An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization. II. Problems with Path Constraints

This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be directly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the ll penalty function and a novel smoothing technique are in-troduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algo-rithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reaCtor operation problem are in agreement with the literature reoorts, and the comoutational efficiency is also high.

An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization (Ⅰ) Problems Without Path Constraints

This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems without path constraints. The approach incorporates the virtues both from indirect and direct methods: it solves the optimality conditions like the traditional indirect methods do, but uses a discretization technique inspired from direct methods. Compared with other indirect approaches, the proposed approach has two main advantages: (1) the discretized optimization problem only employs unconstrained nonlinear programming (NLP) algorithms such as BFGS (Broyden-Fletcher-Goldfarb-Shanno), rather than constrained NLP algorithms, therefore the computational efficiency is increased; (2) the relationship between the number of the discretized time intervals and the integration error of the four-step Adams predictor-corrector algorithm is established, thus the minimal number of time intervals that under desired integration tolerance can be estimated. The classic batch reactor problem is tested and compared in detail with literature reports, and the results reveal the effectiveness of the proposed approach. Dealing with path constraints requires extra techniques, and will be studied in the second paper.

Soft measurement for component content based on adaptive model of Pr/Nd color features

For measurement of component content in the extraction and separation process of praseodymium/neodymium(Pr/Nd), a soft measurement method was proposed based on modeling of ion color features, which is suitable for fast estimation of component content in production field. Feature analysis on images of the solution is conducted,which are captured from Pr/Nd extraction/separation field. H/S components in the HSI color space are selected as model inputs, so as to establish the least squares support vector machine(LSSVM) model for Nd(Pr) content,while the model parameters are determined with the GA algorithm. To improve the adaptability of the model,the adaptive iteration algorithm is used to correct parameters of the LSSVM model, on the basis of model correction strategy and new sample data. Using the field data collected from rare earth extraction production, predictive methods for component content and comparisons are given. The results indicate that the proposed method presents good adaptability and high prediction precision, so it is applicable to the fast detection of element content in the rare earth extraction.

An adaptive beamforming algorithm based on direction vector rotation and joint iterative optimization

An adaptive beamforming algorithm named robust joint iterative optimizationdirection adaptive （RJIO-DA） is proposed for large-array scenarios. Based on the framework of minimum variance distortionless response （MVDR）, the proposed algorithm jointly updates a transforming matrix and a reduced-rank filter. Each column of the transforming matrix is treated as an independent direction vector and updates the weight values of each dimension within a subspace. In addition, the direction vector rotation improves the performance of the algorithm by reducing the uncertainties due to the direction error. Simulation results show that the RJIO-DA algorithm has lower complexity and faster convergence than other conventional reduced-rank algorithms.