Wentao Liu, Junxia Ma, Weili Xiong^*

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.2, pp. 873-892, 2023, DOI:10.32604/cmes.2022.020565 - 31 August 2022

Abstract This paper studies the parameter estimation problems of the nonlinear systems described by the bilinear state space models in the presence of disturbances. A bilinear state observer is designed for deriving identification algorithms to estimate the state variables using the input-output data. Based on the bilinear state observer, a novel gradient iterative algorithm is derived for estimating the parameters of the bilinear systems by means of the continuous mixed p-norm cost function. The gain at each iterative step adapts to the data quality so that the algorithm has good robustness to the noise disturbance. Furthermore, to More >

Luyao Yang^1,#, Hao Chen^2,#, Haocheng Yu¹, Jin Qiu^1,*, Shuxian Zhu^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.1, pp. 731-745, 2023, DOI:10.32604/cmes.2022.020656 - 24 August 2022

Abstract Discrete Tomography (DT) is a technology that uses image projection to reconstruct images. Its reconstruction problem, especially the binary image (0–1 matrix) has attracted strong attention. In this study, a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructed model. The solution process can be divided into two procedures. First, the DT problem is reformulated into a polyhedron judgment problem based on lattice basis reduction. Second, the fixed-point iterative method of Dang and Ye is used to judge whether an integer point exists in the polyhedron of More >

Cheinshan Liu^{1, 2}, Chunglun Kuo¹, Jiangren Chang^{3, *}

CMES-Computer Modeling in Engineering & Sciences, Vol.122, No.1, pp. 33-48, 2020, DOI:10.32604/cmes.2020.08490 - 01 January 2020

Abstract In the optimal control problem of nonlinear dynamical system, the Hamiltonian formulation is useful and powerful to solve an optimal control force. However, the resulting Euler-Lagrange equations are not easy to solve, when the performance index is complicated, because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations. To be a numerical method, it is hard to exactly preserve all the specified conditions, which might deteriorate the accuracy of numerical solution. With this in mind, we develop a novel algorithm to find the solution of the optimal control problem of nonlinear… More >

Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.1, pp. 1-39, 2015, DOI:10.3970/cmes.2015.104.001

Abstract A double optimal solution of an n-dimensional system of linear equations Ax = b has been derived in an affine m « n. We further develop a double optimal iterative algorithm (DOIA), with the descent direction z being solved from the residual equation Az = r₀ by using its double optimal solution, to solve ill-posed linear problem under large noise. The DOIA is proven to be absolutely convergent step-by-step with the square residual error ||r||² = ||b - Ax||² being reduced by a positive quantity ||Az_k||² at each iteration step, which is found to be better than those algorithms based More >

Zichun Yang^1,2,3, Lei Zhang^1,4, Yueyun Cao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.2, pp. 101-130, 2014, DOI:10.3970/cmes.2014.097.101

Abstract Discretization of inverse problems often leads to systems of linear equations with a highly ill-conditioned coefficient matrix. To find meaningful solutions of such systems, one kind of prevailing and representative approaches is the so-called regularized total least squares (TLS) method when both the system matrix and the observation term are contaminated by some noises. We will survey two such regularization methods in the TLS setting. One is the iterative truncated TLS (TTLS) method which can solve a convergent sequence of projected linear systems generated by Lanczos bidiagonalization. The other one is to convert the Tikhonov… More >

Chein-Shan Liu ¹

CMC-Computers, Materials & Continua, Vol.33, No.2, pp. 175-198, 2013, DOI:10.3970/cmc.2013.033.175

Abstract An optimal m-vector descent iterative algorithm in a Krylov subspace is developed, of which the m weighting parameters are optimized from a properly defined objective function to accelerate the convergence rate in solving an ill-posed linear problem. The optimal multi-vector iterative algorithm (OMVIA) is convergent fast and accurate, which is verified by numerical tests of several linear inverse problems, including the backward heat conduction problem, the heat source identification problem, the inverse Cauchy problem, and the external force recovery problem. Because the OMVIA has a good filtering effect, the numerical results recovered are quite smooth More >

Yonghua Zhou¹, Xun Yang¹, Chao Mi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.5, pp. 477-491, 2013, DOI:10.3970/cmes.2013.092.477

Abstract Route selections for vehicles can be equivalent to determine the optimized operation processes for vehicles which intertwine with each other. This paper attempts to utilize the whole methodology of model predictive control to engender rational routes for vehicles, which involves three important parts, i.e. simulation prediction, rolling optimization and feedback adjustment. The route decisions are implemented over the rolling prediction horizon taking the real-time feedback information and the future intertwined operation processes into account. The driving behaviors and route selection speculations of drivers and even traffic propagation models are on-line identified and adapted for the… More >

Chih-Wen Chang^1,2, Chein-Shan Liu³

CMC-Computers, Materials & Continua, Vol.34, No.2, pp. 143-175, 2013, DOI:10.3970/cmc.2013.034.143

Abstract The nonlinear Poisson problems in heat diffusion governed by elliptic type partial differential equations are solved by a modified globally optimal iterative algorithm (MGOIA). The MGOIA is a purely iterative method for searching the solution vector x without using the invert of the Jacobian matrix D. Moreover, we reveal the weighting parameter αc in the best descent vector w = αcE + DTE and derive the convergence rate and find a criterion of the parameter γ. When utilizing αc and γ, we can further accelerate the convergence speed several times. Several numerical experiments are carefully More >

Chih-Wen Chang^1,2, Chein-Shan Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.4, pp. 269-292, 2012, DOI:10.3970/cmes.2012.088.269

Abstract In this article, we utilize an optimal vector driven algorithm (OVDA) to cope with the nonlinear heat conduction problems (HCPs). From this set of nonlinear ordinary differential equations, we propose a purely iterative scheme and the spatial-discretization of finite difference method for revealing the solution vector x, without having to invert the Jacobian matrix D. Furthermore, we introduce three new ideas of bifurcation, attracting set and optimal combination, which are restrained by two parameters g and a. Several numerical instances of nonlinear systems under noise are examined, finding that the OVDA has a fast convergence More >

Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.6, pp. 575-602, 2012, DOI:10.3970/cmes.2012.084.575

Abstract An iterative algorithm based on the concept of best descent vector u in x^· = λu is proposed to solve a system of nonlinear algebraic equations (NAEs): F(x) = 0. In terms of the residual vector F and a monotonically increasing positive function Q(t) of a time-like variable t, we define a future cone in the Minkowski space, wherein the discrete dynamics of the proposed algorithm evolves. A new method to approximate the best descent vector is developed, and we find a critical value of the weighting parameter α_c in the best descent vector u = α_cF + B^TF, where B = ∂F/∂x is the More >