A bilinear fault detection observer is proposed for a class of continuous time singular bilinear systems subject to unknown input disturbance and fault. By singular value decomposition on the original system, a biline...A bilinear fault detection observer is proposed for a class of continuous time singular bilinear systems subject to unknown input disturbance and fault. By singular value decomposition on the original system, a bilinear fault detection observer is proposed for the decomposed system via an algebraic Riccati equation, and the domain of attraction of the state estimation error is estimated. A design procedure is presented to determine the fault detection threshold. A model of flexible joint robot is used to demonstrate the effectiveness of the proposed method.展开更多
In this paper, switched controllers are designed for a class of nonlinear discrete singular systems and a class of discrete singular bilinear systems. An invariant principle is presented for such switched nonlinear si...In this paper, switched controllers are designed for a class of nonlinear discrete singular systems and a class of discrete singular bilinear systems. An invariant principle is presented for such switched nonlinear singular systems. The invariant principle and the switched controllers are used to globally stabilize a class of singular bilinear systems that are not open-loop stable.展开更多
Bilinear singular systems can be used in the investigation of different types of engineering systems.In the past decade,considerable attention has been paid to analyzing and synthesizing singular bilinear systems.Thei...Bilinear singular systems can be used in the investigation of different types of engineering systems.In the past decade,considerable attention has been paid to analyzing and synthesizing singular bilinear systems.Their importance lies in their real world application such as economic,ecological,and socioeconomic processes.They are also applied in several biological processes,such as population dynamics of biological species,water balance,temperature regulation in the human body,carbon dioxide control in lungs,blood pressure,immune system,cardiac regulation,etc.Bilinear singular systems naturally represent different physical processes such as the fundamental law of mass action,the DC motor,the induction motor drives,the mechanical brake systems,aerial combat between two aircraft,the missile intercept problem,modeling and control of small furnaces and hydraulic rotary multimotor systems.The current research work discusses the Legendre Neural Network’s implementation to evaluate time-varying singular bilinear systems for finding the exact solution.The results were obtained from two methods namely the RK-Butcher algorithm and the Runge Kutta Arithmetic Mean(RKAM)method.Compared with the results attained from Legendre Neural Network Method for time-varying singular bilinear systems,the output proved to be accurate.As such,this research article established that the proposed Legendre Neural Network could be easily implemented in MATLAB.One can obtain the solution for any length of time from this method in time-varying singular bilinear systems.展开更多
Controllable canonical forms play important roles in the analysis and design of control systems.In this paper,a fundamental class of discrete-time bilinear systems are considered.Such systems are of interest since,on ...Controllable canonical forms play important roles in the analysis and design of control systems.In this paper,a fundamental class of discrete-time bilinear systems are considered.Such systems are of interest since,on one hand,they have the most complete controllability theory.On the other hand,they can be nearly-controllable even if controllability fails.Firstly,controllability of the systems with positive control inputs is studied and necessary and sufficient algebraic criteria for positive-controllability and positive-near-controllability are derived.Then,controllable canonical forms and nearly-controllable canonical forms of the systems are presented,respectively,where the corresponding transformation matrices are also explicitly constructed.Examples are given to demonstrate the effectiveness of the derived controllability criteria and controllable canonical forms.展开更多
This paper is concerned with the output stabilisation for a class of distributed bilinear system evolving in a spatial domain.We give sufficient conditions for strong and weak output stabilisation.Also,the output sta...This paper is concerned with the output stabilisation for a class of distributed bilinear system evolving in a spatial domain.We give sufficient conditions for strong and weak output stabilisation.Also,the output stabilisation is discussed using a minimisation problem.Examples and simulations are given.展开更多
This paper studies regional stabilization of a distributed bilinear system evolving on a spatial domain Ω. Sufficient conditions for regional weak, strong and exponential stabilization are given. Also we discuss a re...This paper studies regional stabilization of a distributed bilinear system evolving on a spatial domain Ω. Sufficient conditions for regional weak, strong and exponential stabilization are given. Also we discuss a regional optimal stabilization problem. The obtained results are illustrated by examples and simulations.展开更多
This paper addresses a gradient tracking problem of a bilinear reaction–diffusion equation evolvingin a spatial domainΩ ⊂ Rn, n ≤ 3. Such an equation is excited with distributed and boundedcontrols. The problem is ...This paper addresses a gradient tracking problem of a bilinear reaction–diffusion equation evolvingin a spatial domainΩ ⊂ Rn, n ≤ 3. Such an equation is excited with distributed and boundedcontrols. The problem is formulated by the minimisation of a functional constituted of the deviationbetween the desired gradient and the current one all over a time interval and the energyterm. Then we prove the existence of an optimal control that we characterise by an optimalitysystem. Moreover, we discuss two sets of particular controls: the set of time dependent controlsand the space dependent ones. A computational approach and illustrative simulations are alsogiven.展开更多
The paper introduces a new method for finding optimal control of algebraic dynamic systems. The structure of algebraic dynamical systems is nonlinear with quadratic and bilinear terms. A new hybrid extended Fourier se...The paper introduces a new method for finding optimal control of algebraic dynamic systems. The structure of algebraic dynamical systems is nonlinear with quadratic and bilinear terms. A new hybrid extended Fourier series is introduced, and state and control variables of the system are expanded by this series. Moreover, properties of new series are presented, and integration and product operational matrices are obtained. Using operational matrices, optimal control of the systems is converted to a set of simultaneous nonlinear algebraic relations. An illustrative example is included to compare our results with those in the literature.展开更多
基金This work was supported in part by National Nature Science Foundation of China (No. 60325311, 60534010, 60572070)the Funds for Creative Research Groups of China (No. 60521003)the Program for Changjiang Scholars and Innovative Research Team in University (No. IRT0421).
文摘A bilinear fault detection observer is proposed for a class of continuous time singular bilinear systems subject to unknown input disturbance and fault. By singular value decomposition on the original system, a bilinear fault detection observer is proposed for the decomposed system via an algebraic Riccati equation, and the domain of attraction of the state estimation error is estimated. A design procedure is presented to determine the fault detection threshold. A model of flexible joint robot is used to demonstrate the effectiveness of the proposed method.
基金This work was supported by the Science Technical Foundation of Liaoning of China (No. 2001401041)
文摘In this paper, switched controllers are designed for a class of nonlinear discrete singular systems and a class of discrete singular bilinear systems. An invariant principle is presented for such switched nonlinear singular systems. The invariant principle and the switched controllers are used to globally stabilize a class of singular bilinear systems that are not open-loop stable.
文摘Bilinear singular systems can be used in the investigation of different types of engineering systems.In the past decade,considerable attention has been paid to analyzing and synthesizing singular bilinear systems.Their importance lies in their real world application such as economic,ecological,and socioeconomic processes.They are also applied in several biological processes,such as population dynamics of biological species,water balance,temperature regulation in the human body,carbon dioxide control in lungs,blood pressure,immune system,cardiac regulation,etc.Bilinear singular systems naturally represent different physical processes such as the fundamental law of mass action,the DC motor,the induction motor drives,the mechanical brake systems,aerial combat between two aircraft,the missile intercept problem,modeling and control of small furnaces and hydraulic rotary multimotor systems.The current research work discusses the Legendre Neural Network’s implementation to evaluate time-varying singular bilinear systems for finding the exact solution.The results were obtained from two methods namely the RK-Butcher algorithm and the Runge Kutta Arithmetic Mean(RKAM)method.Compared with the results attained from Legendre Neural Network Method for time-varying singular bilinear systems,the output proved to be accurate.As such,this research article established that the proposed Legendre Neural Network could be easily implemented in MATLAB.One can obtain the solution for any length of time from this method in time-varying singular bilinear systems.
基金supported by the National Natural Science Foundation of China under Grant Nos.61973014and 61573044。
文摘Controllable canonical forms play important roles in the analysis and design of control systems.In this paper,a fundamental class of discrete-time bilinear systems are considered.Such systems are of interest since,on one hand,they have the most complete controllability theory.On the other hand,they can be nearly-controllable even if controllability fails.Firstly,controllability of the systems with positive control inputs is studied and necessary and sufficient algebraic criteria for positive-controllability and positive-near-controllability are derived.Then,controllable canonical forms and nearly-controllable canonical forms of the systems are presented,respectively,where the corresponding transformation matrices are also explicitly constructed.Examples are given to demonstrate the effectiveness of the derived controllability criteria and controllable canonical forms.
基金Thiswork was supported byAcadémieHassan II des Sciences et Techniques[630/2016].
文摘This paper is concerned with the output stabilisation for a class of distributed bilinear system evolving in a spatial domain.We give sufficient conditions for strong and weak output stabilisation.Also,the output stabilisation is discussed using a minimisation problem.Examples and simulations are given.
文摘This paper studies regional stabilization of a distributed bilinear system evolving on a spatial domain Ω. Sufficient conditions for regional weak, strong and exponential stabilization are given. Also we discuss a regional optimal stabilization problem. The obtained results are illustrated by examples and simulations.
文摘This paper addresses a gradient tracking problem of a bilinear reaction–diffusion equation evolvingin a spatial domainΩ ⊂ Rn, n ≤ 3. Such an equation is excited with distributed and boundedcontrols. The problem is formulated by the minimisation of a functional constituted of the deviationbetween the desired gradient and the current one all over a time interval and the energyterm. Then we prove the existence of an optimal control that we characterise by an optimalitysystem. Moreover, we discuss two sets of particular controls: the set of time dependent controlsand the space dependent ones. A computational approach and illustrative simulations are alsogiven.
文摘The paper introduces a new method for finding optimal control of algebraic dynamic systems. The structure of algebraic dynamical systems is nonlinear with quadratic and bilinear terms. A new hybrid extended Fourier series is introduced, and state and control variables of the system are expanded by this series. Moreover, properties of new series are presented, and integration and product operational matrices are obtained. Using operational matrices, optimal control of the systems is converted to a set of simultaneous nonlinear algebraic relations. An illustrative example is included to compare our results with those in the literature.