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Design of a bilinear fault detection observer for singular bilinear systems 被引量:2
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作者 Zhanshan WANG Huaguang ZHANG 《控制理论与应用(英文版)》 EI 2007年第1期28-36,共9页
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
关键词 Singular bilinear systems (SBS) bilinear observer Fault detection State estimation Domain of attraction
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Predictive control of a class of bilinear systems based on global off-line models 被引量:1
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作者 ZHANG Ri-dong WANG Shu-qing 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第12期1984-1988,共5页
A new multi-step adaptive predictive control algorithm for a class of bilinear systems is presented. The structure of the bilinear system is converted into a simple linear model by using nonlinear support vector machi... A new multi-step adaptive predictive control algorithm for a class of bilinear systems is presented. The structure of the bilinear system is converted into a simple linear model by using nonlinear support vector machine (SVM) dynamic approximation with analytical control law derived. The method does not need on-line parameters estimation because the system’s internal model has been transformed into an off-line global model. Compared with other traditional methods, this control law reduces on-line parameter estimating burden. In addition, its overall linear behavior treating method allows an analytical control law available and avoids on-line nonlinear optimization. Simulation results are presented in the article to illustrate the efficiency of the method. 展开更多
关键词 bilinear systems Model predictive control (MPC) Adaptive control Support vector machine (SVM)
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Design of switched controllers for discrete singular bilinear systems
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作者 Xiuhua ZHANG Qingling ZHANG 《控制理论与应用(英文版)》 EI 2007年第3期312-316,共5页
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
关键词 Switched controller bilinear systems Singular systems Invariant principle
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Implementation of Legendre Neural Network to Solve Time-Varying Singular Bilinear Systems
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作者 V.Murugesh B.Saravana Balaji +5 位作者 Habib Sano Aliy J.Bhuvana P.Saranya Andino Maseleno K.Shankar A.Sasikala 《Computers, Materials & Continua》 SCIE EI 2021年第12期3685-3692,共8页
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
关键词 Time-varying singular bilinear systems RK-butcher algorithm legendre neural network method
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Positive-Controllability,Positive-Near-Controllability,and Canonical Forms of Driftless Discrete-Time Bilinear Systems
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作者 TIE Lin 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2022年第4期1225-1243,共19页
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
关键词 Canonical forms CONTROLLABILITY discrete-time bilinear systems near-controllability positive control inputs
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ON NEARLY-CONTROLLABLE SUBSPACES OF A CLASS OF DISCRETE-TIME BILINEAR SYSTEMS
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作者 TIE Lin 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2013年第4期512-526,共15页
If a linear time-invariant system is uncontrollable,then the state space can be decomposed as a direct sum of a controllable subspace and an uncontrollable subspace.In this paper,for a class of discrete-time bilinear ... If a linear time-invariant system is uncontrollable,then the state space can be decomposed as a direct sum of a controllable subspace and an uncontrollable subspace.In this paper,for a class of discrete-time bilinear systems which are uncontrollable but can be nearly controllable,by studying the nearly-controllable subspaces and defining the near-controllability index,the controllability properties of the systems are fully characterized.Examples are provided to illustrate the conceptions and results of the paper. 展开更多
关键词 bilinear systems discrete-time systems near-controllability near-controllability index nearly-controllable subspaces.
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Strong and weak output stabilisation for distributed bilinear systems
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作者 Abderrahman Ait Aadi El Hassan Zerrik 《Journal of Control and Decision》 EI 2021年第3期314-321,共8页
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
关键词 bilinear systems output stabilisation feedback controls decay estimate minimisation problem
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Model Order Reduction Methods for Discrete Systems via Discrete Pulse Orthogonal Functions
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作者 XIE Zhen TANG Shengguo WANG Zhaohong 《新疆大学学报(自然科学版中英文)》 CAS 2024年第6期641-650,共10页
This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear syst... This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear systems are expanded in the space spanned by DPOFs,and two recurrence formulas for the expansion coefficients of the system’s state variables are obtained.Then,a modified Arnoldi process is applied to both recurrence formulas to construct the orthogonal projection matrices,by which the reduced-order systems are obtained.Theoretical analysis shows that the output variables of the reducedorder systems can match a certain number of the expansion coefficients of the original system’s output variables.Finally,two numerical examples illustrate the feasibility and effectiveness of the proposed methods. 展开更多
关键词 model order reduction discrete linear systems discrete bilinear systems discrete pulse orthogonal functions
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Output stabilization of distributed bilinear systems
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作者 EI Hassan ZERRIK Lahcen EZZAKI 《Control Theory and Technology》 EI CSCD 2018年第1期58-71,共14页
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
关键词 Distributed bilinear systems STABILIZATION regional stabilization
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Hybrid extended Fourier series for optimal control of nonlinear algebraic dynamical systems
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作者 Jalal NAZARZADEH Hamidreza RADMANESH 《控制理论与应用(英文版)》 EI 2011年第4期487-492,共6页
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
关键词 bilinear systems Hybrid extended Fourier series Nonlinear algebraic dynamic systems Quadratic systems Optimal control
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On the gradient tracking problem for a bilinear reaction–diffusion equation excited by distributed bounded controls
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作者 El Hassan Zerrik Abderrahman Ait Aadi Mohamed Ouhafsaa 《Journal of Control and Decision》 EI 2023年第3期365-373,共9页
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
关键词 Infinite dimensional systems bilinear systems reaction–diffusion equation CONTROLLABILITY optimal control
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Constrained bilinear control problem: Application to a cancer chemotherapy model
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作者 E1 Hassan Zerrik Nihale E1 Boukhari 《International Journal of Biomathematics》 2017年第4期189-209,共21页
The aim of this paper is to investigate the optimal control problem for finite-dimensional bilinear systems and its application to a chemotherapy model. We characterize an opti- mal control that minimizes a quadratic ... The aim of this paper is to investigate the optimal control problem for finite-dimensional bilinear systems and its application to a chemotherapy model. We characterize an opti- mal control that minimizes a quadratic cost functional in two cases of constrained admis- sible controls, then we give sufficient conditions for the uniqueness of such a control, and we derive useful algorithms for the computation of the optimal control. The established results are applied to a cancer chemotherapy bilinear model in order to simulate the opti- mal treatment protocol using two different approaches: one based on a limited instant toxicity, and the other on a limited cumulative toxicity along the therapy session. 展开更多
关键词 bilinear systems optimal control CHEMOTHERAPY instant toxicity cumulativetoxicity.
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