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.     

Sampled-data controllability and stabilizability of Boolean control networks: Nonuniform sampling

Derived from a simplified intelligent traffic control system, sampled-data controllability and stabilizability of Boolean control networks are considered. Compared with the existing case of uniform (periodic) sampling in Boolean control networks, the nonuniform one is more general. Using linear span with integral coefficients, the distribution of sampling points can be obtained. Then by constructing novel systems, some necessary and sufficient conditions are proposed to determine sampled-data controllability and stabilizability. Finally, two illustrative examples, which are on apoptosis networks and traffic control systems, respectively, are worked out to show the effectiveness of the obtained results.     

Stability of memristor neural networks with delays operating in the flux-charge domain

The paper considers a class of neural networks where flux-controlled dynamic memristors are used in the neurons and finite concentrated delays are accounted for in the interconnections. Goal of the paper is to thoroughly analyze the nonlinear dynamics both in the flux-charge domain and in the current-voltage domain. In particular, a condition that is expressed in the form of a linear matrix inequality, and involves the interconnection matrix, the delayed interconnection matrix, and the memristor nonlinearity, is given ensuring that in the flux-charge domain the networks possess a unique globally exponentially stable equilibrium point. The same condition is shown to ensure exponential convergence of each trajectory toward an equilibrium point in the voltage-current domain. Moreover, when a steady state is reached, all voltages, currents and power in the networks vanish, while the memristors act as nonvolatile memories keeping the result of computation, i.e., the asymptotic values of fluxes. Differences with existing results on stability of other classes of delayed memristor neural networks, and potential advantages over traditional neural networks operating in the typical voltage-current domain, are discussed.     

Compressed sensing for real measurements of quaternion signals

The paper concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct – by ?₁ norm minimization – a sparse quaternion signal from a limited number of its real linear measurements, provided the measurement matrix satisfies so-called restricted isometry property with a sufficiently small constant. We also provide error estimates for the approximated reconstruction of a non-sparse quaternion signal from noisy and noiseless data.     

A structural property of the wavelet packet transform method to localise incoherency of a signal

This paper proves a general structural property of the wavelet tree for a given seminorm in the context of the wavelet packet transform method. This structural property can be used in denoising algorithms of different applications to guarantee the optimality of novel search strategies. The property holds for any input signals using any orthogonal analysing wavelet families. The property holds for any norms, which results to be a convex function through the wavelet tree. Using a defined norms, seminorms or pseudonorms, this property can be used to detect incoherent parts of an input signal by using the minimal depth of the tree. In this sense the proposed denoising procedure works without thresholds for the localisation of different kinds of noise, as well as for a stop criterium for an optimal representation of the incoherency. The proof of this property is performed by mathematical induction and the demonstration is based on orthonormality with the help of the multiresolution framework aspects of the wavelets packet tree. The Theorem is independent of the definition of the adopted norm and of the incoherent part of an input signal. In this sense, the discovered property is a general one, which is related to any norm and any nature of the signal incoherence. It can be used in different applications, in which a minimum of a norm is required to be calculated through the wavelet tree.     

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.     

Widely linear estimation for multisensor quaternion systems with mixed uncertainties in the observations

The optimal widely linear state estimation problem for quaternion systems with multiple sensors and mixed uncertainties in the observations is solved in a unified framework. For that, we devise a unified model to describe the mixed uncertainties of sensor delays, packet dropouts and uncertain observations by using three Bernoulli distributed quaternion random processes. The proposed model is valid for linear discrete-time quaternion stochastic systems measured by multiple sensors and it allows us to provide filtering, prediction and smoothing algorithms for estimating the quaternion state through a widely linear processing. Simulation results are employed to show the superior performance of such algorithms in comparison to standard widely linear methods when mixed uncertainties are present in the observations.     

Strong delay-independent stability of linear delay systems

This paper presents a new necessary and sufficient condition for testing the strong delay-independent stability of linear systems subject to a single delay. The proposed method follows from the use of matrix polynomials constraints and the Kalman–Yakubovich–Popov lemma. The resulting condition can be checked exactly by solving a feasibility problem in terms of a linear matrix inequality (LMI). Simple numerical examples are given to show the effectiveness of the proposed method.     

Finite-time stability and stabilization of linear discrete time-varying stochastic systems

This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for the finite-time stability are presented via a state transition matrix approach. Secondly, this paper also develops the Lyapunov function method to study the finite-time stability and stabilization of discrete time-varying stochastic systems based on matrix inequalities and linear matrix inequalities (LMIs) so as to Matlab LMI Toolbox can be used.The state transition matrix-based approach to study the finite-time stability of linear discrete time-varying stochastic systems is novel, and its advantage is that the state transition matrix can make full use of the system parameter informations, which can lead to less conservative results. We also use the Lyapunov function method to discuss the finite-time stability and stabilization, which is convenient to be used in practical computations. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results.     

Chaotic behavior of discrete-time linear inclusion dynamical systems

Given any finite family of real d-by-d nonsingular matrices $\{S_1,\dots ,S_l\},$ by extending the well-known Li–Yorke chaos of a deterministic nonlinear dynamical system to a discrete-time linear inclusion or hybrid or switched system:

$\begin{array}{c}\hfill x_n\in \{S_k{x}_{n?1};1\le k\le l\},x_0\in {\mathbb{R}}^d\mathrm{and}n\ge 1,\end{array}$

we study the chaotic dynamics of the state trajectory (x_n(x₀, σ))_{n ≥ 1} with initial state $x_0\in {\mathbb{R}}^d,$ governed by a switching law $\sigma :\mathbb{N}\to \{1,\dots ,l\}$. Two sufficient conditions are given so that for a “large” set of switching laws σ, there exhibits the scrambled dynamics as follows: for all $x_0,y_0\in {\mathbb{R}}^d,x_0\ne y_0,$

$\begin{array}{c}\hfill \underset{n\to +\infty }{lim\; inf}\parallel x_n(x_0,\sigma )?x_n(y_0,\sigma )\parallel =0\mathrm{and}\underset{n\to +\infty }{lim\; sup}\parallel x_n(x_0,\sigma )?x_n(y_0,\sigma )\parallel =\infty .\end{array}$

This implies that there coexist positive, zero and negative Lyapunov exponents and that the trajectories (x_n(x₀, σ))_{n ≥ 1} are extremely sensitive to the initial states $x_0\in {\mathbb{R}}^d$. We also show that a periodically stable linear inclusion system, which may be product unbounded, does not exhibit any such chaotic behavior. An explicit simple example shows the discontinuity of Lyapunov exponents with respect to the switching laws.     

Leaderless consensus of multi-agent systems via an event-triggered strategy under stochastic sampling

This paper investigates mean square leaderless consensus of networked nonlinear multi-agent systems. An efficient distributed event-triggered mechanism based on stochastic sampling is introduced to reduce the communication cost and controller updates. The stochastic sampling interval randomly switches between two given values. Mean square consensus criteria for multi-agent systems with strongly connected networks or networks containing directed spanning trees are derived, respectively. Moreover, the case with a special event-triggered weighting matrix and the case without even-triggered strategies are also discussed. Finally, an example is given to verify the theoretical results.     

Stability of mode-dependent linear switched singular systems with stable and unstable subsystems

This paper studies the E-exponential stability of mode-dependent linear switched singular systems with stable and unstable subsystems. First, by constructing an appropriate multiple discontinuous Lyapunov function, new sufficient conditions of E-exponential stability for linear switched singular systems are established. Considering the feature of mode-dependent average dwell time switching, we adopt the switching strategy where fast switching and slowing switching are respectively applied to unstable and stable subsystems. Compared with the existing results, our approach is more flexible and tighter bounds can be obtained. Finally, a numerical example is provided to illustrate the effectiveness of the proposed criteria.     

Network-based PI control for output tracking of continuous-time systems with time-varying sampling and network-induced delays

For a continuous-time linear system with constant reference input, the network-based proportional-integral (PI) control is developed to solve the output tracking control problem by taking time-varying sampling and network-induced delays into account. A traditional PI control system is introduced to obtain the equilibriums of state and control input. Using the equilibriums, a discrete-time PI tracking controller in a network environment is constructed. The resulting network-based PI control system is described by an augmented system with two input delays and the output tracking objective is transformed into ensuring asymptotic stability of the augmented system. A delay-dependent stability condition is established by a discontinuous augmented Lyapunov–Krasovskii functional approach. The PI controller design result of in-wheel motor as a case study is provided in terms of linear matrix inequalities. Matlab simulation and experimental results resorting to a test-bed for ZigBee-based control of in-wheel motor are given to validate the proposed method.     

Stabilization of switched linear singular systems with state reset

This paper investigates the stability and stabilization of switched linear singular systems with state reset at switching instants. Based on the dynamics decomposition of singular subsystems, a sufficient stability condition for the system with the given state reset is obtained. Then, the stabilization problem by state reset is investigated and an algorithm for computing the reset matrices is presented. The obtained results extend some previous works on both singular switched systems and reset control for normal switched systems. Finally, a numerical example is presented to illustrate the effectiveness of the proposed approach.     

Uniform exponential stability of periodic discrete switched linear system

Let {Π_τ(m, n): m?≥?n?≥?0} be the family of periodic discrete transition matrices generated by bounded valued square matrices Λ_τ(n), where $\tau :[0,1,2,?)\to \Omega$ is an arbitrary switching signal. We prove that the family {Π_τ(m, n): m?≥?n?≥?0} of bounded linear operator is uniformly exponentially stable if and only if the sequence $n?{\sum }_{k=0}^n{e}^{i\alpha k}{\Pi }_{\tau }(n,k)w\left(k\right):{\mathbb{Z}}_{+}\to \mathbb{R}$ is bounded.     

Subspace predictive control with the data-driven event-triggered law for linear time-invariant systems

In this paper, a subspace predictive control (SPC) method with a novel data-driven event-triggered law is proposed for linear time-invariant systems with unknown model parameters. Based on the conventional SPC method, the event-triggered law is introduced to substitute the typical receding horizon optimization, which reduces the data computation load of the traditional SPC method. The key parameters of the event-triggered law are derived by the Q-learning method via system data and the input-to-state stability of the system can be ensured with the designed event-triggered law. The simulation results illustrate the effect and merits of the proposed method with comparisons.     

Truncation error analysis in computing of SEP and SEP floor for partially coherent receiver of MPSK signals over composite fading channels

In this paper, we analyze detection of multilevel phase-shift keying (MPSK) signals transmitted over a Gamma shadowed Nakagami-m fading channel. We derive novel analytical expression, in terms of Meijer’s G function, for Fourier coefficients of the probability density function of the received signal composite phase. Under the assumption of the imperfect reference signal extraction in the receiver, which is performed from the pilot signal, the analytical expression is derived for the symbol error probability (SEP) in the form of convergent series. The existence of the error floor is identified, and expression for its computation is provided. Mathematical proofs for convergence of Fourier series are provided for both SEP and SEP floor, and novel expressions of upper bounds for truncation errors are derived in terms of elementary mathematical functions. The convergence rate of the derived expressions is examined. Numerical results are confirmed independently by Monte-Carlo simulations.     

Reachable set estimation for linear systems with time-varying delay and polytopic uncertainties

This study is concerned with the problem of reachable set estimation for linear systems with time-varying delays and polytopic parameter uncertainties. Our target is to find an ellipsoid that contains the state trajectory of linear system as small as possible. Specifically, first, in order to utilize more information about the state variables, the RSE problem for time-delay systems is solved based on an augmented Lyapunov-Krasovskii functional. Second, by dividing the time-varying delay into two non-uniformly subintervals, more general delay-dependent stability criteria for the existence of a desired ellipsoid are derived. Third, the integral interval is decomposed in the same way to estimate the bounds of integral terms more exactly. Fourth, an optimized integral inequality is used to deal with the integral terms, which is based on distinguished Wirtinger integral inequality and Reciprocally convex combination inequality. This can be regard as a new method in the delay systems. Finally, three numerical examples are presented to demonstrate the effectiveness and merits of the theoretical results.     

Iterative learning control for linear delay systems with deterministic and random impulses

This paper investigates convergence of iterative learning control for linear delay systems with deterministic and random impulses by virtute of the representation of solutions involving a concept of delayed exponential matrix. We address linear delay systems with deterministic impulses by designing a standard P-type learning law via rigorous mathematical analysis. Next, we extend to consider the tracking problem for delay systems with random impulses under randomly varying length circumstances by designing two modified learning laws. We present sufficient conditions for both deterministic and random impulse cases to guarantee the zero-error convergence of tracking error in the sense of Lebesgue-p norm and the expectation of Lebesgue-p norm of stochastic variable, respectively. Finally, numerical examples are given to verify the theoretical results.