Pub Date : 2014-11-07DOI: 10.4236/IJMNTA.2014.35027
S. A. Alblowi
The aim of this work is to introduce some weak forms of continuity in bitopological spaces. Then we use these new forms of weak continuity to give many decompositions of i-continuity and pairwise continuity.
{"title":"Relative Continuity and New Decompositions of Continuity in Bitopological Spaces","authors":"S. A. Alblowi","doi":"10.4236/IJMNTA.2014.35027","DOIUrl":"https://doi.org/10.4236/IJMNTA.2014.35027","url":null,"abstract":"The aim of this work is to introduce some weak forms of continuity in bitopological spaces. Then we use these new forms of weak continuity to give many decompositions of i-continuity and pairwise continuity.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70705569","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}
Pub Date : 2014-11-07DOI: 10.4236/IJMNTA.2014.35028
Baishun Liu
This paper proposes two kinds of nonlinear general integral controllers, that is, one is generic and another is practical, for a class of uncertain nonlinear system. By extending equal ratio gain technique to a canonical interval system matrix and using Lyapunov method, theorems to ensure regionally as well as semi-globally asymptotic stability are established in terms of some bounded information. Moreover, for the practical nonlinear integral controller, a real time method to evaluate the equal ratio coefficient is proposed such that its value can be chosen moderately. Theoretical analysis and simulation results demonstrated that not only nonlinear general integral control can effectively deal with the uncertain nonlinear system but also equal ratio gain technique is a powerful and practical tool to solve the control design problem of dynamics with the nonlinear and uncertain actions.
{"title":"Nonlinear General Integral Control Design via Equal Ratio Gain Technique","authors":"Baishun Liu","doi":"10.4236/IJMNTA.2014.35028","DOIUrl":"https://doi.org/10.4236/IJMNTA.2014.35028","url":null,"abstract":"This paper proposes two kinds of nonlinear general integral controllers, that is, one is generic and another is practical, for a class of uncertain nonlinear system. By extending equal ratio gain technique to a canonical interval system matrix and using Lyapunov method, theorems to ensure regionally as well as semi-globally asymptotic stability are established in terms of some bounded information. Moreover, for the practical nonlinear integral controller, a real time method to evaluate the equal ratio coefficient is proposed such that its value can be chosen moderately. Theoretical analysis and simulation results demonstrated that not only nonlinear general integral control can effectively deal with the uncertain nonlinear system but also equal ratio gain technique is a powerful and practical tool to solve the control design problem of dynamics with the nonlinear and uncertain actions.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70706032","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}
Pub Date : 2014-11-07DOI: 10.4236/IJMNTA.2014.35025
Ankita Sharma, A. Shaiju
In this article, affine-quadratic control problems are studied. Error bounds are derived for the difference between the performance indices corresponding to the optimal and a class of suboptimal controls. In particular, it is shown that the performance of these suboptimal controls is close to that of the optimal control whenever the error in estimating the costate initial condition is small.
{"title":"Performance of Suboptimal Controllers for Affine-Quadratic Problems","authors":"Ankita Sharma, A. Shaiju","doi":"10.4236/IJMNTA.2014.35025","DOIUrl":"https://doi.org/10.4236/IJMNTA.2014.35025","url":null,"abstract":"In this article, affine-quadratic control problems are studied. Error bounds are derived for the difference between the performance indices corresponding to the optimal and a class of suboptimal controls. In particular, it is shown that the performance of these suboptimal controls is close to that of the optimal control whenever the error in estimating the costate initial condition is small.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70705277","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}
Pub Date : 2014-11-07DOI: 10.4236/IJMNTA.2014.35023
Baishun Liu, Xiang-Qian Luo, Jian-Hui Li
In this paper, a kind of fire new nonlinear integrator and integral action is proposed. Consequently, a conventional Proportional Nonlinear Integral (P_NI) observer and two kinds of added-order P_NI observers are developed to deal with the uncertain nonlinear system. The conditions on the observer gains to ensure the estimated error to be ultimate boundness, which shrinks to zero as the states and control inputs converge to the equilibrium point, are provided. This means that if the observed system is asymptotically stable, the estimated error dynamics is asymptotically stable, too. Moreover, the highlight point of this paper is that the design of nonlinear integral observer is achieved by linear system theory. Simulation results showed that under the normal and perturbed cases, the pure added-order P_NI observer can effectively deal with the uncertain nonlinearities on both the system dynamics and measured outputs.
{"title":"Conventional and Added-Order Proportional Nonlinear Integral Observers","authors":"Baishun Liu, Xiang-Qian Luo, Jian-Hui Li","doi":"10.4236/IJMNTA.2014.35023","DOIUrl":"https://doi.org/10.4236/IJMNTA.2014.35023","url":null,"abstract":"In this paper, a kind of fire new nonlinear integrator and integral action is proposed. Consequently, a conventional Proportional Nonlinear Integral (P_NI) observer and two kinds of added-order P_NI observers are developed to deal with the uncertain nonlinear system. The conditions on the observer gains to ensure the estimated error to be ultimate boundness, which shrinks to zero as the states and control inputs converge to the equilibrium point, are provided. This means that if the observed system is asymptotically stable, the estimated error dynamics is asymptotically stable, too. Moreover, the highlight point of this paper is that the design of nonlinear integral observer is achieved by linear system theory. Simulation results showed that under the normal and perturbed cases, the pure added-order P_NI observer can effectively deal with the uncertain nonlinearities on both the system dynamics and measured outputs.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70705152","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}
Pub Date : 2014-11-07DOI: 10.4236/IJMNTA.2014.35022
A. Hussein
Battery management systems (BMS) must estimate the state-of-charge (SOC) of the battery accurately to prolong its lifetime and ensure a reliable operation. Since batteries have a wide range of applications, the SOC estimation requirements and methods vary from an application to another. This paper compares two SOC estimation methods, namely extended Kalman filters (EKF) and artificial neural networks (ANN). EKF is a nonlinear optimal estimator that is used to estimate the inner state of a nonlinear dynamic system using a state-space model. On the other hand, ANN is a mathematical model that consists of interconnected artificial neurons inspired by biological neural networks and is used to predict the output of a dynamic system based on some historical data of that system. A pulse-discharge test was performed on a commercial lithium-ion (Li-ion) battery cell in order to collect data to evaluate those methods. Results are presented and compared.
{"title":"Kalman Filters versus Neural Networks in Battery State-of-Charge Estimation: A Comparative Study","authors":"A. Hussein","doi":"10.4236/IJMNTA.2014.35022","DOIUrl":"https://doi.org/10.4236/IJMNTA.2014.35022","url":null,"abstract":"Battery management systems (BMS) must estimate the state-of-charge (SOC) of the battery accurately to prolong its lifetime and ensure a reliable operation. Since batteries have a wide range of applications, the SOC estimation requirements and methods vary from an application to another. This paper compares two SOC estimation methods, namely extended Kalman filters (EKF) and artificial neural networks (ANN). EKF is a nonlinear optimal estimator that is used to estimate the inner state of a nonlinear dynamic system using a state-space model. On the other hand, ANN is a mathematical model that consists of interconnected artificial neurons inspired by biological neural networks and is used to predict the output of a dynamic system based on some historical data of that system. A pulse-discharge test was performed on a commercial lithium-ion (Li-ion) battery cell in order to collect data to evaluate those methods. Results are presented and compared.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70705102","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}
Pub Date : 2014-11-07DOI: 10.4236/IJMNTA.2014.35024
Cuicui Tian, Meixia Wang, Guoguang Lin
In this paper, we studied the solution existence and uniqueness and the attractors of the 2D Maxwell-Navier-Stokes with extra force equations.
本文研究了二维带外力的Maxwell-Navier-Stokes方程的解的存在唯一性和吸引子。
{"title":"The Global Attractors of the Solution for 2D Maxwell-Navier-Stokes with Extra Force Equations","authors":"Cuicui Tian, Meixia Wang, Guoguang Lin","doi":"10.4236/IJMNTA.2014.35024","DOIUrl":"https://doi.org/10.4236/IJMNTA.2014.35024","url":null,"abstract":"In this paper, we studied the solution existence and uniqueness and the attractors of the 2D Maxwell-Navier-Stokes with extra force equations.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70705307","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}
Pub Date : 2014-11-07DOI: 10.4236/IJMNTA.2014.35026
Y. Aguilera-Carvajal, S. Pérez-Cortes, J. Hurtado-Cruz, Erick Morales-Quezada
In copper sulfide concentrates smelting, the off-gases from the Pierce Smith converter (PSC) furnace must be treated to prevent environmental impacts as they are highly corrosive and toxic. The purpose of this research project is to present a methodology for the simulation of a capture and cooling system of the smelting off-gases from a Pierce Smith copper converter, using computational fluid dynamics. Through this methodology, it is possible to obtain a simulation model of the smelting off-gases behavior with an average error of 9.88%. Basically, it demonstrates that the simulated tendencies of the metallurgical off-gases on the cooling hood and chamber can be reliable to predict the thermo-fluid dynamic behavior of the off-gases inside the studied off-gases handling system.
{"title":"Computational Thermo-Fluid Dynamic Simulation of a Radiant Off-Gases Cooling System for Copper Smelting in a Pierce Smith Converter","authors":"Y. Aguilera-Carvajal, S. Pérez-Cortes, J. Hurtado-Cruz, Erick Morales-Quezada","doi":"10.4236/IJMNTA.2014.35026","DOIUrl":"https://doi.org/10.4236/IJMNTA.2014.35026","url":null,"abstract":"In copper sulfide concentrates smelting, the off-gases from the Pierce \u0000Smith converter (PSC) furnace must be treated to prevent environmental impacts \u0000as they are highly corrosive and toxic. The purpose of this research project is \u0000to present a methodology for the simulation of a capture and cooling system of \u0000the smelting off-gases from a Pierce Smith copper converter, using computational \u0000fluid dynamics. Through this methodology, it is possible to obtain a simulation \u0000model of the smelting off-gases behavior with an average error of 9.88%. Basically, \u0000it demonstrates that the simulated tendencies of the metallurgical off-gases on \u0000the cooling hood and chamber can be reliable to predict the thermo-fluid \u0000dynamic behavior of the off-gases inside the studied off-gases handling system.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70705327","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}
Pub Date : 2014-09-22DOI: 10.4236/IJMNTA.2014.34017
Muhammad Rizwan S. Khan, R. Loh
This paper addresses the analysis, design, and application of observer-based nonlinear controls by combining feedback linearization (FBL) and backstepping (BS) techniques with Luenberger observers. Complete development of observer-based controls is presented for a bioprocess. Controllers using input-output feedback linearization and backstepping techniques are designed first, assuming that all states are available for feedback. Next, the construction of observer in the transformed domain is presented based on input-output feedback linearization. This approach is then extended to observer design based on backstepping approach using the error equation resulted from the backstepping design procedure. Simulation results demonstrating the effectiveness of the techniques developed are presented and compared.
{"title":"Nonlinear Control of Bioprocess Using Feedback Linearization, Backstepping, and Luenberger Observers","authors":"Muhammad Rizwan S. Khan, R. Loh","doi":"10.4236/IJMNTA.2014.34017","DOIUrl":"https://doi.org/10.4236/IJMNTA.2014.34017","url":null,"abstract":"This paper addresses the analysis, design, and application of observer-based nonlinear controls by combining feedback linearization (FBL) and backstepping (BS) techniques with Luenberger observers. Complete development of observer-based controls is presented for a bioprocess. Controllers using input-output feedback linearization and backstepping techniques are designed first, assuming that all states are available for feedback. Next, the construction of observer in the transformed domain is presented based on input-output feedback linearization. This approach is then extended to observer design based on backstepping approach using the error equation resulted from the backstepping design procedure. Simulation results demonstrating the effectiveness of the techniques developed are presented and compared.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70704725","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}
Pub Date : 2014-09-22DOI: 10.4236/IJMNTA.2014.34018
Meixia Wang, Cuicui Tian, Guoguang Lin
In this paper, firstly, some priori estimates are obtained for the existence and uniqueness of solutions of a two dimensional generalized anisotropy Kuramoto-Sivashinsky Equation. Then we prove the existence of the global attractor. Finally, we get the upper bound estimation of the Haus-dorff and fractal dimension of attractor.
{"title":"Global Attractor and Dimension Estimation for a 2D Generalized Anisotropy Kuramoto-Sivashinsky Equation","authors":"Meixia Wang, Cuicui Tian, Guoguang Lin","doi":"10.4236/IJMNTA.2014.34018","DOIUrl":"https://doi.org/10.4236/IJMNTA.2014.34018","url":null,"abstract":"In this paper, firstly, some priori estimates are obtained for the existence and uniqueness of solutions of a two dimensional generalized anisotropy Kuramoto-Sivashinsky Equation. Then we prove the existence of the global attractor. Finally, we get the upper bound estimation of the Haus-dorff and fractal dimension of attractor.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70704761","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}
Pub Date : 2014-09-22DOI: 10.4236/IJMNTA.2014.34019
Baishun Liu, Xiang-Qian Luo, Jian-Hui Li
This paper proposes a systematic method to design general integral control with the generic integrator and integral control action. No longer resorting to an ordinary control along with a known Lyapunov function, but synthesizing singular perturbation technique, mean value theorem, stability theorem of interval matrix and Lyapunov method, a universal theorem to ensure regionally as well as semi-globally asymptotic stability is established in terms of some bounded information. Its highlight point is that the error of integrator output can be used to stabilize the system, just like the system state, such that it does not need to take an extra and special effort to deal with the integral dynamic. Theoretical analysis and simulation results demonstrated that: general integral controller, which is tuned by this design method, has super strong robustness and can deal with nonlinearity and uncertainties of dynamics more forcefully.
{"title":"General Integral Control Design via Singular Perturbation Technique","authors":"Baishun Liu, Xiang-Qian Luo, Jian-Hui Li","doi":"10.4236/IJMNTA.2014.34019","DOIUrl":"https://doi.org/10.4236/IJMNTA.2014.34019","url":null,"abstract":"This paper proposes a systematic method to design general integral control with the generic integrator and integral control action. No longer resorting to an ordinary control along with a known Lyapunov function, but synthesizing singular perturbation technique, mean value theorem, stability theorem of interval matrix and Lyapunov method, a universal theorem to ensure regionally as well as semi-globally asymptotic stability is established in terms of some bounded information. Its highlight point is that the error of integrator output can be used to stabilize the system, just like the system state, such that it does not need to take an extra and special effort to deal with the integral dynamic. Theoretical analysis and simulation results demonstrated that: general integral controller, which is tuned by this design method, has super strong robustness and can deal with nonlinearity and uncertainties of dynamics more forcefully.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70704885","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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