(3\right)$). This work proposes an alternate way of potential function selection and handles the problem as a stochastic filtering problem. The problem is mapped from $\mathbb{SE}\left(3\right)$ to vector form, using the Rodriguez vector and the position vector, and then followed by the definition of the pose problem in the sense of Stratonovich. The proposed filter guarantees that the errors present in position and Rodriguez vector estimates are semi-globally uniformly ultimately bounded (SGUUB) in mean square, and that they converge to small neighborhood of the origin in probability. Simulation results show the robustness and effectiveness of the proposed filter in presence of high levels of noise and bias associated with the velocity vector as well as body-frame measurements.     

Exact expressions for the bit error rate and channel capacity of a dual-hop cooperative communication systems over Nakagami-m fading channels

Cooperative diversity has been widely used in wireless communication systems since they greatly improves and enhances the quality of service as being virtual antennas without physically placing multiple antennas at the transmitter or the receiver sides. In this paper, we consider the amplify and forward (AF) relay-based communication systems under the influence of Nakagami-m multipath fading channels in both channel links. Several performance metrics are considered in this study, including, the bit error rate (BER), the ergodic channel capacity, and the outage capacity. The obtained expressions are in closed-form and can reduce to the Rayleigh channel model, as a special case. Numerical results are also provided for the obtained expressions and some conclusions are drawn.     

Infinite horizon linear quadratic Pareto game of the stochastic singular systems

This paper is concerned with the linear quadratic (LQ) Pareto game of the stochastic singular systems in infinite horizon. Firstly, the optimal control problem of the weighted sum cost functional is discussed. Utilizing the equivalent transformation method, the weighted sum LQ optimal control problem is transformed into a stochastic LQ optimization problem. Based on the classical stochastic LQ optimal control theory, the necessary and sufficient condition for the solvability of the indefinite weighted sum LQ optimal control is put forward. Then, the LQ Pareto game of the stochastic singular systems is studied. By the discussion of the convexity of the cost functionals, a sufficient condition for the existence of the Pareto solutions is obtained via the solvability of the corresponding generalized algebraic Riccati equation (GARE). Moreover, we derive all Pareto solutions based on the solution of a Lyapunov equation. Finally, an example is given to show the effectiveness of the proposed results.     

Stabilization of collective formations with speed and controller gain heterogeneity and saturation

This paper studies collective formations of multi-agent systems, modeled with unicycle dynamics, while admitting heterogeneity in both controller gains and speeds of the agents along with saturation on the controller outputs. This addresses a practical scenario where the speeds are usually nonidentical and the controller gains may vary due to imperfect implementation. The paper analyzes the effect of both heterogeneous controller gains and speeds simultaneously on the collective formations obtained by optimizing the average linear momentum of the group of agents. A detailed analysis of the two-agent system is given in the paper and some results on the locus of the collective centroid with varying controller gains are obtained. Effect of saturation is also studied for two cases when the controller gains are bounded and when the control efforts are bounded. Simulation examples are given to illustrate the theoretical findings.     

Robust observer design by sign-stability for the monitoring of population systems

Monitoring problem in population ecology can be formalized as observer design for the population system in question: Supposing that we observe only certain species considered indicators, we want to recover or estimate the whole state process of the population system, where the state vector is usually composed from the biomasses of the single populations. In the present paper, for stably coexisting population systems, a new approach to the design of the corresponding observer system is proposed which, from the knowledge of the observed indicator(s), estimates the state process with exponential convergence. In the usual observer design, an auxiliary matrix, the so-called gain matrix must be found that guarantees the mentioned exponential convergence. The novelty is in that due to the required sign-stability (or qualitative stability) of the interaction pattern, the designed observer system (i.e. the gain matrix) is robust against quantitative changes in the inter- and intra-specific interactions. (Here the interaction pattern is described by a matrix having the signs as entries, indicating the quality of the interactions within and between the considered species.) In other words, under sign-stability conditions, in the observer design the same gain matrix can be used even if, due to environmental changes, the intensities of certain interactions suffer a quantitative change in the meanwhile. The requirement of sign-stability of the interaction pattern can be considered rather natural, since in a stably coexisting population system, it means for example that a predator–prey relation does not change into a prey–predator interaction, and interactions neither appear nor disappear within the system. Our approach to robust observer design is illustrated on model population systems, such as trophic chains of type resource-producer-primary consumer-secondary consumer and Lotka–Volterra system with vertical structure. For the latter system a Lyapunov function is also constructed that guarantees the global asymptotic stability of the positive equilibrium of the considered model.     

Fault-tolerant sensorless control of wind turbines achieving efficiency maximization in the presence of electrical faults

This paper proposes a sensorless fault-tolerant control strategy solving the tracking problem of the maximum delivered power characteristic for a wind energy conversion system equipped with a permanent magnet synchronous generator. A previously published control scheme ensuring the maximum power efficiency of the wind turbine, not requiring feedback information about rotor speed and position, and about wind velocity, is here extended to make the control scheme fault-tolerant with respect to possible electrical faults affecting the equations of the permanent magnet synchronous generator (PMSG) in the original (α, β) frame. The control law is based on a number of interconnected nonlinear observers. Closed loop asymptotic vanishing of the observation errors is proved. The proposed control solution has been validated on the National Renewable Energy Laboratory (NREL) 5-MW three-blade wind turbine model.     

A class of fast fixed-time synchronization control for the delayed neural network

This paper deals with the synchronization control of a class of delayed neural networks using a fast fixed-time control theory. By employing Lyapunov stability theory, a novel sufficient criterion is derived such that two neural networks can be synchronized within a fixed-time. Compared with some existing results, the proposed controller can render two neural networks faster synchronized. A numerical example is given to demonstrate the effectiveness of the criterion.     

Using matrix norms to estimate the direction of arrival of planar waves on an ULA

SEAD method estimates the direction-of-arrival angles on an uniformly linear array based on the difference between the two largest singular values, what is called differential spectrum. Although it presented an outstanding performance, the ability to indicate the source positions was not elucidated yet. Inspired by the differential spectrum formulation we derived a total differential spectrum and found out that the matrix norm induced by the vector 2-norm of a modified spatial covariance matrix can be used to estimate the direction-of-arrival of multiple plane waves. Indeed we show that matrix norms are estimators and we propose their use instead of the singular value decomposition in SEAD-based methods. We present a general mathematical expression in order to explicit the operating principles of the proposed methods. Consequently, we were able to explain how the relation between the arriving and the search angles produces the larger peaks on the differential spectrum. To evaluate the important role played by matrix norms, a thousand experiments were carried out. They showed that the proposed approach proved to be as accurate as the previous SEAD-based methods, while providing a significant reduction on runtime. It also outperformed well-established methods like MODEX regarding the estimation error.     

Using matrix norms to estimate the direction of arrival of planar waves on an ULA

SEAD method estimates the direction-of-arrival angles on an uniform linear array based on the difference between the two largest singular values, what is called differential spectrum. Although it presented an outstanding performance, the ability to indicate the source positions was not elucidated yet. Inspired by the differential spectrum formulation we derived a total differential spectrum and found out that the matrix norm induced by the vector 2-norm of a modified spatial covariance matrix can be used to estimate the direction-of-arrival of multiple plane waves. Indeed we show that matrix norms are estimators and we propose their use instead of the singular value decomposition in SEAD-based methods. We present a general mathematical expression in order to explicit the operating principles of the proposed methods. Consequently, we were able to explain how the relation between the arriving and the search angles produces the larger peaks on the differential spectrum. To evaluate the important role played by matrix norms, a thousand experiments were carried out. They showed that the proposed approach proved to be as accurate as the previous SEAD-based methods, while providing a significant reduction on runtime. It also outperformed well-established methods like MODEX regarding the estimation error.     

The characteristics and self-time-delay synchronization of two-time-delay complex Lorenz system

Time-delay is frequently encountered in a variety of practical chaotic systems, such as chaos-communication. The behaviours of time-delay chaotic system are greatly different from those of the original system. Self-time-delay synchronization (STDS) implies that the synchronization between the time-delay system and the original system while maintaining the structure and parameters of systems unchanged, thus these various problems produced by time-delay in practice are avoided. Firstly, we investigate the characteristics of two-time-delay complex Lorenz system. Then we take one-time-delay and two-time-delay complex Lorenz system as examples, and design their controllers to realize STDS. One-time-delay complex Lorenz system is a special case of two-time-delay. Numerical simulations verify the validity of the STDS controllers. The controllers only involve error, and it is easy to realize in practice. Moreover, the time-delay chaotic system exhibits highly stochastic behaviors and unpredictable properties, which can be applied to chaos-communication and enhance the security of communication.     

Measures of generalized magnitude-squared coherence: Differences and similarities

The magnitude-squared coherence (MSC) is a measure that estimates the extent to which one real- or complex-valued signal can be predicted from another real- or complex-valued signal using a linear model. It is also used as a measure of the similarities in the frequency content of two signals. The measure is widely used in signal analysis, especially in fields such as biomedical, where a large number of signals must be processed simultaneously. It is natural to wish to generalize this idea to compare two vector-valued signals, and a variety of approaches have been proposed. This paper reviews these generalizations, presents new relationships among the measures, and demonstrates a series of results that show the similarities and dissimilarities among these measures. Some of the measures have a clear link with total interdependence; some are related to the mutual information rate. Basic results such as the various Sandwich Theorems show how the measures relate, and understanding these properties is key to an informed use of any vector generalization of MSC.