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Jun Huang - One of the best experts on this subject based on the ideXlab platform.
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h observer design for singular one sided lur e Differential Inclusion system
Journal of The Franklin Institute-engineering and Applied Mathematics, 2017Co-Authors: Jun Huang, Wei Zhang, Minjie Shi, Liang ChenAbstract:This paper deals with the H∞ observer design problem for singular Lur’e Differential Inclusion system with one-sided Lipschitz term. The Luenberger observer theory is used to construct the framework of H∞ observer. First, the system without disturbance is considered and sufficient conditions are derived to guarantee that the error system is asymptotically stable. Then, the result is extended to the system subject to disturbance, the conditions for the existence of H∞ observer are also given. Finally, two examples are simulated to show the effectiveness of the proposed observers in this paper.
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a note on adaptive observer for the lur e Differential Inclusion system
Nonlinear Dynamics, 2016Co-Authors: Jun Huang, Junfeng Zhang, Zhengzhi HanAbstract:This paper considers the adaptive observer design problem for the Lur’e Differential Inclusion system with unknown parameters. Different from the current work, the proposed observer does not hold any set-valued mapping and the uncertain parameters can also be identified. Firstly, the adaptive observer is designed for the Lur’e Differential Inclusion system, and it is proved to be valid by Lyapunov stability theory. Then, based on the canonical form of the system matrix, the sufficient and necessary condition for one assumption is presented in both SISO and MIMO cases. Finally, numerical examples are simulated to show the effectiveness of the proposed method.
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novel observer design method for lur e Differential Inclusion systems
International Journal of Systems Science, 2016Co-Authors: Jun Huang, Yu GaoAbstract:This paper proposes a new method to design observers for Lur'e Differential Inclusion systems. The feature of this method is that the designed observers do not contain any set-valued functions. single-input-single-output SISO systems are considered firstly, then the results are extended to multiple-input-multiple-output MIMO systems. For MIMO systems, the form of reduced-order observers is also presented. Simulations are given to show these observers work well.
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Luré Differential Inclusion Systems
Theory of Control Systems Described by Differential Inclusions, 2016Co-Authors: Zhengzhi Han, Xiushan Cai, Jun HuangAbstract:In the former chapter, control problems of linear polytope systems are considered by using the convex hull Lyapunov function. The linear polytope system is a convex combination of a finite set of finite linear systems. Involved set-valued mapping in the Differential Inclusion is the convex combination; hence, convex theory can be applied to deal with these control problems. In this chapter, the Lure Differential Inclusion system and its relative control problems are considered. This kind of Differential Inclusions is different from linear convex hulls; the set-valued mapping satisfies so-called sector condition, i.e., the image of the set-valued mapping is in a cone. Hence, it is a naturally nonlinear mapping.
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actuator fault detection and estimation for the lur e Differential Inclusion system
Applied Mathematical Modelling, 2014Co-Authors: Jun Huang, Maoqing Zhang, Fanglai Zhu, Zhengzhi HanAbstract:Abstract This paper deals with actuator fault detection and estimation for the Lur’e Differential Inclusion system. An adaptive full-order observer is used to detect the occurrence of the actuator fault. Then, based on a reduced-order observer, an approach to estimate the actuator fault is presented. A simulation of rotor system is given to illustrate the effectiveness of the proposed method.
Zhengzhi Han - One of the best experts on this subject based on the ideXlab platform.
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a note on adaptive observer for the lur e Differential Inclusion system
Nonlinear Dynamics, 2016Co-Authors: Jun Huang, Junfeng Zhang, Zhengzhi HanAbstract:This paper considers the adaptive observer design problem for the Lur’e Differential Inclusion system with unknown parameters. Different from the current work, the proposed observer does not hold any set-valued mapping and the uncertain parameters can also be identified. Firstly, the adaptive observer is designed for the Lur’e Differential Inclusion system, and it is proved to be valid by Lyapunov stability theory. Then, based on the canonical form of the system matrix, the sufficient and necessary condition for one assumption is presented in both SISO and MIMO cases. Finally, numerical examples are simulated to show the effectiveness of the proposed method.
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Luré Differential Inclusion Systems
Theory of Control Systems Described by Differential Inclusions, 2016Co-Authors: Zhengzhi Han, Xiushan Cai, Jun HuangAbstract:In the former chapter, control problems of linear polytope systems are considered by using the convex hull Lyapunov function. The linear polytope system is a convex combination of a finite set of finite linear systems. Involved set-valued mapping in the Differential Inclusion is the convex combination; hence, convex theory can be applied to deal with these control problems. In this chapter, the Lure Differential Inclusion system and its relative control problems are considered. This kind of Differential Inclusions is different from linear convex hulls; the set-valued mapping satisfies so-called sector condition, i.e., the image of the set-valued mapping is in a cone. Hence, it is a naturally nonlinear mapping.
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actuator fault detection and estimation for the lur e Differential Inclusion system
Applied Mathematical Modelling, 2014Co-Authors: Jun Huang, Maoqing Zhang, Fanglai Zhu, Zhengzhi HanAbstract:Abstract This paper deals with actuator fault detection and estimation for the Lur’e Differential Inclusion system. An adaptive full-order observer is used to detect the occurrence of the actuator fault. Then, based on a reduced-order observer, an approach to estimate the actuator fault is presented. A simulation of rotor system is given to illustrate the effectiveness of the proposed method.
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observer design for the lur e Differential Inclusion system with markovian jumping parameters
International Journal of Systems Science, 2013Co-Authors: Jun Huang, Zhengzhi Han, Peng Wang, Xiushan CaiAbstract:This article deals with the observer design for the Lur'e Differential Inclusion system with Markovian jumping parameters. The set-valued mapping in the system is assumed to be upper semi-continuous, closed, convex, bounded and monotone. The full-order and reduced-order observers are designed to make the corresponding error systems exponentially stable in the mean square, respectively. The criteria are given to guarantee the existence of both full-order and reduced-order observers. The rotor system is considered as an example to show the validity of the proposed method.
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adaptive terminal sliding mode control for nonlinear Differential Inclusion systems with disturbance
Nonlinear Dynamics, 2013Co-Authors: Jun Huang, Zhengzhi Han, Lining Sun, Leipo LiuAbstract:This paper deals with the adaptive terminal sliding mode control for nonlinear Differential Inclusion systems subjected to disturbance. The upper bound of the disturbance is unknown. First, the fast terminal sliding mode surface is established and sufficient condition for fast convergence is given. Then the adaptive sliding mode controller is designed to make the state of system arrive at the sliding mode in finite time. A numerical example is provided to show the effectiveness of the proposed method.
Leipo Liu - One of the best experts on this subject based on the ideXlab platform.
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adaptive terminal sliding mode control for nonlinear Differential Inclusion systems with disturbance
Nonlinear Dynamics, 2013Co-Authors: Jun Huang, Zhengzhi Han, Lining Sun, Leipo LiuAbstract:This paper deals with the adaptive terminal sliding mode control for nonlinear Differential Inclusion systems subjected to disturbance. The upper bound of the disturbance is unknown. First, the fast terminal sliding mode surface is established and sufficient condition for fast convergence is given. Then the adaptive sliding mode controller is designed to make the state of system arrive at the sliding mode in finite time. A numerical example is provided to show the effectiveness of the proposed method.
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globally asymptotical stabilisation for a class of feedback linearisable Differential Inclusion systems
Iet Control Theory and Applications, 2011Co-Authors: Xiushan Cai, Leipo Liu, Jian Huang, Weidong ZhangAbstract:Globally asymptotical stabilisation for a class of feedback linearisable Differential Inclusion systems with disturbances is dealt with in this study. A systematic method for constructing the control Lyapunov function (CLF) is presented by solving the Lyapunov equation. Sufficient and necessary conditions for a quadratic CLF to be a CLF for single-input and multi-input systems are acquired, respectively. Then, continuous state feedback laws are designed for corresponding systems. Finally, the effectiveness of the proposed method is illustrated by two simulation examples.
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adaptive full order and reduced order observers for the lur e Differential Inclusion system
Communications in Nonlinear Science and Numerical Simulation, 2011Co-Authors: Jun Huang, Zhengzhi Han, Xiushan Cai, Leipo LiuAbstract:Abstract This paper deals with the observer design for the Lur’e Differential Inclusion system with unknown parameters. The set-valued mapping in the Differential Inclusion is upper semi-continuous, closed, convex, bounded and monotone. First, under some assumptions an adaptive full-order observer is designed for the system. Then, under the same assumptions, a reduced-order observer is proved to exist. An example is provided to show the validation of the designed observers.
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stability analysis of linear time delay Differential Inclusion systems subject to input saturation
Iet Control Theory and Applications, 2010Co-Authors: Xiushan Cai, Jian Huang, Leipo LiuAbstract:Stability analysis of linear Differential Inclusion systems with time-delay and input saturation is devoted in this study. The convex hull Lyapunov function is used to construct Lyapunov–Krasovskii functionals. A continuous state feedback law is designed. By the state feedbacks, sufficient conditions for saturated stabilisation are acquired and the domain of attraction is estimated. Furthermore, disturbance rejection with minimal reachable set is studied under two types of disturbances. Moreover, least L2 gain is obtained under the unit energy disturbances. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design technique.
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robust stabilization of linear Differential Inclusion system with time delay
Mathematics and Computers in Simulation, 2010Co-Authors: Leipo Liu, Zhengzhi Han, Xiushan Cai, Jun HuangAbstract:This paper is concerned with robust stabilization of linear Differential Inclusion systems with time delay. A nonlinear feedback law is established by using convex hull quadratic Lyapunov functions to make the state exponentially stable. An example is given to illustrate the effectiveness of the proposed method.
Xiushan Cai - One of the best experts on this subject based on the ideXlab platform.
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Luré Differential Inclusion Systems
Theory of Control Systems Described by Differential Inclusions, 2016Co-Authors: Zhengzhi Han, Xiushan Cai, Jun HuangAbstract:In the former chapter, control problems of linear polytope systems are considered by using the convex hull Lyapunov function. The linear polytope system is a convex combination of a finite set of finite linear systems. Involved set-valued mapping in the Differential Inclusion is the convex combination; hence, convex theory can be applied to deal with these control problems. In this chapter, the Lure Differential Inclusion system and its relative control problems are considered. This kind of Differential Inclusions is different from linear convex hulls; the set-valued mapping satisfies so-called sector condition, i.e., the image of the set-valued mapping is in a cone. Hence, it is a naturally nonlinear mapping.
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observer design for the lur e Differential Inclusion system with markovian jumping parameters
International Journal of Systems Science, 2013Co-Authors: Jun Huang, Zhengzhi Han, Peng Wang, Xiushan CaiAbstract:This article deals with the observer design for the Lur'e Differential Inclusion system with Markovian jumping parameters. The set-valued mapping in the system is assumed to be upper semi-continuous, closed, convex, bounded and monotone. The full-order and reduced-order observers are designed to make the corresponding error systems exponentially stable in the mean square, respectively. The criteria are given to guarantee the existence of both full-order and reduced-order observers. The rotor system is considered as an example to show the validity of the proposed method.
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output tracking and disturbance rejection of linear Differential Inclusion systems
International Journal of Systems Science, 2012Co-Authors: Xiushan Cai, Jun Huang, Qiyue XieAbstract:The globally tracking problem of linear Differential Inclusion systems with disturbances is studied in this article. By using the Hamilton–Caylay Theorem, an operator is constructed such that tracking problem is converted into a standard stabilisation problem. A control law is designed such that the output signal of the closed-loop system tracks some reference signal and rejects the disturbances. A second-order LDI system is used to illustrate the effectiveness of the proposed design technique.
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globally asymptotical stabilisation for a class of feedback linearisable Differential Inclusion systems
Iet Control Theory and Applications, 2011Co-Authors: Xiushan Cai, Leipo Liu, Jian Huang, Weidong ZhangAbstract:Globally asymptotical stabilisation for a class of feedback linearisable Differential Inclusion systems with disturbances is dealt with in this study. A systematic method for constructing the control Lyapunov function (CLF) is presented by solving the Lyapunov equation. Sufficient and necessary conditions for a quadratic CLF to be a CLF for single-input and multi-input systems are acquired, respectively. Then, continuous state feedback laws are designed for corresponding systems. Finally, the effectiveness of the proposed method is illustrated by two simulation examples.
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adaptive full order and reduced order observers for the lur e Differential Inclusion system
Communications in Nonlinear Science and Numerical Simulation, 2011Co-Authors: Jun Huang, Zhengzhi Han, Xiushan Cai, Leipo LiuAbstract:Abstract This paper deals with the observer design for the Lur’e Differential Inclusion system with unknown parameters. The set-valued mapping in the Differential Inclusion is upper semi-continuous, closed, convex, bounded and monotone. First, under some assumptions an adaptive full-order observer is designed for the system. Then, under the same assumptions, a reduced-order observer is proved to exist. An example is provided to show the validation of the designed observers.
Guowei Dai - One of the best experts on this subject based on the ideXlab platform.
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nonsmooth version of fountain theorem and its application to a dirichlet type Differential Inclusion problem
Nonlinear Analysis-theory Methods & Applications, 2010Co-Authors: Guowei DaiAbstract:Abstract In this paper we establish a nonsmooth version of Fountain theorem by adopting the framework of nonsmooth analysis theory, which is a generalization of Theorem 3.6 of Willem (1996) [2] . Then we present an application of this theorem to a Dirichlet-type Differential Inclusion problem.
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three solutions for a Differential Inclusion problem involving the p x laplacian
Nonlinear Analysis-theory Methods & Applications, 2009Co-Authors: Guowei Dai, Wulong LiuAbstract:Abstract In this paper we consider Differential Inclusion problem involving the p ( x ) -Laplacian of the type { − div ( | ∇ u | p ( x ) − 2 ∇ u ) ∈ λ ∂ F ( x , u ) in Ω , u = 0 on ∂ Ω . Applying a version of the non-smooth three-critical-points theorem we obtain the existence of three solutions of the problem in W 0 1 , p ( x ) ( Ω ) .
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infinitely many solutions for a Differential Inclusion problem in rn involving the p x laplacian
Nonlinear Analysis-theory Methods & Applications, 2009Co-Authors: Guowei DaiAbstract:Abstract In this paper we consider the Differential Inclusion problem in R N involving the p ( x ) -Laplacian of the type { − div ( | ∇ u | p ( x ) − 2 ∇ u ) + | u | p ( x ) − 2 u ∈ ∂ F ( x , u ) in R N , u ∈ W 1 , p ( x ) ( R N ) . We prove the existence of infinitely many radially symmetric solutions of the problem under suitable hypotheses by applying a nonsmooth variational principle due to Marano and Motreanu and the theory of the variable exponent Sobolev spaces.
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three solutions for a neumann type Differential Inclusion problem involving the p x laplacian
Nonlinear Analysis-theory Methods & Applications, 2009Co-Authors: Guowei DaiAbstract:Abstract In this paper we consider Neumann-type Differential Inclusion problems involving the p ( x ) -Laplacian of the type { − div ( | ∇ u | p ( x ) − 2 ∇ u ) + | u | p ( x ) − 2 u ∈ λ ∂ F ( x , u ) in Ω , ∂ u ∂ γ = 0 on ∂ Ω . Applying a version of the non-smooth three-critical-points theorem we obtain the existence of three solutions of the problem in W 0 1 , p ( x ) ( Ω ) .
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infinitely many solutions for a neumann type Differential Inclusion problem involving the p x laplacian
Nonlinear Analysis-theory Methods & Applications, 2009Co-Authors: Guowei DaiAbstract:Abstract In this paper we consider a Differential Inclusion problem involving the p ( x ) -Laplacian of the type { − div ( | ∇ u | p ( x ) − 2 ∇ u ) + λ ( x ) | u | p ( x ) − 2 u ∈ ∂ F ( x , u ) + ∂ G ( x , u ) in Ω , ∂ u ∂ γ = 0 on ∂ Ω . We prove the existence of infinitely many solutions of this problem under suitable hypotheses by applying a non-smooth Ricceri-type variational principle and the theory of the variable exponent Sobolev spaces.