This paper shows how to obtain the values of the numerator and denominator Kharitonov polynomials of an interval plant from its value set at a given frequency. Moreover, it is proven that given a value set, all the assigned polynomials of the vertices can be determined if and only if there is a complete edge or a complete arc lying on a quadrant. This algorithm is nonconservative in the sense that if the value-set boundary of an interval plant is exactly known, and particularly its vertices, then the Kharitonov rectangles are exactly those used to obtain these value sets.

The solution of least squares support vector machines (LS-SVMs) is characterized by a specific linear system, that is, a saddle point system. Approaches for its numerical solutions such as conjugate methods Sykens and Vandewalle (1999) and null space methods Chu et al. (2005) have been proposed. To speed up the solution of LS-SVM, this paper employs the minimal residual (MINRES) method to solve the above saddle point system directly. Theoretical analysis indicates that the MINRES method is more efficient than the conjugate gradient method and the null space method for solving the saddle point system. Experiments on benchmark data sets show that compared with mainstream algorithms for LS-SVM, the proposed approach significantly reduces the training time and keeps comparable accuracy. To heel, the LS-SVM based on MINRES method is used to track a practical problem originated from blast furnace iron-making process: changing trend prediction of silicon content in hot metal. The MINRES method-based LS-SVM can effectively perform feature reduction and model selection simultaneously, so it is a practical tool for the silicon trend prediction task.

A novel fault detection technique is proposed to explicitly account for the nonlinear, dynamic, and multimodal problems existed in the practical and complex dynamic processes. Just-in-time (JIT) detection method and k-nearest neighbor (KNN) rule-based statistical process control (SPC) approach are integrated to construct a flexible and adaptive detection scheme for the control process with nonlinear, dynamic, and multimodal cases. Mahalanobis distance, representing the correlation among samples, is used to simplify and update the raw data set, which is the first merit in this paper. Based on it, the control limit is computed in terms of both KNN rule and SPC method, such that we can identify whether the current data is normal or not by online approach. Noted that the control limit obtained changes with updating database such that an adaptive fault detection technique that can effectively eliminate the impact of data drift and shift on the performance of detection process is obtained, which is the second merit in this paper. The efficiency of the developed method is demonstrated by the numerical examples and an industrial case.

This paper presents a modelling of an unmanned airship. We are studying a quadrotor flying wing. The modelling of this airship includes an aerodynamic study. A special focus is done on the computation of the added masses. Considering that the velocity potential of the air surrounding the airship obeys the Laplace's equation, the added masses matrix will be determined by means of the velocity potential flow theory. Typically, when the shape of the careen is quite different from that of an ellipsoid, designers in preprocessing prefer to avoid complications arising from mathematical analysis of the velocity potential. They use either complete numerical studies, or geometric approximation methods, although these methods can give relatively large differences compared to experimental measurements performed on the airship at the time of its completion. We tried to develop here as far as possible the mathematical analysis of the velocity potential flow of this unconventional shape using certain assumptions. The shape of the careen is assumed to be an elliptic cone. To retrieve the velocity potential shapes, we use the spheroconal coordinates. This leads to the Lamé's equations. The whole system of equations governing the interaction air-structure, including the boundary conditions, is solved in an analytical setting.

In this study, a gene positive network is proposed based on a weighted undirected graph, where the weight represents the positive correlation of the genes. A Pearson agglomerative clustering algorithm is employed to build a clustering tree, where dotted lines cut the tree from bottom to top leading to a number of subsets of the modules. In order to achieve better module partitions, the Pearson correlation coefficient modularity is addressed to seek optimal module decomposition by selecting an optimal threshold value. For the liver cancer gene network under study, we obtain a strong threshold value at 0.67302, and a very strong correlation threshold at 0.80086. On the basis of these threshold values, fourteen strong modules and thirteen very strong modules are obtained respectively. A certain degree of correspondence between the two types of modules is addressed as well. Finally, the biological significance of the two types of modules is analyzed and explained, which shows that these modules are closely related to the proliferation and metastasis of liver cancer. This discovery of the new modules may provide new clues and ideas for liver cancer treatment.

According to the integrated pest management strategies, we propose a model for pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove the existence of order one periodic solution of such system, and further, the attractiveness of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results. Our results show that our method used in this paper is more efficient and easier than the existing ones for proving the existence of order one periodic solution.

A theoretical model of the drug release process from polymeric microparticles (a particular type of polymer matrix), through dispersive fractal approximation of motion, is built. As a result, the drug release process takes place through cnoidal oscillations modes of a normalized concentration field. This indicates that, in the case of long-time-scale evolutions, the drug particles assemble in a lattice of nonlinear oscillators occur macroscopically, through variations of drug concentration. The model is validated by experimental results.

Control of fluid flow is an important, underutilized process possessing potential benefits ranging from avoidance of separation and stall on aircraft wings to reduction of friction in oil and gas pipelines to mitigation of noise from wind turbines. But the Navier-Stokes (N.-S.) equations, whose solutions describe such flows, consist of a system of time-dependent, multidimensional, nonlinear partial differential equations (PDEs) which cannot be solved in real time using current computing hardware. The poor man's Navier-Stokes (PMNS) equations comprise a discrete dynamical system that is algebraic—hence, easily (and rapidly) solved—and yet which retains many (possibly all) of the temporal behaviors of the PDE N.-S. system at specific spatial locations. Herein, we outline derivation of these equations and discuss their basic properties. We consider application of these equations to the control problem by adding a control force. We examine the range of behaviors that can be achieved by changing this control force and, in particular, consider controllability of this (nonlinear) system via numerical experiments. Moreover, we observe that the derivation leading to the PMNS equations is very general and may be applied to a wide variety of problems governed by PDEs and (possibly) time-delay ordinary differential equations such as, for example, models of machining processes.

Travel time estimation in urban arterials is challenging compared to freeways and multilane highways. This becomes more complex under Indian conditions due to the additional issues related to heterogeneity, lack of lane discipline, and difficulties in data availability. The fact that most of the urban arterials in India do not employ automatic detectors demands the need for an effective, yet less data intensive way of estimating travel time. An attempt has been made in this direction to estimate total travel time in an urban road stretch using the location based flow data and sparse travel time data obtained using GPS equipped probe vehicles. Three approaches are presented and compared in this study: (1) a combination of input-output analysis for mid-blocks and Highway Capacity Manual (HCM) based delay calculation at signals named as base method, (2) data fusion approach which employs Kalman filtering technique (nonhybrid method), and (3) a hybrid data fusion HCM (hybrid DF-HCM) method. Data collected from a stretch of roadway in Chennai, India was used for the corroboration. Simulated data were also used for further validation. The results showed that when data quality is assured (simulated data) the base method performs better. However, in real field situations, hybrid DF-HCM method outperformed the other methods.

The prediction of the aero-engine performance parameters is very important for aero-engine condition monitoring and fault diagnosis. In this paper, the chaotic phase space of engine exhaust temperature (EGT) time series which come from actual air-borne ACARS data is reconstructed through selecting some suitable nearby points. The partial least square (PLS) based on the cubic spline function or the kernel function transformation is adopted to obtain chaotic predictive function of EGT series. The experiment results indicate that the proposed PLS chaotic prediction algorithm based on biweight kernel function transformation has significant advantage in overcoming multicollinearity of the independent variables and solve the stability of regression model. Our predictive NMSE is 16.5 percent less than that of the traditional linear least squares (OLS) method and 10.38 percent less than that of the linear PLS approach. At the same time, the forecast error is less than that of nonlinear PLS algorithm through bootstrap test screening.

This paper considers a multiitem inventory model with unknown demand rate coefficients. An adaptive control approach with a nonlinear feedback is applied to track the output of the system toward the inventory goal level. The Lyapunov technique is used to prove the asymptotic stability of the adaptive controlled system. Also, the updating rules of the unknown demand rate coefficients are derived from the conditions of the asymptotic stability of the perturbed system. The linear stability analysis of the model is discussed. The adaptive controlled system is modeled by a system of nonlinear differential equations, and its solution is discussed numerically.

We propose a metapopulation model for malaria with two control variables, treatment and prevention, distributed between $n$ different patches (localities). Malaria spreads between these localities through human travel. We used the theory of optimal control and applied a mathematical model for three connected patches. From previous studies with the same data, two patches were identified as reservoirs of malaria infection, namely, the patches that sustain malaria epidemic in the other patches. We argue that to reduce the number of infections and semi-immunes (i.e., asymptomatic carriers of parasites) in overall population, two considerations are needed, (a) For the reservoir patches, we need to apply both treatment and prevention to reduce the number of infections and to reduce the number of semi-immunes; neither the treatment nor prevention were specified at the beginning of the control application, except prevention that seems to be effective at the end. (b) For unreservoir patches, we should apply the treatment to reduce the number of infections, and the same strategy should be applied to semi-immune as in (a).

The dynamic behaviors of a predator-prey (pest) model with disease in prey and involving an impulsive control strategy to release infected prey at fixed times are investigated for the purpose of integrated pest management. Mathematical theoretical works have been pursuing the investigation of the local asymptotical stability and global attractivity for the semitrivial periodic solution and population persistent, which depicts the threshold expression of some critical parameters for carrying out integrated pest management. Numerical analysis indicates that the impulsive control strategy has a strong effect on the dynamical complexity and population persistent using bifurcation diagrams and power spectra diagrams. These results show that if the release amount of infective prey can satisfy some critical conditions, then all biological populations will coexist. All these results are expected to be of use in the study of the dynamic complexity of ecosystems.

This paper presents Pareto design of decoupled sliding-mode controllers based on a multiobjective genetic algorithm for several fourth-order coupled nonlinear systems. In order to achieve an optimum controller, at first, the decoupled sliding mode controller is applied to stablize the fourth-order coupled nonlinear systems at the equilibrium point. Then, the multiobjective genetic algorithm is applied to search the optimal coefficients of the decoupled sliding-mode control to improve the performance of the control system. Considered objective functions are the angle and distance errors. Finally, the simulation results implemented in the MATLAB software environment are presented for the inverted pendulum, ball and beam, and seesaw systems to assure the effectiveness of this technique.

The synchronization of coupled networks with mixed delays is investigated by employing Lyapunov functional method and intermittent control. A sufficient condition is derived to ensure the global synchronization of coupled networks, which is controlled by the designed intermittent controller. Finally, a numerical simulation is constructed to justify the theoretical analysis.

An investigation is carried out on the systematic analysis of the dynamic behavior of the hybrid squeeze-film damper (HSFD) mounted a rotor-bearing system with strongly nonlinear oil-film force and nonlinear rub-impact force in the present study. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless rotating speed ratio as control parameters. The onset of chaotic motion is identified from the phase diagrams, power spectra, Poincaré maps, bifurcation diagrams, maximum Lyapunov exponents, and fractal dimension of the rotor-bearing system. The dynamic behaviors are unlike the usual ways into chaos ($1T\Rightarrow 2T\Rightarrow 4T\Rightarrow 8T\Rightarrow 16T\Rightarrow 32T\cdots \Rightarrow$ chaos or periodic $\Rightarrow$ quasi-periodic $\Rightarrow$ chaotic), it suddenly gets in chaos from the periodic motion without any transition. The results presented in this study provide some useful insights into the design and development of a rotor-bearing system for rotating machinery that operates in highly rotating speed and highly nonlinear regimes.

A recursive gradient identification algorithm based on the bundle method for sandwich systems with backlash-like hysteresis is presented in this paper. In this method, a dynamic parameter estimation scheme based on a subgradient is developed to handle the nonsmooth problem caused by the backlash embedded in the system. The search direction of the algorithm is estimated based on the so-called bundle method. Then, the convergence of the algorithm is discussed. After that, simulation results on a nonsmooth sandwich system are presented to validate the proposed estimation algorithm. Finally, the application of the proposed method to an X-Y moving positioning stage is illustrated.

Based on the niche characteristics, a hybrid adaptive fuzzy control method with the function of continuous supervisory control is proposed in this paper. Considering the close degree of Niche as the consequent of adaptive T-S fuzzy control system, the hybrid control law is designed by tracking, continuous supervisory, and adaptive compensation. Adaptive compensator is used in the controller to compensate the approximation error of fuzzy logic system and the effect of the external disturbance. The adaptive law of consequent parameters, which is achieved in this paper, embodies system adaptability as biological individual. It is proved that all signals in the closed-loop system are bounded and tracking error converges to zero by Lyapunov stability theory. The effectiveness of the approach is demonstrated by the simulation results.

To depict the rule of epidemic diffusion, two different models, the Susceptible-Exposure-Infected-Recovered-Susceptible (SEIRS) model and the Susceptible-Exposure-Infected-Quarantine-Recovered-Susceptible (SEIQRS) model, are proposed and analyzed within small-world network in this paper. Firstly, the epidemic diffusion models are constructed with mean-filed theory, and condition for the occurrence of disease diffusion is explored. Then, the existence and global stability of the disease-free equilibrium and the endemic equilibrium for these two complex epidemic systems are proved by differential equations knowledge and Routh-Hurwiz theory. At last, a numerical example which includes key parameters analysis and critical topic discussion is presented to test how well the proposed two models may be applied in practice. These works may provide some guidelines for decision makers when coping with epidemic diffusion controlling problems.

This paper investigates the presence of limit oscillations in an adaptive sampling system. The basic sampling criterion operates in the sense that each next sampling occurs when the absolute difference of the signal amplitude with respect to its currently sampled signal equalizes a prescribed threshold amplitude. The sampling criterion is extended involving a prescribed set of amplitudes. The limit oscillations might be interpreted through the equivalence of the adaptive sampling and hold device with a nonlinear one consisting of a relay with multiple hysteresis whose parameterization is, in general, dependent on the initial conditions of the dynamic system. The performed study is performed on the time domain.

To keep the resources renewable, a singular ecological-economic model is proposed for the populations with harvesting and migration. The local stability and the dynamic behavior of the model are studied. Singular induced bifurcation appears when economic interest is zero, which is different from the ordinary differential models. In order to apply variable structure control to eliminate these complex behaviors, the singular model is transformed into a single-input and single-output model with parameter varying within definite intervals. And then, a variable structure controller is designed to make the model stable. Finally, an inshore-offshore fishery model is given to illustrate the proposed method, and some numerical simulations are shown to demonstrate the control results.

The eigenvalues and the stability of a singular neutral differential system with single delay are considered. Firstly, by applying the matrix pencil and the linear operator methods, new algebraic criteria for the imaginary axis eigenvalue are derived. Second, practical checkable criteria for the asymptotic stability are introduced.

Order-preserving and convergent results of delay functional differential equations without quasimonotone condition are established under type-K exponential ordering. As an application, the model of delayed Hopfield-type neural networks with a type-K monotone interconnection matrix is considered, and the attractor result is obtained.

We establish a result on existence and uniqueness on mean square almost periodic solutions for a class of impulsive stochastic differential equations with delays, which extends some earlier works reported in the literature.

We investigate the stochastic dynamics of bank liquidity parameters such as liquid assets and nett cash outflow in relation to the global financial crisis. These parameters enable us to determine the liquidity coverage ratio that is one of the metrics used in ratio analysis to measure bank liquidity. In this regard, numerical results show that bank behavior related to liquidity was highly procyclical during the financial crisis. We also consider a theoretical-quantitative approach to bank liquidity provisioning. In this case, we provide an explicit expression for the aggregate liquidity risk when a locally risk-minimizing strategy is utilized.

This paper proposes the optimal control methods for a class of chaotic systems via state feedback. By converting the chaotic systems to the form of uncertain piecewise linear systems, we can obtain the optimal controller minimizing the upper bound on cost function by virtue of the robust optimal control method of piecewise linear systems, which is cast as an optimization problem under constraints of bilinear matrix inequalities (BMIs). In addition, the lower bound on cost function can be achieved by solving a semidefinite programming (SDP). Finally, numerical examples are given to illustrate the results.

A kind of nonlinear finance system with time-delayed feedback is considered. Firstly, by employing the polynomial theorem to analyze the distribution of the roots to the associate characteristic equation, the conditions of ensuring the existence of Hopf bifurcation are given. Secondly, by using the normal form theory and center manifold argument, we derive the explicit formulas determining the stability, direction, and other properties of bifurcating periodic solutions. Finally, we give several numerical simulations, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable steady state or a stable periodic orbit.

Traditional pump scheduling models neglect the operation reliability which directly relates with the unscheduled maintenance cost and the wear cost during the operation. Just for this, based on the assumption that the vibration directly relates with the operation reliability and the degree of wear, it could express the operation reliability as the normalization of the vibration level. The characteristic of the vibration with the operation point was studied, it could be concluded that idealized flow versus vibration plot should be a distinct bathtub shape. There is a narrow sweet spot (80 to 100 percent BEP) to obtain low vibration levels in this shape, and the vibration also follows similar law with the square of the rotation speed without resonance phenomena. Then, the operation reliability could be modeled as the function of the capacity and rotation speed of the pump and add this function to the traditional model to form the new. And contrast with the tradition method, the result shown that the new model could fix the result produced by the traditional, make the pump operate in low vibration, then the operation reliability could increase and the maintenance cost could decrease.