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Predictive control of a class of bilinear systems based on global off-line models

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2006年第12期7卷 1984-1988页

作者： ZHANG Ri-dong WANG Shu-qing Institute of Advanced Process Control National Key Laboratory of Industrial Control Technology Zbejiang University Hangzhou 310027 China

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.

关键词： bilinear systems Model predictive control (MPC) Adaptive control Support vector machine (SVM)

Strong and weak output stabilisation for distributed bilinear systems

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Journal of Control and Decision 2021年第3期8卷 314-321页

作者： Abderrahman Ait Aadi El Hassan Zerrik MACS Laboratory Department of MathematicsUniversity of Moulay IsmailMeknesMorocco

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 ***,the output stabilisation is d... 详细信息

关键词： bilinear systems output stabilisation feedback controls decay estimate minimisation problem

Design of switched controllers for discrete singular bilinear systems

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控制理论与应用（英文版） 2007年第3期5卷 312-316页

作者： Xiuhua ZHANG Qingling ZHANG Institute of systems Science College of Sciences Northeastern University Shenyang Liaoning 110004 China

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.

关键词： Switched controller bilinear systems Singular systems Invariant principle

An Approximate Optimal Tracking Control Algorithm For bilinear systems With General Disturbances Rejection

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An Approximate Optimal Tracking Control Algorithm For Biline...

2010 Chinese Control and Decision Conference

作者： Dexin Gao~(1 2),Peipei Yang~1 1.College of Automation and Electronic engineer,Qingdao University of Science & Technology,Qingdao 266042 2.College of Communication and Control Engineering Jiangnan University WuXi China

＜正＞It is shown in this paper that the successive approximation procedure simplifies computations of the optimal solution of a bilinear-quadratic optimal tacking control（OTC） *** bilinear system we study is affected by external *** the bases of the studies of Zijad and Hofer where the optimal solution has been obtained in the terms of a sequence of the differential equations,in the presented method only solutions of a sequence of the differential equations are required.A chemical reactor example is used to demonstrate the efficiency of the method.

关键词： bilinear systems Disturbances Optimal Tracking Control

Feedback Linearization Optimal Control for bilinear systems with Time-Delay in Control Input

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Feedback Linearization Optimal Control for Bilinear Systems ...

2013年中国智能自动化学术会议

作者： Dexin Gao College of Automation and Electronic Engineer Qingdao University of Science & Technology

This paper considers the optimal control problem for bilinear system with time-delay in control input based on state ***,we change a bilinear system with time-delay in control action model to a time-delay pseudo linear system model by local *** the Artstein transformation,a linear controllable system without delay is *** based on the theory of linear quadratic optimal control,a optimal controller is designed by solving the Riccati *** last,the simulation results show the effectiveness of the method.

关键词： bilinear systems Optimal control Feedback linearization Time-delay

Laguerre-Gramian-based model order reduction of bilinear systems

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Laguerre-Gramian-based model order reduction of bilinear sys...

第40届中国控制会议

作者： Liu Dai Zhi-Hua Xiao Ren-Zheng Zhang School of Information and Mathematics Yangtze University

In this paper, we propose a model order reduction algorithm based on low-rank Gramian approximation for bilinear systems. The main idea of the approach is to use approximate low-rank factors of the controllability and observability Gramians,which are constructed from the expansion coefficients of the matrix exponential functions in the space spanned by Laguerre functions using a recurrence formula, to generate approximate balanced system for the large-scale bilinear system. Then, the reduced-order model is obtained by truncating the states corresponding to the small approximate generalized Hankel singular values. Finally, a numerical experiment is provided to demonstrate the effectiveness of the proposed method.

关键词： Model order reduction bilinear systems balanced truncation Laguerre functions

On the Global Stabilization for Planar bilinear Control systems

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On the Global Stabilization for Planar Bilinear Control Syst...

第37届中国控制会议

作者： Yimin SUN Guangdong Province Key Laboratory of Computational Science School of MathematicsSun Yat-sen University

The global stabilization for nonlinear systems is a fundamental concept in control theory,and up to date,it is still a problem full of *** planar bilinear control systems are a class of important and seemingly simple nonlinear ***,it is still lacking sufficient research for the global stabilization of bilinear *** this work,we will study the planar bilinear control system with the form: x = Ax +(b + Cx)u,x ∈ *** using some advances on the research of Markus-Yamabe Conjecture,we obtained a simple sufficient condition for the global stabilization of planar nonlinear *** conditions are imposed on the matrixes(A,b,C) of the system ***,we give three examples to show the application of our results and the simulation results also show that our methods are effective.

关键词： Global stabilization bilinear systems planar system Markus-Yamabe Conjecture

State-Feedback Based Fuzzy Control Design for Discrete-Time Interval Type-2 Fuzzy bilinear Delay systems

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State-Feedback Based Fuzzy Control Design for Discrete-Time ...

第三十九届中国控制会议

作者： Lin Li Jiangrong Li Chenfei Mao College of Mathematics and Computer Science Yanan University

In this paper, we consider the fuzzy bilinear state-feedback control problem of discrete-time interval type-2 fuzzy bilinear systems with constant delay. First, considering the uncertainties in the membership functions, the nonlinear system are modeled into the interval type-2 fuzzy bilinear systems. Second, based on the Lyapunov stability theory,an interval type-2 fuzzy state-feedback control criterion is proposed to guarantee the interval type-2 fuzzy closed-loop bilinear system to be stable. The fuzzy controller can be obtained by using sequential linear programming matrix ***, one example is introduced to demonstrate the effectiveness of the results.

关键词： Interval type-2 fuzzy systems bilinear systems state-feedback

On the gradient tracking problem for a bilinear reaction–diffusion equation excited by distributed bounded controls

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Journal of Control and Decision 2023年第3期10卷 365-373页

作者： El Hassan Zerrik Abderrahman Ait Aadi Mohamed Ouhafsaa MACS Laboratory Faculty of SciencesMoulay Ismail UniversityMeknesMorocco Department of Sciences Ecole Normale SupérieureMoulay Ismail UniversityMeknesMorocco

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.

关键词： Infinite dimensional systems bilinear systems reaction–diffusion equation controllability optimal control