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Construction of Control Lyapunov Functions for a Class of Nonlinear Systems 被引量:5
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作者 CAI Xiu-Shan HAN Zheng-Zhi WANG Xiao-Dong 《自动化学报》 EI CSCD 北大核心 2006年第5期796-799,共4页
The construction of control Lyapunov functions for a class of nonlinear systems is considered. We develop a method by which a control Lyapunov function for the feedback linearizable part can be constructed systematica... The construction of control Lyapunov functions for a class of nonlinear systems is considered. We develop a method by which a control Lyapunov function for the feedback linearizable part can be constructed systematically via Lyapunov equation. Moreover, by a control Lyapunov function of the feedback linearizable part and a Lyapunov function of the zero dynamics, a control Lyapunov function for the overall nonlinear system is established. 展开更多
关键词 Nonlinear systems control Lyapunov functions semiglobal stabilization zero dynamics.
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Stabilization of discrete nonlinear systems based on control Lyapunov functions 被引量:1
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作者 Cai Xiushan Wang Xiaodong Lü Ganyun 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第1期131-133,共3页
The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this cond... The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this condition, a continuous state feedback law is constructed explicitly. It can globally asymptotically stabilize the equilibrium of the closed-loop system. A simulation example shows the effectiveness of the proposed method. 展开更多
关键词 control Lyapunov functions discrete systems STABILIZATION
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Universal construction of control Lyapunov functions for a class of nonlinear systems 被引量:1
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作者 Cai Xiushan Wang Xiaodong Zhang Haoran 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2007年第3期598-602,共5页
A method is developed by which control Lyapunov functions of a class of nonlinear systems can be constructed systematically. Based on the control Lyapunov function, a feedback control is obtained to stabilize the clos... A method is developed by which control Lyapunov functions of a class of nonlinear systems can be constructed systematically. Based on the control Lyapunov function, a feedback control is obtained to stabilize the closed-loop system. In addition, this method is applied to stabilize the Benchmark system. A simulation shows the effectiveness of the method. 展开更多
关键词 control Lyapunov functions nonlinear systems stabilization.
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STUDY ON DYNAMICS, STABILITY AND CONTROL OF MULTI-BODY FLEXIBLE STRUCTURE SYSTEM IN FUNCTIONAL SPACE 被引量:1
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作者 XU Jian-guo(徐建国) +1 位作者 JIA Jun-guo(贾军国) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第12期1410-1421,共12页
The dynamics, stability and control problem of a kind of infinite dimensional system are studied in the functional space with the method of modern Mathematics. First, the dynamical control model of the distributed par... The dynamics, stability and control problem of a kind of infinite dimensional system are studied in the functional space with the method of modern Mathematics. First, the dynamical control model of the distributed parameter system with multi-body flexible and multi-topological structure was established which has damping, gyroscopic parts and constrained damping. Secondly, the necessary and sufficient condition of controllability and observability, the stability theory and asymptotic property of the system were obtained. These results expand the theory of the field about the dynamics and control of the system with multi-body flexible structure, and have important engineering significance. 展开更多
关键词 multi-body flexible system DYNAMICS STABILITY control functional space
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Direct adaptive control for nonlinear uncertain system based on control Lyapunov function method 被引量:1
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作者 Chen Yimei Han Zhengzhi Tang Houjun 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2006年第3期619-623,共5页
The problem of adaptive stabilization of a class of multi-input nonlinear systems with unknown parameters both in the state vector-field and the input vector-field has been considered. By employing the control Lyapuno... The problem of adaptive stabilization of a class of multi-input nonlinear systems with unknown parameters both in the state vector-field and the input vector-field has been considered. By employing the control Lyapunov function method, a direct adaptive controller is designed to complete the global adaptive stability of the uncertain system. At the same time, the controller is also verified to possess the optimality. Example and simulations are provided to illustrate the effectiveness of the proposed method. 展开更多
关键词 adaptive control control Lyapunov function nonlinear uncertain system optimality.
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Fuzzy Adaptive Control of Stochastic Nonlinear Systems with Unknown Virtual Control Gain Function 被引量:11
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作者 WANG Ying-Chun ZHANG Hua-Guang WANG Yi-Zhong 《自动化学报》 EI CSCD 北大核心 2006年第2期170-178,共9页
The problem of track control is studied for a class of strict-feedback stochastic nonlinear systems in which unknown virtual control gain function is the main feature. First, the so-called stochastic LaSalle theory is... The problem of track control is studied for a class of strict-feedback stochastic nonlinear systems in which unknown virtual control gain function is the main feature. First, the so-called stochastic LaSalle theory is extended to some extent, and accordingly, the results of global ultimate boundedness for stochastic nonlinear systems are developed. Next, a new design scheme of fuzzy adaptive control is proposed. The advantage of it is that it does not require priori knowledge of virtual control gain function sign, which is usually demanded in many designs. At the same time, the track performance of closed-loop systems is improved by adaptive modifying the estimated error upper bound. By theoretical analysis, the signals of closed-loop systems are globally ultimately bounded in probability and the track error converges to a small residual set around the origin in 4th-power expectation. 展开更多
关键词 随机非线性系统 模糊自适应控制 虚拟控制 增益函数
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Stability control of multi-parameter adaptive wireless communication systems based on multi-Lyapunov function 被引量:1
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作者 Song Xiaoqi Dong Li +2 位作者 Li Wenfa Tong Tinging Lei Lei 《High Technology Letters》 EI CAS 2017年第4期375-383,共9页
With the occurrence of burst interference,bit error rate( BER) stability of the wireless communication system( WCS) always degrades significantly. To cope with it,a stability control algorithm is proposed,utilizing th... With the occurrence of burst interference,bit error rate( BER) stability of the wireless communication system( WCS) always degrades significantly. To cope with it,a stability control algorithm is proposed,utilizing the stability theory of switched systems,which is specifically applicable for multi-parameter adaptive WCS with spectrum sensing ability,and it is capable of stabilizing BER within a reasonable range. Firstly,WCS is modeled as a switched system. Then,based on the multi-Lyapunov function,controlling rules are presented to enable the switched system to satisfy stable condition asymptotically. Finally,analysis and numerical simulation results demonstrate that the switched WCS with the proposed controlling rules is superior to conventional power-controlled WCS with or without state feedback control in terms of stability performance. 展开更多
关键词 switched system stability control multi-Lyapunov function(MLF) power control burst interference
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A novel methodology for constructing a multi-wing chaotic and hyperchaotic system with a unified step function switching control 被引量:3
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作者 张朝霞 禹思敏 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第5期83-94,共12页
This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively... This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively adjusting multiple parameters of conventional multi-parameter control, this paper introduces a unified step function controlled by a single parameter for constructing various multi-wing chaotic and hyperchaotic systems. In particular, to the best of the authors' knowledge, this is also the first time to find a non-equilibrium multi-wing hyperchaotic system by means of the unified step function control. According to the heteroclinic loop Shilnikov theorem, some properties for multi-wing attractors and its chaos mechanism are further discussed and analyzed. A circuit for multi-wing systems is designed and implemented for demonstration, which verifies the effectiveness of the proposed approach. 展开更多
关键词 non-equilibrium multi-wing hyperchaotic system single parameter control unified step function circuit implementation
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Transfer Function Model of Multirate Feedback Control Systems
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作者 肖建 唐磊 《Journal of Modern Transportation》 2001年第1期1-7,共7页
Based on the suitably defined multivariable version of Kranc operators and the extended input and output vectors, the multirate sampling plant is transformed to a equivalent time invariant single rate one, then the t... Based on the suitably defined multivariable version of Kranc operators and the extended input and output vectors, the multirate sampling plant is transformed to a equivalent time invariant single rate one, then the transfer function model of the multivariable multirate sampling plant is obtained. By combining this plant model with the time invariant description of the multirate controller in terms of extended vectors, the closed loop transfer function model of the multirate feedback control system can be determinated. This transfer function model has a very simple structure, and can be used as a basis for the analysis and synthesis of the multirate sampling feedback control systems in the frequency domain. 展开更多
关键词 feedback control transfer functions multirate digital control systems computer control
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Design of bounded feedback controls for linear dynamical systems by using common Lyapunov functions
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作者 Igor Ananievskii Nickolai Anokhin Alexander Ovseevich 《Theoretical & Applied Mechanics Letters》 CAS 2011年第1期66-68,共3页
For a linear dynamical system,we address the problem of devising a bounded feedback control,which brings the system to the origin in finite time.The construction is based on the notion of a common Lyapunov function.It... For a linear dynamical system,we address the problem of devising a bounded feedback control,which brings the system to the origin in finite time.The construction is based on the notion of a common Lyapunov function.It is shown that the constructed control remains effective in the presence of small perturbations. 展开更多
关键词 linear control system feedback control bounded control common Lyapunov function
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Predictive functional control based on fuzzy T-S model for HVAC systems temperature control 被引量:6
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作者 Hongli LU Lei JIA +1 位作者 Shulan KONG Zhaosheng ZHANG 《控制理论与应用(英文版)》 EI 2007年第1期94-98,共5页
In heating, ventilating and air-conditioning (HVAC) systems, there exist severe nonlinearity, time-varying nature, disturbances and uncertainties. A new predictive functional control based on Takagi-Sugeno (T-S) f... In heating, ventilating and air-conditioning (HVAC) systems, there exist severe nonlinearity, time-varying nature, disturbances and uncertainties. A new predictive functional control based on Takagi-Sugeno (T-S) fuzzy model was proposed to control HVAC systems. The T-S fuzzy model of stabilized controlled process was obtained using the least squares method, then on the basis of global linear predictive model from T-S fuzzy model, the process was controlled by the predictive functional controller. Especially the feedback regulation part was developed to compensate uncertainties of fuzzy predictive model. Finally simulation test results in HVAC systems control applications showed that the proposed fuzzy model predictive functional control improves tracking effect and robustness. Compared with the conventional PID controller, this control strategy has the advantages of less overshoot and shorter setting time, etc. 展开更多
关键词 T-S fuzzy model Predictive functional control Least squares method HVAC systems
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Shape control on probability density function in stochastic systems 被引量:4
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作者 Lingzhi Wang Fucai Qian Jun Liu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2014年第1期144-149,共6页
A novel strategy of probability density function (PDF) shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimiza... A novel strategy of probability density function (PDF) shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively. 展开更多
关键词 stochastic systems probability density function (PDF) shape control improved particle swarm optimization.
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Optimal control of quadratic functionals for affine nonlinear systems
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作者 M.Popescu A.Dumitrache 《Theoretical & Applied Mechanics Letters》 CAS 2012年第4期56-59,共4页
In this paper we analyze the optimal control problem for a class of afflne nonlinear systems under the assumption that the associated Lie algebra is nilpotent. The Lie brackets generated by the vector fields which def... In this paper we analyze the optimal control problem for a class of afflne nonlinear systems under the assumption that the associated Lie algebra is nilpotent. The Lie brackets generated by the vector fields which define the nonlinear system represent a remarkable mathematical instrument for the control of affine systems. We determine the optimal control which corresponds to the nilpotent operator of the first order. In particular, we obtain the control that minimizes the energy of the given nonlinear system. Applications of this control to bilinear systems with first order nilpotent operator are considered. 展开更多
关键词 optimal control affine nonlinear systems nilpotent operator quadratic functionals
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Finite-Time H Control of Switched Nonlinear Systems under State-Dependent Switching
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作者 Xiaoyue Zhang Yao Wang 《Journal of Applied Mathematics and Physics》 2023年第7期2053-2068,共16页
This paper investigates the finite-time H<sub>∞</sub> control problem of switched nonlinear systems via state-dependent switching and state feedback control. Unlike the existing approach based on time-dep... This paper investigates the finite-time H<sub>∞</sub> control problem of switched nonlinear systems via state-dependent switching and state feedback control. Unlike the existing approach based on time-dependent switching strategy, in which the switching instants must be given in advance, the state-dependent switching strategy is used to design switching signals. Based on multiple Lyapunov-like functions method, several criteria for switched nonlinear systems to be finite-time H<sub>∞</sub> control are derived. Finally, a numerical example with simulation results is provided to show the validity of the conclusions. 展开更多
关键词 Finite-Time H control Switched Nonlinear systems Multiple Lyapunov-Like functions State-Dependent Switching
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Function Observer Based Event-triggered Control for Linear Systems with Guaranteed L_∞-Gain
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作者 Pei Jia Fei Hao Hao Yu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI 2015年第4期394-402,共9页
This paper is devoted to event-triggered control design for linear systems based on function observer. More specifically, the main purpose is to design event-triggered mechanisms that trigger transmissions when the di... This paper is devoted to event-triggered control design for linear systems based on function observer. More specifically, the main purpose is to design event-triggered mechanisms that trigger transmissions when the difference between the current value of the system and its previously transmitted value which includes the plant output or the function observer output exceeds an additional threshold. For such an eventtriggered mechanism, we derive conditions in terms of matrix inequality to guarantee the stability as well as longer inter-event time. We propose two approaches to investigate the closed-loop model, namely, reformulating the event-triggered control system as a hybrid system and interpreting the event-induced error as exogenous disturbance. Furthermore, the minimum inter-event time is guaranteed to be strictly positive. An example is presented to illustrate the feasibility and efficiency of the theoretic results. © 2014 Chinese Association of Automation. 展开更多
关键词 Dynamical systems Hybrid systems
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Anti-Windup Digital Control Design for Time-Delayed Analog Nonlinear Systems Using Approximated Scalar Sign Function
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作者 Warsame H. Ali Yongpeng Zhang +2 位作者 Jian Zhang John H. Fuller Leang-San Shieh 《Circuits and Systems》 2014年第1期27-37,共11页
This paper describes an approximated-scalar-sign-function-based anti-windup digital control design for analog nonlinear systems subject to input constraints. As input saturation occurs, the non-smooth saturation const... This paper describes an approximated-scalar-sign-function-based anti-windup digital control design for analog nonlinear systems subject to input constraints. As input saturation occurs, the non-smooth saturation constraint is modeled with the approximated scalar sign function which is a smooth nonlinear function. The resulting nonlinear model is further linearized at any operating point with the optimal linearization technique, and Linear Quadratic Regulator (LQR) is then applied for a state-feedback controller optimal for each operating point. As input saturation is encountered, an iterative procedure is developed to adjust control gains by systematically updating LQR weighting matrices until the inputs lie within the saturation limits. Through global digital redesign, the analog LQR controller is converted to an equivalent digital one for keeping the essential control performance, and moreover, delay compensation is taken into account during digital redesign for compensating the potential time delays in a control loop. The swing-up and stabilization control of single rotary inverted pendulum system is used to illustrate and verify the proposed method. 展开更多
关键词 ANTI-WINDUP control SCALAR SIGN function SAMPLED-DATA system Time-Delayed system
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Hybrid Predictive Control Based on High-Order Differential State Observers and Lyapunov Functions for Switched Nonlinear Systems 被引量:1
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作者 Baili Su Guoyuan Qi Barend J. van Wyk 《Applied Mathematics》 2013年第9期32-42,共11页
In this paper, a hybrid predictive controller is proposed for a class of uncertain switched nonlinear systems based on high-order differential state observers and Lyapunov functions. The main idea is to design an outp... In this paper, a hybrid predictive controller is proposed for a class of uncertain switched nonlinear systems based on high-order differential state observers and Lyapunov functions. The main idea is to design an output feedback bounded controller and a predictive controller for each subsystem using high-order differential state observers and Lyapunov functions, to derive a suitable switched law to stabilize the closed-loop subsystem, and to provide an explicitly characterized set of initial conditions. For the whole switched system, based on the high-order differentiator, a suitable switched law is designed to ensure the whole closed-loop’s stability. The simulation results for a chemical process show the validity of the controller proposed in this paper. 展开更多
关键词 SWITCHED system LYAPUNOV function High Order DIFFERENTIATOR control Constraint Output Feedback Model Predictive control Stable Region
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Sliding mode control of uncertain systems with distributed time-delay: parameter-dependent Lyapunov functional approach 被引量:2
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作者 Ligang WU Changhong WANG Huijun GAO Qingshuang ZENG 《控制理论与应用(英文版)》 EI 2006年第2期159-167,共9页
The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional ... The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities (LMIs), which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme. 展开更多
关键词 Parameter-dependent Lyapunov functional Distributed delay systems Sliding mode control Robust stabilization Linear matrix inequalities (LMIs)
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GH_2 Control for Uncertain Discrete-time-delay Fuzzy Systems Based on a Switching Fuzzy Model and Piecewise Lyapunov Function
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作者 Zhi-Le Xia Jun-Min Li 《International Journal of Automation and computing》 EI 2009年第3期261-266,共6页
Generalized H2 (GH2) stability analysis and controller design of the uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems with state delay are studied based on a switching fuzzy model and piecewise Lyapunov f... Generalized H2 (GH2) stability analysis and controller design of the uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems with state delay are studied based on a switching fuzzy model and piecewise Lyapunov function. GH2 stability sufficient conditions are derived in terms of linear matrix inequalities (LMIs). The interactions among the fuzzy subsystems are considered. Therefore, the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. To illustrate the validity of the proposed method, a design example is provided. 展开更多
关键词 Generalized H2 (GH2) control fuzzy systems linear matrix inequalities (LMIs) piecewise Lyapunov function switchingfuzzy model.
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Regression Optimal Functional Control for a Kind of Unsymmetrical System
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作者 Xixi Yue Baili Su 《Applied Mathematics》 2020年第5期363-376,共14页
Because of the widespread existence of unsymmetrical system in the production process, its research is getting more and more attention. In this paper, a regression optimal functional control method is proposed for a c... Because of the widespread existence of unsymmetrical system in the production process, its research is getting more and more attention. In this paper, a regression optimal functional control method is proposed for a class of unsymmetrical system. For the positive-negative model of the unsymmetrical system, a regression optimal functional controller is designed, which can make the system stable. The proposed algorithm has less computation and good control effect. Finally, three simulation examples are given to verify the effectiveness of the proposed algorithm. 展开更多
关键词 UNSYMMETRICAL system Positive-Negative Model Basis functions Regression Optimal functional control
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