Journal of Applied Mathematics

Volume 2014 (2014), Article ID 718595, 2 pages

http://dx.doi.org/10.1155/2014/718595

Editorial

Mathematical Approaches in Advanced Control Theories 2013

Baocang Ding,¹ Weihai Zhang,² Tianming Liu,³ Xianxia Zhang,⁴ Dewei Li,⁵ and Tao Zou⁶

¹Department of Automation, School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China

²College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266590, China

³Department of Computer Science and Bioimaging Research Center, University of Georgia, Boyd SRC 420, Athens, GA 30602, USA

⁴School of Mechatronics Engineering and Automation, Shanghai Key Laboratory of Power Station Automation Technology, Shanghai University, Shanghai 200072, China

⁵Department of Automation, Shanghai Jiaotong University, Shanghai 200240, China

⁶Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China

Received 17 April 2014; Accepted 17 April 2014; Published 28 April 2014

Copyright © 2014 Baocang Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advanced control theory fills a gap between the mathematical control theory and modern control engineering practices. Conceptually, advanced control theories can include any theoretical problems related to the controller design. But in this issue it may include model predictive control, sliding mode control, robust control, real-time optimization, and identification and estimation, which are not limited to controller design. Advanced control technologies have become ubiquitous in various engineering applications (e.g., chemical process control, robot control, air traffic control, vehicle control, multiagent control, and networked control). The development of mathematical methods is essential for the applications of advanced control theories. Sometimes it lacks effective methods to tackle the computational issue (e.g., model predictive control of a fast process). Sometimes, a new application requires a brand-new solver for applying the advanced control theory (e.g., a new production line far exceeding the usual speed). The main focus of this special issue will be on the new research ideas and results for the mathematical problems in advanced control theories.

A total number of 83 papers were submitted for this special issue. Out of the submitted papers, 39 contributions have been included in this special issue. The 39 contributions consider several closely related and interesting topics.

The subjects in controller design/synthesis and system analysis have occupied 24 contributions. These contributions include, for example, adaptive control (see the work of C. Hu and Y. Liu for the air-breathing hypersonic vehicles and the work of W. Gai et al. for the neural network dynamic inversion with prescribed performance in aircraft flight control), control (see the work of A. Moutsopoulou et al. for the active vibration control in intelligent structures and the work of Z. H. Ismail and M. W. Dunnigan for the robust technique for an autonomous underwater vehicle with region tracking function), model predictive control (see the work of H. Shen et al. for the vanadium redox flow battery modeled by neural network and the work of H. Shi et al. for the two-layered control of a continuous biodiesel transesterification reactor), sliding model control (see the work of H. Pang and X. Yang for robustifying the linear quadratic tracking controller and the work of S. I. Serna-Garcés et al. for an active postfilter based on two buck converters), networked control (see the work of L. Qiu et al. for the stability under random time delays and packet dropouts based on unified Markov jump model), backstepping technique (see the work of J. Liu et al. for output-feedback stabilization of stochastic nonlinear systems), fuzzy logic control (see the work of X.-X. Zhang et al. which presents a reference function based 3D design methodology using support vector regression learning), and neural network control (see the work of X. Li et al. which is designed under small world neural network model and is investigated in both linear and nonlinear controls).

Closely related to the controller design and synthesis are the 9 contributions on the estimation problem. These contributions include, for example, time series prediction (see the work of H. Huang et al. for forecasting the urban traffic flow modeled by the fuzzy clustering and neural network), the compressed sensing (see the two works of J. Liu et al. for the direction of arrival estimation problem in phased array radar system and for discussing splitting matching pursuit method in reconstructing sparse signal), Kalman filter (see the work of X. Yuan et al. for integrating the cardinality balanced multitarget multi-Bernoulli filter with the interacting multiple models algorithm), and robust filter (see the work of Z. Chen and Q. Huang for the filter design for stochastic systems with mixed delays and nonlinear perturbations).

There are also 3 contributions on the fault diagnosis/detection/separation. These contributions can be seen as the extensions of the estimation problem, in the context of this special issue. For example, H. Zhu et al. propose a method for broken rotor bars detection in the voltage-source-inverter-fed squirrel-cage induction motors, and Y. Su et al. introduce an improved kernel Fisher distinguish analysis method for the nonlinear fault separation of redundancy process variables.

The last 3 contributions are for the mathematical programming (including the heuristic programming). For example, Q. Wang et al. consider the wireless sensor networks node localization based on the time of arrival; W. Shen et al. apply dynamic programming algorithm to the parameter matching analysis of hydraulic hybrid excavators; and Y. Wang et al. propose a hybrid differential evolution algorithm with multipopulation and apply it to solve a multiobjective optimization model of a grinding and classification process. Note that several other contributions mentioned above have also considered optimizations.

In the above, some contributions are included in the statistics but not mentioned, due to either more specific or more compounded technicalities. We hope the readers of this special issue will find it interesting and stimulating and expect that the included papers will contribute to further advance the area of advanced control.

Acknowledgments

Finally, we would like to thank all the authors who have submitted papers to the special issue and the reviewers involved in the refereeing of the submissions.

Baocang Ding

Weihai Zhang

Tianming Liu

Xianxia Zhang

Dewei Li

Tao Zou