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Xin-zhuang Dong - One of the best experts on this subject based on the ideXlab platform.
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Output Feedback Admissible Control for Singular Systems: Delta Operator (Discretised) Approach
East Asian Journal on Applied Mathematics, 2017Co-Authors: Xin-zhuang Dong, Mingqing XiaoAbstract:AbstractSingular systems simultaneously capture the dynamics and algebraic constraints in many practical applications. Output feedback Admissible Control for singular systems through a delta operator method is considered in this article. Two novel admissibility conditions, derived for the singular delta operator system (SDOS) from a singular continuous system through sampling, can not only produce unified admissibility for both continuous and discrete singular systems but also practical procedures. To solve the problem of output feedback Admissible Control for the SDOS, an existence condition and design procedure is given for the determination of a physically realisable observer for the state estimation, and then a suitable state-feedback-like Admissible Controller design based on the observer is developed. All of the conditions presented are necessary and sufficient, involving strict linear matrix inequalities (LMI) with feasible solutions obtained with low computational costs. Numerical examples illustrate our approach.
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d Admissible Control of singular delta operator systems
International Congress on Image and Signal Processing, 2016Co-Authors: Guopeng Zhao, Xin-zhuang Dong, Yujiao SunAbstract:We mainly research the method of designing the D-Admissible Controller for singular delta operator systems. In order to ensure that the generalized Delta operator system is D-Admissible, we design a state feedback Controller. According to the definition of the generalized discrete system and the generalized Delta operator system, the relationship between them is analyzed. And the necessary and sufficient conditions for the D-admissibility of the singular Delta operator system are derived. Secondly, on account of the condition, the method of solving this D-Admissible Controller is to use linear matrix inequalities (LMI). Finally, in order to verify the effectiveness of the method, we give some numerical examples. Thus, the design method of this paper is feasible, and the D-Admissible Controller is reasonable and effective.
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CISP-BMEI - D-Admissible Control of singular delta operator systems
2016 9th International Congress on Image and Signal Processing BioMedical Engineering and Informatics (CISP-BMEI), 2016Co-Authors: Guopeng Zhao, Xin-zhuang Dong, Yujiao SunAbstract:We mainly research the method of designing the D-Admissible Controller for singular delta operator systems. In order to ensure that the generalized Delta operator system is D-Admissible, we design a state feedback Controller. According to the definition of the generalized discrete system and the generalized Delta operator system, the relationship between them is analyzed. And the necessary and sufficient conditions for the D-admissibility of the singular Delta operator system are derived. Secondly, on account of the condition, the method of solving this D-Admissible Controller is to use linear matrix inequalities (LMI). Finally, in order to verify the effectiveness of the method, we give some numerical examples. Thus, the design method of this paper is feasible, and the D-Admissible Controller is reasonable and effective.
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Admissible Control of Linear Singular Delta Operator Systems
Circuits Systems and Signal Processing, 2014Co-Authors: Xin-zhuang Dong, Mingqing XiaoAbstract:In this paper, we study the problem of state feedback Admissible Control for the linear singular delta operator systems that result from linear singular continuous systems. By introducing the concept of delta operator, for a given linear singular continuous system, we establish its corresponding delta operator model and this discrete model converges to its continuous counterpart as the sampling period decreases. Sufficient conditions for desirable Controllers in terms of matrix inequalities and linear matrix inequalities are given, and the explicit expressions of the Controllers are derived. Some examples as well as numerical simulations are provided to demonstrate the effectiveness of the proposed approaches.
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Observer-based Admissible Control for singular delta operator systems
2014 14th International Conference on Control Automation and Systems (ICCAS 2014), 2014Co-Authors: Xin-zhuang Dong, Mingqing Xiao, Yushun WangAbstract:This paper studies the problem of designing an observer-based Admissible Controller for singular delta operator systems. Sufficient conditions are provided for the existence of an asymptotical and physically realizable observer. Then an observer-based Admissible Controller is obtained in terms of strict linear matrix inequalities. The corresponding gain matrices appeared in our proposed approach can be constructed through the feasible solutions of a set of linear matrix inequalities. Some numerical examples are presented to demonstrate the theoretical outcomes of the paper.
Yushun Wang - One of the best experts on this subject based on the ideXlab platform.
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Observer-based Admissible Control for singular delta operator systems
2014 14th International Conference on Control Automation and Systems (ICCAS 2014), 2014Co-Authors: Xin-zhuang Dong, Mingqing Xiao, Yushun WangAbstract:This paper studies the problem of designing an observer-based Admissible Controller for singular delta operator systems. Sufficient conditions are provided for the existence of an asymptotical and physically realizable observer. Then an observer-based Admissible Controller is obtained in terms of strict linear matrix inequalities. The corresponding gain matrices appeared in our proposed approach can be constructed through the feasible solutions of a set of linear matrix inequalities. Some numerical examples are presented to demonstrate the theoretical outcomes of the paper.
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ICARCV - H ∞ Control of singular systems via delta operator approach
2014 13th International Conference on Control Automation Robotics & Vision (ICARCV), 2014Co-Authors: Xin-zhuang Dong, Mingqing Xiao, Yushun WangAbstract:This paper investigates the problem of state feedback H ∞ Control for singular systems through delta operator approach. Firstly, a bounded real lemma corresponding to a singular continuous system under the framework of the delta operator model is obtained. Then, the existence condition and explicit expression of a desirable H ∞ Controller for the singular delta operator system are presented. As special cases, the results of Admissible Control for the singular delta operator system and H ∞ Control as well as Admissible Control for the singular continuous system are also derived. All required conditions in this paper are characterized in the form of strict linear matrix inequalities whose feasible solutions can be obtained easily and directly. Finally, some numerical examples are provided to illustrate the effectiveness of the obtained theoretical results in the paper.
Mingqing Xiao - One of the best experts on this subject based on the ideXlab platform.
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Output Feedback Admissible Control for Singular Systems: Delta Operator (Discretised) Approach
East Asian Journal on Applied Mathematics, 2017Co-Authors: Xin-zhuang Dong, Mingqing XiaoAbstract:AbstractSingular systems simultaneously capture the dynamics and algebraic constraints in many practical applications. Output feedback Admissible Control for singular systems through a delta operator method is considered in this article. Two novel admissibility conditions, derived for the singular delta operator system (SDOS) from a singular continuous system through sampling, can not only produce unified admissibility for both continuous and discrete singular systems but also practical procedures. To solve the problem of output feedback Admissible Control for the SDOS, an existence condition and design procedure is given for the determination of a physically realisable observer for the state estimation, and then a suitable state-feedback-like Admissible Controller design based on the observer is developed. All of the conditions presented are necessary and sufficient, involving strict linear matrix inequalities (LMI) with feasible solutions obtained with low computational costs. Numerical examples illustrate our approach.
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Admissible Control of Linear Singular Delta Operator Systems
Circuits Systems and Signal Processing, 2014Co-Authors: Xin-zhuang Dong, Mingqing XiaoAbstract:In this paper, we study the problem of state feedback Admissible Control for the linear singular delta operator systems that result from linear singular continuous systems. By introducing the concept of delta operator, for a given linear singular continuous system, we establish its corresponding delta operator model and this discrete model converges to its continuous counterpart as the sampling period decreases. Sufficient conditions for desirable Controllers in terms of matrix inequalities and linear matrix inequalities are given, and the explicit expressions of the Controllers are derived. Some examples as well as numerical simulations are provided to demonstrate the effectiveness of the proposed approaches.
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Observer-based Admissible Control for singular delta operator systems
2014 14th International Conference on Control Automation and Systems (ICCAS 2014), 2014Co-Authors: Xin-zhuang Dong, Mingqing Xiao, Yushun WangAbstract:This paper studies the problem of designing an observer-based Admissible Controller for singular delta operator systems. Sufficient conditions are provided for the existence of an asymptotical and physically realizable observer. Then an observer-based Admissible Controller is obtained in terms of strict linear matrix inequalities. The corresponding gain matrices appeared in our proposed approach can be constructed through the feasible solutions of a set of linear matrix inequalities. Some numerical examples are presented to demonstrate the theoretical outcomes of the paper.
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ICARCV - H ∞ Control of singular systems via delta operator approach
2014 13th International Conference on Control Automation Robotics & Vision (ICARCV), 2014Co-Authors: Xin-zhuang Dong, Mingqing Xiao, Yushun WangAbstract:This paper investigates the problem of state feedback H ∞ Control for singular systems through delta operator approach. Firstly, a bounded real lemma corresponding to a singular continuous system under the framework of the delta operator model is obtained. Then, the existence condition and explicit expression of a desirable H ∞ Controller for the singular delta operator system are presented. As special cases, the results of Admissible Control for the singular delta operator system and H ∞ Control as well as Admissible Control for the singular continuous system are also derived. All required conditions in this paper are characterized in the form of strict linear matrix inequalities whose feasible solutions can be obtained easily and directly. Finally, some numerical examples are provided to illustrate the effectiveness of the obtained theoretical results in the paper.
Nesir Huseyin - One of the best experts on this subject based on the ideXlab platform.
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Approximation of the set of trajectories of the nonlinear Control system with limited Control resources
Mathematical Modelling and Analysis, 2018Co-Authors: Nesir Huseyin, Anar Huseyin, Khalik G. GuseinovAbstract:In this paper the Control system described by a Urysohn type integral equation is studied. It is assumed that the Control functions have integral constraint. Approximation of the set of trajectories generated by all Admissible Control functions is considered. Step by step way, the set of Admissible Control functions is replaced by a set consisting of a finite number of Control functions which generates a finite number of trajectories. An evaluation of the Hausdorff distance between the set of trajectories of the system and the set, consisting of a finite number of trajectories is obtained.
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Compactness of the Set of Trajectories of the Control System Described by a Urysohn Type Integral Equation
An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 2016Co-Authors: Nesir HuseyinAbstract:The Control system with integralconstraint on the Controls is studied, where the behavior of the system by a Urysohn type integral equation is described. It is assumed thatthe system is nonlinear with respect to the state vector, affine with respect to the Control vector. The closed ball ofthe space $L_p(E;\mathbb{R}^m)$ $(p>1)$ with radius $r$ and centered at theorigin, is chosen as the set of Admissible Control functions, where $E\subset \mathbb{R}^k$ is a compact set. Itis proved that the set of trajectories generated by all Admissible Control functions is a compact subset of the space of continuous functions.
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Compactness of the set of trajectories of the Control system described by a Urysohn type integral equation with quadratic integral constraints on the Control functions
Journal of Inequalities and Applications, 2016Co-Authors: Idham Arif Alias, Nesir Huseyin, Anar HuseyinAbstract:In this paper the Control system is considered described by a Urysohn type integral equation which is nonlinear with respect to the state vector and is affine with respect to the Control vector. The functions from the space \(L_{2} ( [t_{0},\theta ];\mathbb {R}^{m} )\) satisfying a quadratic integral constraint are chosen as Admissible Control functions. The set of trajectories generated by all Admissible Control functions is studied. The boundedness, closedness, precompactness, and hence the compactness of the set of trajectories in the space of continuous functions is proved.
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Approximation of the Sections of the Set of Trajectories of the Control System Described by a Nonlinear Volterra Integral Equation
Mathematical Modelling and Analysis, 2015Co-Authors: Anar Huseyin, Nesir Huseyin, Khalik G. GuseinovAbstract:Approximation of the sections of the set of trajectories of the Control system described by a nonlinear Volterra integral equation is studied. The Admissible Control functions are chosen from the closed ball of the space Lp, p > 1, with radius µ and centered at the origin. The set of Admissible Control functions is replaced by the set of Control functions, which includes a finite number of Control functions and generates a finite number of trajectories. It is proved that the sections of the set of trajectories can be approximated by the sections of the set of trajectories, generated by a finite number of Control functions.
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Dependence on the parameters of the set of trajectories of the Control system described by a nonlinear Volterra integral equation
Applications of Mathematics, 2014Co-Authors: Anar Huseyin, Nesir HuseyinAbstract:In this paper the Control system with limited Control resources is studied, where the behavior of the system is described by a nonlinear Volterra integral equation. The Admissible Control functions are chosen from the closed ball centered at the origin with radius µ in Lp (p > 1). It is proved that the set of trajectories generated by all Admissible Control functions is Lipschitz continuous with respect to µ for each fixed p, and is continuous with respect to p for each fixed µ. An upper estimate for the diameter of the set of trajectories is given.
Anar Huseyin - One of the best experts on this subject based on the ideXlab platform.
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Approximation of the set of trajectories of the nonlinear Control system with limited Control resources
Mathematical Modelling and Analysis, 2018Co-Authors: Nesir Huseyin, Anar Huseyin, Khalik G. GuseinovAbstract:In this paper the Control system described by a Urysohn type integral equation is studied. It is assumed that the Control functions have integral constraint. Approximation of the set of trajectories generated by all Admissible Control functions is considered. Step by step way, the set of Admissible Control functions is replaced by a set consisting of a finite number of Control functions which generates a finite number of trajectories. An evaluation of the Hausdorff distance between the set of trajectories of the system and the set, consisting of a finite number of trajectories is obtained.
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Compactness of the set of trajectories of the Control system described by a Urysohn type integral equation with quadratic integral constraints on the Control functions
Journal of Inequalities and Applications, 2016Co-Authors: Idham Arif Alias, Nesir Huseyin, Anar HuseyinAbstract:In this paper the Control system is considered described by a Urysohn type integral equation which is nonlinear with respect to the state vector and is affine with respect to the Control vector. The functions from the space \(L_{2} ( [t_{0},\theta ];\mathbb {R}^{m} )\) satisfying a quadratic integral constraint are chosen as Admissible Control functions. The set of trajectories generated by all Admissible Control functions is studied. The boundedness, closedness, precompactness, and hence the compactness of the set of trajectories in the space of continuous functions is proved.
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Approximation of the Sections of the Set of Trajectories of the Control System Described by a Nonlinear Volterra Integral Equation
Mathematical Modelling and Analysis, 2015Co-Authors: Anar Huseyin, Nesir Huseyin, Khalik G. GuseinovAbstract:Approximation of the sections of the set of trajectories of the Control system described by a nonlinear Volterra integral equation is studied. The Admissible Control functions are chosen from the closed ball of the space Lp, p > 1, with radius µ and centered at the origin. The set of Admissible Control functions is replaced by the set of Control functions, which includes a finite number of Control functions and generates a finite number of trajectories. It is proved that the sections of the set of trajectories can be approximated by the sections of the set of trajectories, generated by a finite number of Control functions.
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Dependence on the parameters of the set of trajectories of the Control system described by a nonlinear Volterra integral equation
Applications of Mathematics, 2014Co-Authors: Anar Huseyin, Nesir HuseyinAbstract:In this paper the Control system with limited Control resources is studied, where the behavior of the system is described by a nonlinear Volterra integral equation. The Admissible Control functions are chosen from the closed ball centered at the origin with radius µ in Lp (p > 1). It is proved that the set of trajectories generated by all Admissible Control functions is Lipschitz continuous with respect to µ for each fixed p, and is continuous with respect to p for each fixed µ. An upper estimate for the diameter of the set of trajectories is given.
