地下水污染源识别的数学方法研究进展

地下水污染源识别模型可利用有限的观测资料估计污染源位置、污染物泄露强度及其泄露过程,是制定地下水污染修复方案的依据。在阐明地下水污染源识别基本问题基础上,综述了污染源识别研究的两大类数学方法,一类为直接方法,包括反向追踪法和基于正则化的方法;另一类为间接方法,包括基于优化的方法和基于概率统计的方法。同时指出了当前污染源识别数学方法应用中存在的主要问题:地下水污染源识别问题的复杂性、地下水有机污染问题和模型求解效率的低下性。对土壤-地下水的联合管理、基于物联网的地下水污染监测、对非水相流体(Non-aqueous Phase Liquid,NAPL)类污染源识别以及基于图形处理器(GPU)的异构并行计算将是未来研究的重点方向。

Novel disturbance compensating dynamic positioning of dredgers based on adaptive backstepping

In order to deal with the dynamic positioning system control problems of dredgers working under strong dredging reaction or harsh environments,an adaptive backstepping method is proposed.Disturbances are estimated and compensated for by the adaptive method without extra sensors on dredging equipment,and the control mechanism is simplified.Adaptive control is used to compensate for the reaction and environmental disturbances on the dredger,so the dredger can maintain the desired position with a minimum error and shock.The proposed adaptive robust controller guarantees the global asymptotic stability of the closed-loop system and rapid position tracking of the dredger.The simulation results show that the proposed controller has superior performance in position tracking and robustness to large disturbances.

Study and Application of Fault Prediction Methods with Improved Reservoir Neural Networks

Time-series prediction is one of the major methodologies used for fault prediction. The methods based on recurrent neural networks have been widely used in time-series prediction for their remarkable non-liner mapping ability. As a new recurrent neural network, reservoir neural network can effectively process the time-series prediction. However, the ill-posedness problem of reservoir neural networks has seriously restricted the generalization performance. In this paper, a fault prediction algorithm based on time-series is proposed using improved reservoir neural networks. The basic idea is taking structure risk into consideration, that is, the cost function involves not only the experience risk factor but also the structure risk factor. Thus a regulation coefficient is introduced to calculate the output weight of the reservoir neural network. As a result, the amplitude of output weight is effectively controlled and the ill-posedness problem is solved. Because the training speed of ordinary reservoir networks is naturally fast, the improved reservoir networks for time-series prediction are good in speed and generalization ability. Experiments on Mackey–Glass and sunspot time series prediction prove the effectiveness of the algorithm. The proposed algorithm is applied to TE process fault prediction. We first forecast some timeseries obtained from TE and then predict the fault type adopting the static reservoirs with the predicted data.The final prediction correct rate reaches 81%.

Adaptive control using interval Type-2 fuzzy logic for uncertain nonlinear systems

A new adaptive Type-2 （T2） fuzzy controller was developed and its potential performance advantage over adaptive Type-1 （T1） fuzzy control was also quantified in computer simulation. Base on the Lyapunov method, the adaptive laws with guaranteed system stability and convergence were developed. The controller updates its parameters online using the laws to control a system and tracks its output command trajectory. The simulation study involving the popular inverted pendulum control problem shows theoretically predicted system stability and good tracking performance. And the comparison simulation experiments subjected to white noige or step disturbance indicate that the T2 controller is better than the T1 controller by 0--18%, depending on the experiment condition and performance measure.

A Control of Uncertain Nonlinear Systems with Unknown Control Direction Via Adaptive Backstepping

The adaptive stabilization problem of nonlinear systems are studied. For a class of uncertain nonlinear systems with unknown control direction, we proposed a robust adaptive backstepping scheme withσ-modification by introducing Nussbaum function and Backstep- ping methods, and proved that all the signals of the closed-loop systems are bounded.

Comparing dynamical systems concepts and techniques for biomechanical analysis

Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predominately nonlinear.For this reason,nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature.These analysis techniques have provided new insights into how systems(1) maintain pattern stability,(2) transition into new states,and(3) are governed by short-and long-term(fractal) correlational processes at different spatio-temporal scales.These different aspects of system dynamics are typically investigated using concepts related to variability,stability,complexity,and adaptability.The purpose of this paper is to compare and contrast these different concepts and demonstrate that,although related,these terms represent fundamentally different aspects of system dynamics.In particular,we argue that variability should not uniformly be equated with stability or complexity of movement.In addition,current dynamic stability measures based on nonlinear analysis methods(such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics,but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored.Finally,systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints.

Robust adaptive control for a class of uncertain non-affine nonlinear systems using neural state feedback compensation

A robust adaptive control is proposed for a class of uncertain nonlinear non-affine SISO systems. In order to approximate the unknown nonlinear function, an affine type neural network(ATNN) and neural state feedback compensation are used, and then to compensate the approximation error and external disturbance, a robust control term is employed. By Lyapunov stability analysis for the closed-loop system, it is proven that tracking errors asymptotically converge to zero. Moreover, an observer is designed to estimate the system states because all the states may not be available for measurements. Furthermore, the adaptation laws of neural networks and the robust controller are given based on the Lyapunov stability theory. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed control method. Finally, two simulation examples show that the proposed method exhibits strong robustness, fast response and small tracking error, even for the non-affine nonlinear system with external disturbance, which confirms the effectiveness of the proposed approach.

L_1 adaptive controller of nonlinear reference system in presence of unmatched uncertainties

An extension of L_1 adaptive control is proposed for the unmatched uncertain nonlinear system with the nonlinear reference system that defines the performance specifications. The control law adapts fast and tracks the reference system with the guaranteed robustness and transient performance in the presence of unmatched uncertainties. The interval analysis is used to build the quasi-linear parameter-varying model of unmatched nonlinear system, and the robust stability of the proposed controller is addressed by sum of squares programming. The transient performance analysis shows that within the limit of hardware a large adaption gain can improve the asymptotic tracking performance. Simulation results are provided to demonstrate the theoretical findings of the proposed controller.

ON LIMITATIONS OF THE SAMPLED-DATA FEEDBACK FOR NONPARAMETRIC DYNAMICAL SYSTEMS

In this paper, we study a basic class of first order sampled-data control systems with unknown nonlinear structure and with sampling rate not necessarily fast enough, aiming at understanding the capability and limitations of the sampled-data feedback. We show that if the unknown nonlinear function has a linear growth rate with its 'slope' (denoted by L) being a measure of the 'size' of uncertainty, then the sampling rate should not exceed 1/L multiplied by a constant (≈ 7.53) for the system to be globally stabilizable by the sampled-data feedback. If, however, the unknown nonlinear function has a growth rate faster than linear, and if the system is disturbed by noises modeled as the standard Brownian motion, then an example is given, showing that the corresponding sampled-data system is not stabilizable by the sampled-data feedback in general, no matter how fast the sampling rate is.

STATE-FEEDBACK ADAPTIVE STABILIZING CONTROL DESIGN FOR A CLASS OF HIGH-ORDER NONLINEAR SYSTEMS WITH UNKNOWN CONTROL COEFFICIENTS

In this paper, a new approach is successfully addressed to design the state-feedback adaptive stabilizing control law for a class of high-order nonlinear systems in triangular form and with unknown and nonidentical control coefficients, whose stabilizing control has been investigated recently under the knowledge that the lower bounds of the control coefficients are exactly known. In the present paper, without any knowledge of the lower bounds of the control coefficients, based on the adaptive technique and appropriately choosing design parameters, we give the recursive design procedure of the stabilizing control law by utilizing the approach of adding a power integrator together with tuning functions. The state-feedback adaptive control law designed not only preserves the equilibrium at the origin, but also guarantees the global asymptotic stability of the closed-loop states and the uniform boundedness of all the other closed-loop signals.

Well-posedness of a kind of nonlinear coupled system of fractional differential equations

We study the boundary value problem of a coupled differential system of fractional order, and prove the existence and uniqueness of solutions to the considered problem. The underlying differential system is featured by a fractional differential operator, which is defined in the Riemann-Liouville sense, and a nonlinear term in which different solution components are coupled. The analysis is based on the reduction of the given system to an equivalent system of integral equations. By means of the nonlinear alternative of Leray-Schauder,the existence of solutions of the factional differential system is obtained. The uniqueness is established by using the Banach contraction principle.

On the Well-Posedness for Stochastic Schrodinger Equations with Quadratic Potential

The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI（R^n）, ｜·｜f ∈ L^2（R^n）}. When the nonlinearity is focusing and L2-supercritical, the authors give sufficient conditions for the solutions to blow up in finite time for both confining and repulsive potential. Especially for the repulsive case, the solution to the deterministic equation with the initial data satisfying the stochastic blow-up condition will also blow up in finite time. Thus, compared with the deterministic equation for the repulsive case, the blow-up condition is stronger on average, and depends on the regularity of the noise. If φ = 0, our results coincide with the ones for the deterministic equation.

THE GLOBAL WELL-POSEDNESS OF THE SMOLUCHOWSKI EQUATION FOR ROTATIONAL MOTION OF RODLIKE POLYMERS

In this paper, we prove the global existence and uniqueness of non-negative classical solutions of the Smoluchowski equation with viscosity ε>0. The existence of weak solutions when ε=0 is also obtained.

The Well-Posedness for Generalized Fuzzy Games

This paper establishes the stable results for generalized fuzzy games by using a nonlinear scalarization technique. The authors introduce some concepts of well-posedness for generalized fuzzy games. Moreover, the authors identify a class of generalized fuzzy games such that every element of the collection is generalized well-posed, and there exists a dense residual subset of the collection, where every generalized fuzzy game is robust well-posed.