The approximate solution for solving a class of composition fractional order optimal control problems (FOCPs) is suggested and studied in detail. However, the properties of Caputo and Riemann-Liouville derivatives are also given with complete details on Chebyshev approximation function to approximate the solution of fractional differential equation with different approach. Also, the relation between Caputo and Riemann-Liouville of fractional derivative took a big role for simplifying the fractional differential equation that represents the constraints of optimal control problems. The approximate solutions are defined on interval [0,1] and are compared with the exact solution of order one which is an important condition to support the working method. Finally, illustrative examples are included to confirm the efficiency and accuracy of the proposed method.
{"title":"Solution of Some Types for Composition Fractional Order Differential Equations Corresponding to Optimal Control Problems","authors":"Sameer Qasim Hasan, Moataz Abbas Holel","doi":"10.1155/2018/3767263","DOIUrl":"https://doi.org/10.1155/2018/3767263","url":null,"abstract":"The approximate solution for solving a class of composition fractional order optimal control problems (FOCPs) is suggested and studied in detail. However, the properties of Caputo and Riemann-Liouville derivatives are also given with complete details on Chebyshev approximation function to approximate the solution of fractional differential equation with different approach. Also, the relation between Caputo and Riemann-Liouville of fractional derivative took a big role for simplifying the fractional differential equation that represents the constraints of optimal control problems. The approximate solutions are defined on interval [0,1] and are compared with the exact solution of order one which is an important condition to support the working method. Finally, illustrative examples are included to confirm the efficiency and accuracy of the proposed method.","PeriodicalId":46052,"journal":{"name":"Journal of Control Science and Engineering","volume":"115 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77908585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Through studying tracking problems of the wheeled mobile robot, this paper proposed a discrete iterative learning control approach based on PID with strong adaptability, fast convergence, and small error. This algorithm used discrete PID to filter rejection and restrained the influence of interference and noise on trajectory tracking, which made it more suitable for engineering application. The PID-type iterative learning convergence condition and certification procedure are presented. The results of simulation reveal that the PID-type ILC holds the features of simplicity, strong robustness, and high repeating precision and can well meet the control requirement of nonlinear discrete system.
{"title":"Discrete PID-Type Iterative Learning Control for Mobile Robot","authors":"Hongbin Wang, Jianwei Dong, Yueling Wang","doi":"10.1155/2016/2320746","DOIUrl":"https://doi.org/10.1155/2016/2320746","url":null,"abstract":"Through studying tracking problems of the wheeled mobile robot, this paper proposed a discrete iterative learning control approach based on PID with strong adaptability, fast convergence, and small error. This algorithm used discrete PID to filter rejection and restrained the influence of interference and noise on trajectory tracking, which made it more suitable for engineering application. The PID-type iterative learning convergence condition and certification procedure are presented. The results of simulation reveal that the PID-type ILC holds the features of simplicity, strong robustness, and high repeating precision and can well meet the control requirement of nonlinear discrete system.","PeriodicalId":46052,"journal":{"name":"Journal of Control Science and Engineering","volume":"81 1","pages":"1-7"},"PeriodicalIF":1.7,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86852888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In a plate rolling production line, thermomechanically controlled processing is critical for plate quality. In this paper, a set of intermediate cooling equipment of a two-stand plate mill with super density nozzles, medium pressure, and small flow is developed. Based on a simplified dynamic model, a cooling control scheme with combined feedforward, feedback, and adaptive algorithms is put forward. The new controlled rolling process and the highly efficient control system improve the controlled rolling efficiency by an average of 17.66%. The proposed intermediate cooling system can also effectively inhibit the growth of austenite grain, improve the impact toughness and yield strength of Q345B steel plate, reduce the formation of secondary oxide scale on the plate surface and the chromatic aberration of the plate surface, and greatly improve the surface quality of the steel plate.
{"title":"Development of Intermediate Cooling Technology and Its Control for Two-Stand Plate Rolling","authors":"Fei Zhang, Wei Yu, Tao Liu","doi":"10.1155/2016/4192186","DOIUrl":"https://doi.org/10.1155/2016/4192186","url":null,"abstract":"In a plate rolling production line, thermomechanically controlled processing is critical for plate quality. In this paper, a set of intermediate cooling equipment of a two-stand plate mill with super density nozzles, medium pressure, and small flow is developed. Based on a simplified dynamic model, a cooling control scheme with combined feedforward, feedback, and adaptive algorithms is put forward. The new controlled rolling process and the highly efficient control system improve the controlled rolling efficiency by an average of 17.66%. The proposed intermediate cooling system can also effectively inhibit the growth of austenite grain, improve the impact toughness and yield strength of Q345B steel plate, reduce the formation of secondary oxide scale on the plate surface and the chromatic aberration of the plate surface, and greatly improve the surface quality of the steel plate.","PeriodicalId":46052,"journal":{"name":"Journal of Control Science and Engineering","volume":"3 1","pages":"1-9"},"PeriodicalIF":1.7,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82425566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a continuous linear time invariant system with ellipsoidal parametric uncertainty structured into subsystems. Since the design of a local controller uses only information on a subsystem and its neighbours, we combine the plug and play idea and robust distributed control to propose one distributed control strategy for linear system with ellipsoidal parametric uncertainty. Firstly for linear system with ellipsoidal parametric uncertainty, a necessary and sufficient condition for robust state feedback control is proposed by means of linear matrix inequality. If this necessary and sufficient condition is satisfied, this robust state feedback gain matrix can be easily derived to guarantee robust stability and prescribed closed loop performance. Secondly the plug and play idea is introduced in the design process. Finally by one example of aircraft flutter model parameter identification, the efficiency of the proposed control strategy can be easily realized.
{"title":"Plug and Play Robust Distributed Control with Ellipsoidal Parametric Uncertainty System","authors":"Hong Wang-jian, Wang Yan-xiang","doi":"10.1155/2016/8753657","DOIUrl":"https://doi.org/10.1155/2016/8753657","url":null,"abstract":"We consider a continuous linear time invariant system with ellipsoidal parametric uncertainty structured into subsystems. Since the design of a local controller uses only information on a subsystem and its neighbours, we combine the plug and play idea and robust distributed control to propose one distributed control strategy for linear system with ellipsoidal parametric uncertainty. Firstly for linear system with ellipsoidal parametric uncertainty, a necessary and sufficient condition for robust state feedback control is proposed by means of linear matrix inequality. If this necessary and sufficient condition is satisfied, this robust state feedback gain matrix can be easily derived to guarantee robust stability and prescribed closed loop performance. Secondly the plug and play idea is introduced in the design process. Finally by one example of aircraft flutter model parameter identification, the efficiency of the proposed control strategy can be easily realized.","PeriodicalId":46052,"journal":{"name":"Journal of Control Science and Engineering","volume":"132 1 1","pages":"1-8"},"PeriodicalIF":1.7,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84046430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
N. Cai, R. Sabatini, Xiwang Dong, M. J. Khan, Yaowei Yu
1School of Electrical Engineering, Northwest University for Nationalities, Lanzhou, China 2Key Laboratory of National Language Intelligent Processing, Gansu, China 3School of Engineering-Aerospace and Aviation Discipline, RMIT University, Melbourne, VIC, Australia 4School of Automation Science and Electrical Engineering, Beihang University, Beijing, China 5School of PN Engineering, National University of Sciences and Technology, Islamabad, Pakistan 6School of Automation, University of Science and Technology Beijing, Beijing, China
{"title":"Decentralized Modeling, Analysis, Control, and Application of Distributed Dynamic Systems","authors":"N. Cai, R. Sabatini, Xiwang Dong, M. J. Khan, Yaowei Yu","doi":"10.1155/2016/8985017","DOIUrl":"https://doi.org/10.1155/2016/8985017","url":null,"abstract":"1School of Electrical Engineering, Northwest University for Nationalities, Lanzhou, China 2Key Laboratory of National Language Intelligent Processing, Gansu, China 3School of Engineering-Aerospace and Aviation Discipline, RMIT University, Melbourne, VIC, Australia 4School of Automation Science and Electrical Engineering, Beihang University, Beijing, China 5School of PN Engineering, National University of Sciences and Technology, Islamabad, Pakistan 6School of Automation, University of Science and Technology Beijing, Beijing, China","PeriodicalId":46052,"journal":{"name":"Journal of Control Science and Engineering","volume":"16 1","pages":"1-2"},"PeriodicalIF":1.7,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73209587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yu-Jun Zhang, Libing Wu, H. Zhao, X. Hu, Wen-Yu Zhang, D. Ju
In this paper, the problem of adaptive fuzzy tracking control is considered for a class of uncertain nonaffine nonlinear systems with external disturbances, multiple time delays, and nonsymmetric saturation constrains. First, the mean value theorem is employed to deal with the nonaffine term with input nonlinearity. Then, a new adaptive fuzzy tracking controller with parameter updating laws is designed by using fuzzy approximation technique. Moreover, it is shown that all the closed-loop signals are bounded and the tracking errors can asymptotically converge to zero via the Lyapunov stability analysis. Finally, the simulation example for van der Pol oscillator system is worked out to verify the effectiveness of the proposed adaptive fuzzy design approach.
{"title":"Adaptive Fuzzy Tracking Control for a Class of Uncertain Nonlinear Time-Delayed Systems with Saturation Constrains","authors":"Yu-Jun Zhang, Libing Wu, H. Zhao, X. Hu, Wen-Yu Zhang, D. Ju","doi":"10.1155/2016/2931524","DOIUrl":"https://doi.org/10.1155/2016/2931524","url":null,"abstract":"In this paper, the problem of adaptive fuzzy tracking control is considered for a class of uncertain nonaffine nonlinear systems with external disturbances, multiple time delays, and nonsymmetric saturation constrains. First, the mean value theorem is employed to deal with the nonaffine term with input nonlinearity. Then, a new adaptive fuzzy tracking controller with parameter updating laws is designed by using fuzzy approximation technique. Moreover, it is shown that all the closed-loop signals are bounded and the tracking errors can asymptotically converge to zero via the Lyapunov stability analysis. Finally, the simulation example for van der Pol oscillator system is worked out to verify the effectiveness of the proposed adaptive fuzzy design approach.","PeriodicalId":46052,"journal":{"name":"Journal of Control Science and Engineering","volume":"2 1","pages":"1-8"},"PeriodicalIF":1.7,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87736760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper studies the problem of state estimation for a class of delayed static neural networks. The purpose of the problem is to design a delay-dependent state estimator such that the dynamics of the error system is globally exponentially stable and a prescribed performance is guaranteed. Some improved delay-dependent conditions are established by constructing augmented Lyapunov-Krasovskii functionals (LKFs). The desired estimator gain matrix can be characterized in terms of the solution to LMIs (linear matrix inequalities). Numerical examples are provided to illustrate the effectiveness of the proposed method compared with some existing results.
{"title":"Improved Results on State Estimation of Static Neural Networks with Time Delay","authors":"Bin Wen, Hui Li, S. Zhong","doi":"10.1155/2016/1759650","DOIUrl":"https://doi.org/10.1155/2016/1759650","url":null,"abstract":"This paper studies the problem of state estimation for a class of delayed static neural networks. The purpose of the problem is to design a delay-dependent state estimator such that the dynamics of the error system is globally exponentially stable and a prescribed performance is guaranteed. Some improved delay-dependent conditions are established by constructing augmented Lyapunov-Krasovskii functionals (LKFs). The desired estimator gain matrix can be characterized in terms of the solution to LMIs (linear matrix inequalities). Numerical examples are provided to illustrate the effectiveness of the proposed method compared with some existing results.","PeriodicalId":46052,"journal":{"name":"Journal of Control Science and Engineering","volume":"18 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86585409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is about the nonfragile H∞ filtering problem for a class of Markovian jumping systems MJSs subject to mode-dependent time delays and quantization. Mode switching is considered not only in the system parameters but also in the time delays. Signal quantization is taken into account to reflect the phenomenon of incomplete measurement. Norm bound uncertainty is utilized to indicate the filter gain variation due to the inaccuracy of actual filtering realization. The purpose of this paper is to design a nonfragile filter so that the filtering error dynamics is stochastically stable with a prescribed disturbance attenuation level. By the Lyapunov stability theory, stochastic analysis theory, and linear matrix inequalities LMIs technique, some new sufficient conditions are derived for the existence of the desired nonfragile filter which ensures the stochastic stability and H∞ performance of the filtering error dynamics. The expression of the filter can be obtained via solving the feasible solution to the LMIs. A simulation example is presented to illustrate the performance of the proposed filtering scheme.
{"title":"Nonfragile H∞ Filtering for Nonlinear Markovian Jumping Systems with Mode-Dependent Time Delays and Quantization","authors":"Yanqin Wang, Weijian Ren, Yang Lu","doi":"10.1155/2016/7167692","DOIUrl":"https://doi.org/10.1155/2016/7167692","url":null,"abstract":"This paper is about the nonfragile H∞ filtering problem for a class of Markovian jumping systems MJSs subject to mode-dependent time delays and quantization. Mode switching is considered not only in the system parameters but also in the time delays. Signal quantization is taken into account to reflect the phenomenon of incomplete measurement. Norm bound uncertainty is utilized to indicate the filter gain variation due to the inaccuracy of actual filtering realization. The purpose of this paper is to design a nonfragile filter so that the filtering error dynamics is stochastically stable with a prescribed disturbance attenuation level. By the Lyapunov stability theory, stochastic analysis theory, and linear matrix inequalities LMIs technique, some new sufficient conditions are derived for the existence of the desired nonfragile filter which ensures the stochastic stability and H∞ performance of the filtering error dynamics. The expression of the filter can be obtained via solving the feasible solution to the LMIs. A simulation example is presented to illustrate the performance of the proposed filtering scheme.","PeriodicalId":46052,"journal":{"name":"Journal of Control Science and Engineering","volume":"52 1","pages":"1-11"},"PeriodicalIF":1.7,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80212431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The reachable set estimation problem for discrete-time systems with delay-range-dependent and bounded disturbances is investigated. A triple-summation term, the upper bound, and the lower bound of time-varying delay are introduced into the Lyapunov function. In this case, an improved delay-range-dependent criterion is established for the addressed problem by constructing the appropriate Lyapunov functional, which guarantees that the reachable set of discrete-time systems with time-varying delay and bounded peak inputs is contained in the ellipsoid. It is worth mentioning that the initial value of the system does not need to be zero. Then, the reachable set estimation problem for time-delay systems with polytopic uncertainties is investigated. The effectiveness and the reduced conservatism of the derived results are demonstrated by an illustrative example.
{"title":"Reachable Set Estimation for Discrete-Time Systems with Interval Time-Varying Delays and Bounded Disturbances","authors":"Jiemei Zhao, Yin Sheng","doi":"10.1155/2016/5214147","DOIUrl":"https://doi.org/10.1155/2016/5214147","url":null,"abstract":"The reachable set estimation problem for discrete-time systems with delay-range-dependent and bounded disturbances is investigated. A triple-summation term, the upper bound, and the lower bound of time-varying delay are introduced into the Lyapunov function. In this case, an improved delay-range-dependent criterion is established for the addressed problem by constructing the appropriate Lyapunov functional, which guarantees that the reachable set of discrete-time systems with time-varying delay and bounded peak inputs is contained in the ellipsoid. It is worth mentioning that the initial value of the system does not need to be zero. Then, the reachable set estimation problem for time-delay systems with polytopic uncertainties is investigated. The effectiveness and the reduced conservatism of the derived results are demonstrated by an illustrative example.","PeriodicalId":46052,"journal":{"name":"Journal of Control Science and Engineering","volume":"236 1","pages":"5"},"PeriodicalIF":1.7,"publicationDate":"2016-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75872511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A nonautonomous food-chain system with Holling II functional response is studied, in which multiple delays of digestion are also considered. By applying techniques in differential inequalities, comparison theorem in ordinary differential equations, impulsive differential equations, and functional differential equations, some effective control strategies are obtained for the permanence of the system. Furthermore, effects of some important coefficients and delays on the permanence of the system are intuitively and clearly shown by series of numerical examples.
{"title":"Impulsive Control Strategy for a Nonautonomous Food-Chain System with Multiple Delays","authors":"Baodan Tian, Yanhong Qiu, Yucai Ding","doi":"10.1155/2016/6126545","DOIUrl":"https://doi.org/10.1155/2016/6126545","url":null,"abstract":"A nonautonomous food-chain system with Holling II functional response is studied, in which multiple delays of digestion are also considered. By applying techniques in differential inequalities, comparison theorem in ordinary differential equations, impulsive differential equations, and functional differential equations, some effective control strategies are obtained for the permanence of the system. Furthermore, effects of some important coefficients and delays on the permanence of the system are intuitively and clearly shown by series of numerical examples.","PeriodicalId":46052,"journal":{"name":"Journal of Control Science and Engineering","volume":"21 1","pages":"1-9"},"PeriodicalIF":1.7,"publicationDate":"2016-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82168710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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