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
This survey provides a brief overview on the control Lyapunov function(CLF)and control barrier function(CBF)for general nonlinear-affine control systems.The problem of control is formulated as an optimization problem ...This survey provides a brief overview on the control Lyapunov function(CLF)and control barrier function(CBF)for general nonlinear-affine control systems.The problem of control is formulated as an optimization problem where the optimal control policy is derived by solving a constrained quadratic programming(QP)problem.The CLF and CBF respectively characterize the stability objective and the safety objective for the nonlinear control systems.These objectives imply important properties including controllability,convergence,and robustness of control problems.Under this framework,optimal control corresponds to the minimal solution to a constrained QP problem.When uncertainties are explicitly considered,the setting of the CLF and CBF is proposed to study the input-to-state stability and input-to-state safety and to analyze the effect of disturbances.The recent theoretic progress and novel applications of CLF and CBF are systematically reviewed and discussed in this paper.Finally,we provide research directions that are significant for the advance of knowledge in this area.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 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 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
The Spring-Loaded Inverted Pendulum(SLIP)has been regarded as a canonical model for hopping and running dynamics of legged robots.This paper presents a novel control of the actuated-SLIP hopping on unknown terrains.We...The Spring-Loaded Inverted Pendulum(SLIP)has been regarded as a canonical model for hopping and running dynamics of legged robots.This paper presents a novel control of the actuated-SLIP hopping on unknown terrains.We propose that in the neighborhood of the desired stable hybrid limit cycle,the local dynamical behavior of a hybrid system can be expressed by a set of phase coordinates and transverse coordinates.Under some acceptable assumptions,the hybrid averaging theorem is applied on the SLIP non-integrable dynamics to simplify the controller design.Using the inherent symmetry of SLIP dynamics,a control Lyapunov function-based hybrid averaging controller is developed to ensure the exponential stability of the desired gait orbit.This results in a set of linear constraints on the control signal,which can be readily solved by a quadratic programming optimization.Furthermore,a novel method is introduced to improve the robustness against unknown disturbances through the online constraint adjustment.The proposed controller is evaluated in various simulations,demonstrating the SLIP hopping on diverse terrains,including flat,sin-wave,and unregular terrains.The performance of the approach is also validated on a quadruped robot SCIT Dog for generating dynamic gaits such as pronking.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
The objective of this paper is to present a robust safety-critical control system based on the active disturbance rejection control approach, designed to guarantee safety even in the presence of model inaccuracies, un...The objective of this paper is to present a robust safety-critical control system based on the active disturbance rejection control approach, designed to guarantee safety even in the presence of model inaccuracies, unknown dynamics, and external disturbances. The proposed method combines control barrier functions and control Lyapunov functions with a nonlinear extended state observer to produce a robust and safe control strategy for dynamic systems subject to uncertainties and disturbances. This control strategy employs an optimization-based control, supported by the disturbance estimation from a nonlinear extended state observer. Using a quadratic programming algorithm, the controller computes an optimal, stable, and safe control action at each sampling instant. The effectiveness of the proposed approach is demonstrated through numerical simulations of a safety-critical interconnected adaptive cruise control system.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
In this paper we consider general nonlinear switching systems. Under an additional assumption, we prove that there exists a state space depending switching rule which stabilizes the system in a very general sense.
This paper deals with the robust stabilization problem for a class of nonlinear systems with structural uncertainty. Based on robust control Lyapunov function, a sufficient and necessary condition for a function to be...This paper deals with the robust stabilization problem for a class of nonlinear systems with structural uncertainty. Based on robust control Lyapunov function, a sufficient and necessary condition for a function to be a robust control Lyapunov function is given. From this condition, simply sufficient condition for the robust stabilization （robust practical stabilization） is deduced. Moreover, if the equilibrium of the closed-loop system is unique, the existence of such a robust control Lyapunnv function will also imply robustly globally asymptotical stabilization. Then a continuous state feedback law can be constructed explicitly. The simulation shows the effectiveness of the method.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
In this paper, we introduce a new Control Lyapunov Function (CLF) approach for controlling the behavior of nonlinear uncertain HIV-1 models. The uncertainty is in decay parameters and also external control setting. CL...In this paper, we introduce a new Control Lyapunov Function (CLF) approach for controlling the behavior of nonlinear uncertain HIV-1 models. The uncertainty is in decay parameters and also external control setting. CLF is then applied to different strategies. One such strategy considers input into infected cells population stage and the other considers input into a virus population stage. Furthermore, by adding noise to the HIV-1 model a realistic comparison between control strategies is presented to evaluate the system’s dynamics. It has been demonstrated that nonlinear control has effectiveness and robustness, in reducing virus loading to an undetectable level.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 this paper, we introduce a non-linear torque control for an interior permanent-magnet synchronous motor (IPMSM). The nonlinear control is based on a Control Lyapunov Function (CLF) technique. The proposed stabilizi...In this paper, we introduce a non-linear torque control for an interior permanent-magnet synchronous motor (IPMSM). The nonlinear control is based on a Control Lyapunov Function (CLF) technique. The proposed stabilizing feedback law for the IPMSM drive is a damping control method and is shown to be globally asymptotically stable. The CLF method takes the system nonlinearities into account in the control system design stage. Such nonlinearities are due to the cross coupling between the q and the q currents in addition to the system parameters like the inductances and the flux linkages. The complete IPMSM drive incorporating the proposed CLF has been successfully simulated in a plant model for both motor and inverter. The performance of the proposed drive is investigated in simulation at different operating conditions. It is found that the proposed control technique provides a good torque control performance for the IPMSM drive ensuring the global stability. In later work, we are planning to investigate other phenomena such as magnetic saturation, nonlinear loads, mechanical friction and flexibilities.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
This paper deals with global stabilization problem for the nonlinear systems with structural uncertainty. Based on control Lyapunov function, a sufficient and necessary condition for the globally and asymptotically st...This paper deals with global stabilization problem for the nonlinear systems with structural uncertainty. Based on control Lyapunov function, a sufficient and necessary condition for the globally and asymptotically stabilizing the equailibrium of the closed system is given. Moreovery, an almost smooth state feedback control law is constructed. The simulation shows the effectiveness of the method.展开更多
An obstacle avoidance scheme of a two-wheeled mobile robot is shown by selecting an appropriate Lya- punov function. When considering the obstacle, the Lyapunov function may have some local minima. A method which eras...An obstacle avoidance scheme of a two-wheeled mobile robot is shown by selecting an appropriate Lya- punov function. When considering the obstacle, the Lyapunov function may have some local minima. A method which erases the local minima is proposed by using a function which covers the minima with a plane surface. The effectiveness of the proposed method is verified by numerical simulations.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supported in part by the National Natural Science Foundation of China(U22B2046,62073079,62088101)in part by the General Joint Fund of the Equipment Advance Research Program of Ministry of Education(8091B022114)in part by NPRP(NPRP 9-466-1-103)from Qatar National Research Fund。
文摘This survey provides a brief overview on the control Lyapunov function(CLF)and control barrier function(CBF)for general nonlinear-affine control systems.The problem of control is formulated as an optimization problem where the optimal control policy is derived by solving a constrained quadratic programming(QP)problem.The CLF and CBF respectively characterize the stability objective and the safety objective for the nonlinear control systems.These objectives imply important properties including controllability,convergence,and robustness of control problems.Under this framework,optimal control corresponds to the minimal solution to a constrained QP problem.When uncertainties are explicitly considered,the setting of the CLF and CBF is proposed to study the input-to-state stability and input-to-state safety and to analyze the effect of disturbances.The recent theoretic progress and novel applications of CLF and CBF are systematically reviewed and discussed in this paper.Finally,we provide research directions that are significant for the advance of knowledge in this area.
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 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supported by HeilongJiang Touyan Innovation Team Program.
文摘The Spring-Loaded Inverted Pendulum(SLIP)has been regarded as a canonical model for hopping and running dynamics of legged robots.This paper presents a novel control of the actuated-SLIP hopping on unknown terrains.We propose that in the neighborhood of the desired stable hybrid limit cycle,the local dynamical behavior of a hybrid system can be expressed by a set of phase coordinates and transverse coordinates.Under some acceptable assumptions,the hybrid averaging theorem is applied on the SLIP non-integrable dynamics to simplify the controller design.Using the inherent symmetry of SLIP dynamics,a control Lyapunov function-based hybrid averaging controller is developed to ensure the exponential stability of the desired gait orbit.This results in a set of linear constraints on the control signal,which can be readily solved by a quadratic programming optimization.Furthermore,a novel method is introduced to improve the robustness against unknown disturbances through the online constraint adjustment.The proposed controller is evaluated in various simulations,demonstrating the SLIP hopping on diverse terrains,including flat,sin-wave,and unregular terrains.The performance of the approach is also validated on a quadruped robot SCIT Dog for generating dynamic gaits such as pronking.
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supported by the Fondo para el Primer Proyecto of the Comitépara el Desarrollo de la Investigación(CODI)at the Universidad de Antioquia(Grant Number PRV2024-78509)。
文摘The objective of this paper is to present a robust safety-critical control system based on the active disturbance rejection control approach, designed to guarantee safety even in the presence of model inaccuracies, unknown dynamics, and external disturbances. The proposed method combines control barrier functions and control Lyapunov functions with a nonlinear extended state observer to produce a robust and safe control strategy for dynamic systems subject to uncertainties and disturbances. This control strategy employs an optimization-based control, supported by the disturbance estimation from a nonlinear extended state observer. Using a quadratic programming algorithm, the controller computes an optimal, stable, and safe control action at each sampling instant. The effectiveness of the proposed approach is demonstrated through numerical simulations of a safety-critical interconnected adaptive cruise control system.
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Supported by the NSF of Commission of Education of Henan Province(200510459002)
文摘In this paper we consider general nonlinear switching systems. Under an additional assumption, we prove that there exists a state space depending switching rule which stabilizes the system in a very general sense.
基金Sponsored by the Natural Science Foundation of Zhejiang Province in China(Grant No. Y105141).
文摘This paper deals with the robust stabilization problem for a class of nonlinear systems with structural uncertainty. Based on robust control Lyapunov function, a sufficient and necessary condition for a function to be a robust control Lyapunov function is given. From this condition, simply sufficient condition for the robust stabilization （robust practical stabilization） is deduced. Moreover, if the equilibrium of the closed-loop system is unique, the existence of such a robust control Lyapunnv function will also imply robustly globally asymptotical stabilization. Then a continuous state feedback law can be constructed explicitly. The simulation shows the effectiveness of the method.
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In this paper, we introduce a new Control Lyapunov Function (CLF) approach for controlling the behavior of nonlinear uncertain HIV-1 models. The uncertainty is in decay parameters and also external control setting. CLF is then applied to different strategies. One such strategy considers input into infected cells population stage and the other considers input into a virus population stage. Furthermore, by adding noise to the HIV-1 model a realistic comparison between control strategies is presented to evaluate the system’s dynamics. It has been demonstrated that nonlinear control has effectiveness and robustness, in reducing virus loading to an undetectable level.
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.
文摘In this paper, we introduce a non-linear torque control for an interior permanent-magnet synchronous motor (IPMSM). The nonlinear control is based on a Control Lyapunov Function (CLF) technique. The proposed stabilizing feedback law for the IPMSM drive is a damping control method and is shown to be globally asymptotically stable. The CLF method takes the system nonlinearities into account in the control system design stage. Such nonlinearities are due to the cross coupling between the q and the q currents in addition to the system parameters like the inductances and the flux linkages. The complete IPMSM drive incorporating the proposed CLF has been successfully simulated in a plant model for both motor and inverter. The performance of the proposed drive is investigated in simulation at different operating conditions. It is found that the proposed control technique provides a good torque control performance for the IPMSM drive ensuring the global stability. In later work, we are planning to investigate other phenomena such as magnetic saturation, nonlinear loads, mechanical friction and flexibilities.
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.
基金Supported by National Key Basic Research Program of China（973 Program）（2006CB922004） National Natural Science Foundation of China（60904033 60774098）+1 种基金 the Chinese Postdoctoral Science Foundation（20100470848） K.C.Wong Education Foundation HongKong
基金Technological Project of Fujian EducationDepartment,China(No.JA0 3 163 )
文摘This paper deals with global stabilization problem for the nonlinear systems with structural uncertainty. Based on control Lyapunov function, a sufficient and necessary condition for the globally and asymptotically stabilizing the equailibrium of the closed system is given. Moreovery, an almost smooth state feedback control law is constructed. The simulation shows the effectiveness of the method.
文摘An obstacle avoidance scheme of a two-wheeled mobile robot is shown by selecting an appropriate Lya- punov function. When considering the obstacle, the Lyapunov function may have some local minima. A method which erases the local minima is proposed by using a function which covers the minima with a plane surface. The effectiveness of the proposed method is verified by numerical simulations.
