Analysis of Properties of the Solutions to Parametric Time-Optimal Problems

We consider a linear time-optimal problem in which initial state values depend on a parameter and study the problem of the solution structure identification for small parameter perturbations. Properties of the time-optimal function and a point-set mapping, defined by optimal Lagrange vectors, are studied as well as the dependence of the solution on the parameter. Special attention is paid to the solution properties in irregular points.     

Fractal regularities of sub-harmonic motions perspective for pulse dynamics monitoring

The pulse energy conversion systems demonstrate a complex dynamics at parameter variations in a wide range. The problem of one-to-one decision-making about system dynamics using a priori information in the form of the parameter diagram is considered. The step-by-step approach to the problem solution based on fractal regularities of the dynamics is proposed. The first stage is the type of motion identification; the second one is the parameter vector identification within this motion type. The parallel and sequential algorithm schemes for this approach realization are presented. The problem of dynamics evolution forecasting is suggested to consider as a pointer to future research.     

三维种群生态动力系统的参数识别

研究具有反应一扩散现象的三维种群生态动力系统的参数识别问题，依该系统正问题解的性质，建立了参数识别的数学模型；论证了系统正问题解关于待识别参数的连续依赖性与参数识别问题最优解的存在性。     

Variational approach to a non-local identification problem related to non-linear ion transport

A variational approach to a non-linear non-local identification problem related to the non-linear transport equation is studied. Introducing a similarity transformation, the problem is formulated as an identification problem for a non-linear differential equation of second order with an additional non-local condition. For the solution of the forward problem stability in H¹-norm with respect to the identification parameter is obtained. Using this result the existence of a solution to the identification problem is proved. Some results of computational experiments are given. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.     

Parameters identification of chaotic system by chaotic gravitational search algorithm

In this paper, for the parameter identification problem of chaotic system, a chaotic gravitational search algorithm (CGSA) is proposed. At first, an iterative chaotic map with infinite collapses is introduced and chaotic local search (CLS) is designed, then CLS and basic gravitational search are combined in the procedure frame. The CGSA is composed of coarse gravitational search and fine chaotic local search, while chaotic search seeks the optimal solution further, based on the current best solution found by the coarse gravitational search. In order to show the effectiveness of CGSA, both offline and online parameter identifications of Lorenz system are conducted in comparative experiments, while the performances of CGSA are compared with GA, PSO and GSA. The results demonstrate the effectiveness and efficiency of CGSA in solving the problem of parameter identification of chaotic system, and the improvement to GSA has been verified.     

Parameters Identification as Identification of External Loads

Substitution of traditional problem of parameters identification to a problem of identification of some additional external load to researched system is offered in conditions, when the initial information on researched parameter and about statistical properties of measurements is absent or is insignificant. Such substitution is always possible as the contribution of any parameter can be considered as the contribution of additional external load in the response of researched system. At the given approach the mistake in a choice of structure of mathematical model with identified parameters does not lead to principle errors of the solution. This additional load compensates all errors. Besides it is possible to carry out check of a hypothesis about a constancy of parameter size.The problem was reduced to solution of the integral equation of the first kind with an inexact kernel and inexact right part. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

热传导(对流-扩散)方程源项识别的粒子群优化算法

提出了利用粒子群优化(PSO)算法反演热传导方程与对流-扩散方程源项的一种新方法,在已有文献方法的基础上,求解出这两类方程正问题的解析解,再把源项识别问题转化为最优化问题,结合粒子群优化算法寻优求解.通过数值模拟与统计检验,结果表明,此方法可快速有效地实现热传导方程与对流-扩散方程源项的识别,并可推广应用到其它数学物理方程的源项或参数的反演识别.     

Value-Estimation Function Method for Constrained Global Optimization

A novel value-estimation function method for global optimization problems with inequality constraints is proposed in this paper. The value-estimation function formulation is an auxiliary unconstrained optimization problem with a univariate parameter that represents an estimated optimal value of the objective function of the original optimization problem. A solution is optimal to the original problem if and only if it is also optimal to the auxiliary unconstrained optimization with the parameter set at the optimal objective value of the original problem, which turns out to be the unique root of a basic value-estimation function. A logarithmic-exponential value-estimation function formulation is further developed to acquire computational tractability and efficiency. The optimal objective value of the original problem as well as the optimal solution are sought iteratively by applying either a generalized Newton method or a bisection method to the logarithmic-exponential value-estimation function formulation. The convergence properties of the solution algorithms guarantee the identification of an approximate optimal solution of the original problem, up to any predetermined degree of accuracy, within a finite number of iterations.     

Identification de la Non-Linearité D'Une équation Parabolique Quasilineaire

In this work, we study the problem of the determination of the non-linearity in a parabolic equation from measurements over its solution. This corresponds to an usual physical situation, in which the parameter depends on the state of the system (for instance, the heat conduction coefficient depends on the temperature). We first state the problem as a control problem, for which we show the existence of a solution, and we calculate the derivative of the criterion with respect to the nonlinearity without any assumption on the algebraic form of this latter. We finally give a numerical application of the algorithm, which shows that the situation which is here taken in account (estimation of a parameter function depending on the state) is much better, from the identification point of view, than the usually studied situation for distributed system (estimation of a parameter function depending on space and/or time variables).     

Identification of Parameters of Nonlinear Dynamical Systems Simulated by Volterra Polynomials

We study the identification methods for the nonlinear dynamical systems described by Volterra series. One of the main problems in the dynamical system simulation is the problem of the choice of the parameters allowing the realization of a desired behavior of the system. If the structure of the model is identified in advance, then the solution to this problem closely resembles the identification problem of the system parameters. We also investigate the parameter identification of continuous and discrete nonlinear dynamical systems. The identification methods in the continuous case are based on application of the generalized Borel Theorem in combination with integral transformations. To investigate discrete systems, we use a discrete analog of the generalized Borel Theorem in conjunction with discrete transformations. Using model examples, we illustrate the application of the developed methods for simulation of systems with specified characteristics.     

一类非光滑分布参数系统的可辨识性及最优性条件

变压器温度场参数辨识问题是一种分片光滑的分布参数辨识问题,以流速为辨识参数,针对传质传热的一类分布参数系统参数辨识问题,证明了系统最优参数的存在性和控制参数为最优的必要条件,为变压器温度场的数值模拟研究提供了理论基础.     

Properties of solutions of parametric time-optimal problems in a neighborhood of an abnormal point

We consider a linear time-optimal problem in which the initial state vector depends on a parameter. We analyze the dependence of the solutions on the parameter and justify rules for the identification of the structure of the solution under small variations of the parameter. Attention is mainly paid to the analysis of properties of solutions in a neighborhood of an abnormal value of the parameter for which the function of determining elements of solutions of the original family of problems has no finite derivatives with respect to the parameter. For the function of determining elements, we obtain an asymptotic expansion to fractional powers of the parameter increment.     

On two-coefficient identification in elliptic variational inequalities

Abstract

This paper is concerned with elliptic variational inequalities that depend on two parameters. First, we investigate the dependence of the solution of the forward problem on these parameters and prove a Lipschitz estimate. Then, we study the inverse problem of identification of these two parameters and formulate two optimization approaches to this parameter identification problem. We extend the output least-squares approach, provide an existence result and establish a convergence result for finite-dimensional approximation. Further, we investigate the modified output least-squares approach which is based on energy functionals. This latter approach can be related to vector approximation.     

Algorithms for solving matrix polynomial equations of special form

In this paper we consider a series of algorithms for calculating radicals of matrix polynomial equations. A particular aspect of this problem arise in author’s work, concerning parameter identification of linear dynamic stochastic system. Special attention is given to searching the solution of an equation in a neighbourhood of some initial approximation. The offered approaches and algorithms allow us to receive fast and quite exact solution. We give some recommendations for application of given algorithms.     

Construction of Invertible Input-Output Mappings and Parameter Identification

The problem of continuation of an input-output mapping to a right invertible mapping is solved. The proposed solution is based on transforming the system to a normal form and solving the problem for such systems. The well-known Singh inversion algorithm is modified to calculate the normal forms. It is proved that each step of the modified algorithm can be realized and the result of the algorithm application is a normal form. A new approach to the parameter identification problem based on the inversion of the input-output mapping is proposed to illustrate the application of the results.     

An Optimal Control Method for Nonlinear Inverse Diffusion Coefficient Problem

This paper investigates the solution of a parameter identification problem associated with the two-dimensional heat equation with variable diffusion coefficient. The singularity of the diffusion coefficient results in a nonlinear inverse problem which makes theoretical analysis rather difficult. Using an optimal control method, we formulate the problem as a minimization problem and prove the existence and uniqueness of the solution in weighted Sobolev spaces. The necessary conditions for the existence of the minimizer are also given. The results can be extended to more general parabolic equations with singular coefficients.     

Parameter identification of Rossler’s chaotic system by an evolutionary algorithm

In this paper, a differential evolution (DE) algorithm is applied to parameter identification of Rossler’s chaotic system. The differential evolution has been shown to possess a powerful searching capability for finding the solutions for a given optimization problem, and it allows for parameter solution to appear directly in the form of floating point without further numerical coding or decoding. Three unknown parameters of Rossler’s Chaotic system are optimally estimated by using the DE algorithm. Finally, a numerical example is given to verify the effectiveness of the proposed method.     

Robust Solution to Fuzzy Identification Problem with Uncertain Data by Regularization

This study considers the robust identification of the parameters describing a Sugeno type fuzzy inference system with uncertain data. The objective is to minimize the worst-case residual error using a numerically efficient algorithm. The Sugeno type fuzzy systems are linear in consequent parameters but nonlinear in antecedent parameters. The robust consequent parameters identification problem can be formulated as second-order cone programming problem. The optimal solution of this second-order cone problem can be interpreted as solution of a Tikhonov regularization problem with a special choice of regularization parameter which is optimal for robustness (Ghaoui and Lebret (1997). SAIM Journal of Matrix Analysis and Applications 18, 1035–1064). The final regularized nonlinear optimization problem allowing simultaneous identification of antecedent and consequent parameters is solved iteratively using a generalized Gauss–Newton like method. To illustrate the approach, several simulation studies on numerical examples including the modelling of a spectral data function (one-dimensional benchmark example) is provided. The proposed robust fuzzy identification scheme has been applied to approximate the physical fitness of patients with a fuzzy expert system. The identified fuzzy expert system is shown to be capable of capturing the decisions (experiences) of a medical expert.     

Source Identification for the Time-Fractional Diffusion Equation With Robin Boundary Conditions北大核心CSCD

对Robin边界条件时间分数阶扩散方程的源项辨识问题进行了研究。这类问题是不适定的,因此提出了一种迭代型正则化方法,得到了源项辨识问题的正则近似解。给出了先验和后验参数选取规则下正则近似解和精确解之间的误差估计,数值算例验证了该方法的有效性。