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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
基金Supported by Natural Science Foundation of Zhejiang Province P. R. China (Y105141)Natural Science Foundation of Fujian Province P.R.China (A0510025)Technological Project of Zhejiang Education Department,P. R. China(20050291)
文摘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.
基金the Natural Science Foundation of China (60774011)the Natural ScienceFoundation of Zhejiang Province in China (Y105141)
文摘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.
基金the Natural Science Foundation of Zhejiang Province,China (Y105141)Technological Project of Zhejiang Education Department,China (20050291).
文摘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.
文摘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.
文摘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.
基金Supported by National Natural Science Foundation of P. R. China (60572070, 60325311, 60534010) Natural Science Foundation of Liaoning Province (20022030)
文摘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.
基金Supported by the National Natural Science Foundation of China(No.61572254,61301103)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant No.61403143)the Natural Science Foundation of Guangdong Province,China(Grant No.2014A030313739)+1 种基金the Science and Technology Foundation Program of Guangzhou City,China(Grant No.201510010124)the Excellent Doctorial Dissertation Foundation of Guangdong Province,China(Grant No.XM080054)
文摘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.
文摘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.
基金supported by Russian Foundation for Basic Research(Grant No.08-01-00234,08-01-00411,08-08- 00292)
文摘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.
基金This work was supported by Young Scientists Fundamental Research Program of Shandong Province of China (No. 031B5147).
文摘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.
基金supported by the National Natural Science Fundation of China(61273127)the Specialized Research Fund of the Doctoral Program in Higher Education(20106118110009+2 种基金20116118110008)the Scientific Research Plan Projects of Shaanxi Education Department(12JK0524)the Young Teachers Scientific Research Fund of Xi’an University of Posts and Telecommunications(1100434)
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
基金This work was partially supported by the National Natural Science Foundation of China(No.60504008).
文摘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.
文摘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.
文摘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.