Smoothed L1/2 regularizer learning for split-complex valued neuro-fuzzy algorithm for TSK system and its convergence results

This paper investigates an evolving split-complex valued neuro-fuzzy (SCVNF) algorithm for Takagi–Sugeno–Kang (TSK) system. In a bid to avoid the contradiction between boundedness and analyticity, splitting technique is traditionally employed to independently process the real part and the imaginary part of weight parameters in the system, which doubles weight dimension and causes oversized structure. For improving efficiency of structural optimization, previous studies have revealed that L_1/2-norm regularizer can be effective in such sparse tasks thus is regarded as a representative of L_q (0?<?q?<?1) regularizer. To eliminate oscillation phenomenon and stabilize training procedure, a smoothed L_1/2 regularizer learning is facilitated by smoothing the original one at the origin flexibly. It is rigorously proved that the real-valued cost function is monotonic decreasing during learning course, and the sum of gradient norm trends closer to zero. Plus some very general condition, the weight sequence itself is also convergent to a fixed point. Experimental results for the SCVNF are demonstrated, which match the theoretical analysis.     

Observer-based fault detection for uncertain nonlinear systems

This paper addresses L₂ observer-based fault detection issues for a class of nonlinear systems in the presence of parametric and dynamic uncertainties, respectively. To this end, three different types of uncertain affine nonlinear system models studied in this paper are described first. Then, the integrated design schemes of L₂ observer-based fault detection systems are derived with the aid of Hamilton–Jacobi inequalities (HJIs), respectively. Numerical examples are also provided in the end to demonstrate the effectiveness of the proposed results.     

Multiple-prespecified-dictionary sparse representation for compressive sensing image reconstruction with nonconvex regularization

Multiple-prespecified-dictionary sparse representation (MSR) has shown powerful potential in compressive sensing (CS) image reconstruction, which can exploit more sparse structure and prior knowledge of images for minimization. Due to the popular L₁ regularization can only achieve the suboptimal solution of L₀ regularization, using the nonconvex regularization can often obtain better results in CS reconstruction. This paper proposes a nonconvex adaptive weighted L_p regularization CS framework via MSR strategy. We first proposed a nonconvex MSR based L_p regularization model, then we propose two algorithms for minimizing the resulting nonconvex L_p optimization problem. According to the fact that the sparsity levels of each regularizers are varying with these prespecified-dictionaries, an adaptive scheme is proposed to weight each regularizer for optimization by exploiting the difference of sparsity levels as prior knowledge. Simulated results show that the proposed nonconvex framework can make a significant improvement in CS reconstruction than convex L₁ regularization, and the proposed MSR strategy can also outperforms the traditional nonconvex L_p regularization methodology.     

L1-gain analysis and control of impulsive positive systems with interval uncertainty and time delay

This paper investigates L₁-gain analysis and control of impulsive positive systems (IPSs) with interval uncertainty and time delay. For different types of impulsive effect, by means of the Razumikhin techniques and Lyapunov function theory, conditions are developed for guaranteeing the robust exponential stability with L₁-gain performance. Then the positive stabilization with L₁-gain performance is also addressed for IPSs with interval uncertainty and time delay through the state feedback control. In addition, the way to explore the minimum L₁-gain is discussed. All the obtained conditions can be easily inspected by the linear programming (LP) method when some parameters are preset. Finally, simulations are provided to demonstrate the validity of the theoretical results.     

Stability analysis of linear continuous-time delay-difference systems with multiple time-delays

This paper is concerned with the stability analysis of linear continuous-time delay-difference systems with multiple delays. Firstly, a new method for testing the L₂-exponential stability of the considered system is proposed, which is easier to use than the one in the existing literature. In view of the conservatism and the complexity of the obtained stability conditions in the existing literature, a complete Lyapunov–Krasovskii functional (LKF) is constructed by analyzing the relationship among the multiple delays. Sufficient conditions for both L₂-exponential stability and exponential stability are then derived based on the constructed LKFs, which are delay-independent. Exponential convergence rate for the considered system is also investigated by a new method, which is shown to be equivalent to the existing approach by using weighted LKFs. Robust stability under parameter uncertainties is also investigated. Numerical examples are provided to demonstrate the effectiveness and less conservativeness of the proposed method.     

Stability and L1-gain analysis for switched positive T–S fuzzy systems under asynchronous switching

This paper is concerned with the exponential stability and L₁-gain analysis problem for switched positive T–S fuzzy systems under both time-varying delays and asynchronous switching. By permitting the increase of the designed multiple Lyapunov functionals during the running time of the activated subsystem, solvable conditions for the stability and L₁-gain are developed by adopting the mode-dependent average dwell time (MDADT) technique. The desired controllers guaranteeing the stability and the L₁-gain performance are designed based on the obtained solvable conditions. An example is given to demonstrate the effectiveness of the proposed methods.     

Event-based weighted residual generator design via non-PDC scheme for fault diagnosis in T–S fuzzy systems

This paper is concerned with the event-based weighted residual generator design via non-parallel distribution compensation (PDC) scheme for fault diagnosis in discrete-time T–S fuzzy systems, under consideration of the imperfect premise matching membership functions. An event-triggered mechanism is firstly introduced to save communication resources, which leads to the premise variables of the system and observer to be asynchronous. Then, a fuzzy diagnostic observer with mismatched premise variables is designed to estimate the unmeasurable states of the system. Moreover, by using non-PDC method, a diagnostic observer-based weighted residual generator is established to improve the fault detection (FD) performance by using the information provided by each local system, in which the membership functions structure of the diagnostic observer and residual generator need not to be the same as the systems, and the L_∞/L₂ and L_∞ FD scheme is used to optimize the FD performance. Finally, two simulation results are provided to show the efficiency of the proposed non-PDC method.     

Stability, L1-gain analysis and asynchronous L1-gain control of uncertain discrete-time switched positive linear systems with dwell time

In this paper, the stability, L₁-gain analysis and asynchronous L₁-gain control problems of uncertain discrete-time switched positive linear systems (DSPLSs) with dwell time are investigated. First, several convex and non-convex conditions on dwell time stability of DSPLSs with interval and polytopic uncertainties are presented, and the relation between these conditions is revealed. Then, via a switched dwell-time-dependent co-positive Lyapunov functions (SDTLFs) approach, convex sufficient conditions on L₁-gain analysis and asynchronous L₁-gain control of DSPLSs with interval uncertainties are derived. Meanwhile, via the switched parameter-dwell-time-dependent co-positive Lyapunov functions (SPDTLFs) approach, the L₁-gain analysis and asynchronous L₁-gain controller design problems of DSPLSs with polytopic uncertainties are also solved. The stability and L₁-gain analysis results are given in terms of linear programming (LP). The controller design results are presented in terms of bilinear programming (BP), which can be solved with the help of iterative algorithm. At last, both numerical and practical examples are provided to show the effectiveness of the results.     

Finite-size scaling of O(n) systems at the upper critical dimensionality

Logarithmic finite-size scaling of the O(n) universality class at the upper critical dimensionality (d_c = 4) has a fundamental role in statistical and condensed-matter physics and important applications in various experimental systems. Here, we address this long-standing problem in the context of the n-vector model (n = 1, 2, 3) on periodic four-dimensional hypercubic lattices. We establish an explicit scaling form for the free-energy density, which simultaneously consists of a scaling term for the Gaussian fixed point and another term with multiplicative logarithmic corrections. In particular, we conjecture that the critical two-point correlation g(r, L), with L the linear size, exhibits a two-length behavior: follows governed by the Gaussian fixed point at shorter distances and enters a plateau at larger distances whose height decays as with a logarithmic correction exponent. Using extensive Monte Carlo simulations, we provide complementary evidence for the predictions through the finite-size scaling of observables, including the two-point correlation, the magnetic fluctuations at zero and nonzero Fourier modes and the Binder cumulant. Our work sheds light on the formulation of logarithmic finite-size scaling and has practical applications in experimental systems.     

Stability and L2-gain analysis for switched neutral systems with mixed time-varying delays

This paper considers the stability and L₂-gain for a class of switched neutral systems with time-varying discrete and neutral delays. Some new delay-dependent sufficient conditions for exponential stability and weighted L₂-gain are developed for a class of switching signals with average dwell time. These conditions are formulated in terms of linear matrix inequalities (LMIs) and are derived by employing free weighting matrices method. As a special case of such switching signals, we can obtain exponential stability and normal L₂-gain under arbitrary switching signals. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results.     

Vector incremental L2-gain and incremental stability for switched nonlinear systems

This paper studies vector incremental L₂-gain and incremental stability for switched nonlinear systems using individual incremental gains and multiple storage functions. Firstly, a vector incremental L₂-gain concept for switched nonlinear systems is proposed. Each subsystem is not required to have incremental L₂-gain, but it has its own incremental L₂-gain and the related storage function, when it is active. The transformation of “energy” from the active subsystem to each inactive subsystem is characterized by cross-supply rates. Then, we show that a switched nonlinear system who has vector incremental L₂-gain can be incrementally stabilized under some constraints on the energy change of inactive subsystems. Secondly, a state-dependent switching law is designed to achieve vector incremental L₂-gain, even if each subsystem does not have incremental L₂-gain in the classic sense. Thirdly, each switched system is not required to have vector incremental L₂-gain, but the feedback interconnection of switched nonlinear systems is incrementally stabilized by the design of a composite switching law. The switching law allows the two switched systems switch asynchronously. Two examples are provided to verify the effectiveness of the proposed method.     

Label-free viscosity measurement of complex fluids using reversal flow switching manipulation in a microfluidic channel

The accurate viscosity measurement of complex fluids is essential for characterizing fluidic behaviors in blood vessels and in microfluidic channels of lab-on-a-chip devices. A microfluidic platform that accurately identifies biophysical properties of blood can be used as a promising tool for the early detections of cardiovascular and microcirculation diseases. In this study, a flow-switching phenomenon depending on hydrodynamic balancing in a microfluidic channel was adopted to conduct viscosity measurement of complex fluids with label-free operation. A microfluidic device for demonstrating this proposed method was designed to have two inlets for supplying the test and reference fluids, two side channels in parallel, and a junction channel connected to the midpoint of the two side channels. According to this proposed method, viscosities of various fluids with different phases (aqueous, oil, and blood) in relation to that of reference fluid were accurately determined by measuring the switching flow-rate ratio between the test and reference fluids, when a reverse flow of the test or reference fluid occurs in the junction channel. An analytical viscosity formula was derived to measure the viscosity of a test fluid in relation to that of the corresponding reference fluid using a discrete circuit model for the microfluidic device. The experimental analysis for evaluating the effects of various parameters on the performance of the proposed method revealed that the fluidic resistance ratio (R_JL/R_L, fluidic resistance in the junction channel (R_JL) to fluidic resistance in the side channel (R_L)) strongly affects the measurement accuracy. The microfluidic device with smaller R_JL/R_L values is helpful to measure accurately the viscosity of the test fluid. The proposed method accurately measured the viscosities of various fluids, including single-phase (Glycerin and plasma) and oil-water phase (oil vs. deionized water) fluids, compared with conventional methods. The proposed method was also successfully applied to measure viscosities of blood with varying hematocrits, chemically fixed RBC_S, and channel sizes. Based on these experimental results, the proposed method can be effectively used to measure the viscosities of various fluids easily, without any fluorescent labeling and tedious calibration procedures.     

Sampled-data distributed H∞ control of a class of 1-D parabolic systems under spatially point measurements

This paper considers the sampled-data distributed $H_{\infty }$ control problem for 1-D semilinear transport reaction equations with external disturbances. It is assumed that a finite number of point spatial state measurements are available. A Razumikhin-type approach is developed for stability and L₂-gain analysis of the closed-loop system. In contrast to Halanay?s inequality based approach, the proposed Razumikhin-type approach not only provides a subtle decay estimate of the selected Lyapunov functional, but also guarantees the $H_{\infty }$ performance index to be negative if certain conditions are satisfied. By introducing a time-dependent Lyapunov functional combined with the use of Wirtinger?s inequality, sufficient conditions for the internal exponential stability and finite L₂-gain are derived in terms of linear matrix inequalities. The obtained conditions establish a quantitative relation among the upper bounds on the spatial sampling intervals and the time sampling intervals, and L₂-gain. Two numerical examples are provided to illustrate the usefulness of the proposed theoretical results.     

Growth dynamics of citations of cumulative papers of individual authors according to progressive nucleation mechanism: Concept of citation acceleration

Using data generated by progressive nucleation mechanism on the cumulative fraction of citations of individual papers published successively by a hypothetical author, an expression for the time dependence of the cumulative number L_sum(t) of citations of progressively published papers is proposed. It was found that, for all nonzero values of constant publication rate ΔN, the cumulative citations L_sum(t) of the cumulative N papers published by an author in his/her entire publication career spanning over T years may be represented in distinct regions: (1) in the region 0 < t < Θ₀ (where Θ₀ ≈ T/3), L_sum(t) slowly increases proportionally to the square of the citation time t, and (2) in the region t > Θ₀, L_sum(t) approaches a constant L_sum(max) at T. In the former region, the time dependence of L_sum(t) of an author is associated with three parameters, viz. the citability parameter λ₀, the publication rate ΔN and his/her publication career t. Based on the predicted dependence of L_sum(t) on t, a useful scientometric age-independent measure, defined as citation acceleration a = L_sum(t)/t², is suggested to analyze and compare the scientific activities of different authors. Confrontation of the time dependence of cumulative number L_sum(t) of citations of papers with the theoretical equation reveals one or more citation periods during the publication careers of different authors.     

Effect of L-carnitine Supplementation on Nutritional Status and Physical Performance Under Calorie Restriction

L-carnitine is popular as a potential ergogenic aid because of its role in the conversion of fat into energy. The present study was undertaken to investigate the effect of short term supplementation of L-carnitine on metabolic markers and physical efficiency tests under short term calorie restriction. Male albino rats were divided into four groups (n = 12 in each)—control, calorie restricted (CR for 5 days, 25 % of basal food intake), L-carnitine supplemented (CAR, given orally for 5 days at a dose of 100 mg/kg), CR with L-carnitine supplementation (CR + CAR). Food intake and body weight of the rats were measured along with biochemical variables like blood glucose, tissue glycogen, plasma and muscle protein and enzymatic activities of CPT-1 (carnitine palmitoyl transferase-1) and AMP kinase. Results demonstrated that L-carnitine caused marked increase in muscle glycogen, plasma protein, CPT-1 activity and swim time of rats (P < 0.05) on short term supplementation. In addition to the substantive effects caused by CR alone, L-carnitine under CR significantly affected muscle glycogen, plasma protein, CPT-1 activity and AMP kinase (P < 0.05). Short term CR along with L-carnitine also resulted in increased swim time of rats than control, CR and L-carnitine treated rats (P < 0.05). The present study was an attempt towards developing an approach for better adherence to dietary restriction regimen, with the use of L-carnitine.     

H∞ output-feedback control for discrete-time switched linear systems via asynchronous switching

In this paper, we consider the H_∞ hybrid dynamical output-feedback control problem for discrete-time switched linear systems under asynchronous switching. A time-varying multiple Lyapunov-like-function (MLF) approach is applied to derive sufficient conditions that guarantee the stability and weighted l₂-gain performance of the closed-loop systems, where the established conditions explicitly depend on the upper and lower bounds of asynchronous switching delays. An alternative approach is proposed to decouple the bilinear problems of the control synthesis conditions. Convex optimization algorithms are also proposed based on the established conditions to determine the minimum l₂-gain performance. Two numerical examples are provided to illustrate the effectiveness of the proposed method, demonstrating significant improvement over the existing results.     

Fixed point properties of the binomial function

Fixed point properties of the binomial function

are developed. It is shown that for any 1 < L < N, T^L_Nhas a unique fixed point p? in (0, 1), and that for large N, the fixed point is L/N. This has application to signal detection schemes commonly used in communication systems. When detecting the presence or absence of a signal with an initial false alarm probability p_FAand an initial detection probability p_D, then T^L_N(p_FA) < p_FAand T^L_N(p_D) > p_Dif, and only if, p_FA < p? < p_D. When this condition is satisfied, as N → ∞, T^L_N(p_FA) → 0 and T^L_N(p_D → 1.     

Stabilities and Settling Times of Nonlinear and Time-varying Feedback Systems

The bounded-input bounded-output stability, finite time stability and settling time of a single-loop feedback system consisting of a nonlinear time-varying gain followed by a linear time-invariant system are investigated via a nonlinear integral inequality. The gain has the form k₀+k₁(t)+k₂(t)g(bd) where g(bd) is a monotonic increasing function. The system is bounded-input bounded-output stable provided the time-varying gains are L¹(0, t8) functions and is finite time stable for bounded gains. The nonlinear integral inequality, which is used to obtain explicit and useful bounds on the output of the system, is also employed to determine the settling time.     

The solutions of vibration control problems using artificial neural networks

This paper introduces an alternative method artificial neural networks (ANN) used to obtain numerical solutions of mathematical models of dynamic systems, represented by ordinary differential equations (ODEs) and partial differential equations (PDEs). The proposed trial solution of differential equations (DEs) consists of two parts: The initial and boundary conditions (BCs) should be satisfied by the first part. However, the second part is not affected from initial and BCs, but it only tries to satisfy DE. This part involves a feedforward ANN containing adjustable parameters (weight and bias). The proposed solution satisfying boundary and initial condition uses a feedforward ANN with one hidden layer varying the neuron number in the hidden layer according to complexity of the considered problem. The ANN having appropriate architecture has been trained with backpropagation algorithm using an adaptive learning rate to satisfy DE. Moreover, we have, first, developed the general formula for the numerical solutions of nth-order initial-value problems by using ANN.For numerical applications, the ODEs that are the mathematical models of linear and non-linear mass-damper-spring systems and the second- and fourth-order PDEs that are the mathematical models of the control of longitudinal vibrations of rods and lateral vibrations of beams have been considered. Finally, the responses of the controlled and non-controlled systems have been obtained. The obtained results have been graphically presented and some conclusion remarks are given.     

Extended dissipative analysis for uncertain T–S fuzzy system with time-varying delay and randomly occurring gain variations

This paper is concerned with the non-fragile dynamic output feedback control for uncertain T–S fuzzy systems with time-varying delay and randomly occurring gain variations (ROGVs). Considering the imperfect premise matching that the T–S fuzzy model and the fuzzy controller do not have the same membership function, the purpose is to enhance the robustness of the system and the flexibility of the controller design. By adjusting the free weight matrix in the concept of extended dissipative, H_∞, $L_2-L_{\infty },$ passive and (Q, S, R)-dissipative performance are solved in a unified framework. Stochastic phenomenon ROGVs is considered to describe the impact of the controller gain variations in the system, which is designed into two sequences of random variables and obey the Bernoulli distribution. Based on Lyapunov–Krasovskii functional (LKF) and integral inequality technique, some less conservative sufficient conditions are obtained to guarantee the close-loop system is asymptotically stable and extended dissipative. By solving the linear matrix inequalities (LMIs), a non-fragile dynamic output feedback controller can be developed. The advantage and effectiveness of the proposed design method can be illustrated by several numerical examples.