In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First,...In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First, the density matrix interested in quantum system is transferred to vector formation.Then, in order to obtain a controller with higher accuracy and faster convergence rate, a Lyapunov function based on the matrix logarithm function is designed. After that, a procedure for the controller design is derived based on the Lyapunov stability theorem. Finally, the numerical simulation experiments for an amplitude damping Markovian open quantum system are performed to prepare the desired quantum gate. The simulation results show that the preparation of Hadamard gate based on the proposed control laws can achieve the fidelity up to 0.9985 for the different coupling strengths.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
We demonstrate that an arbitrary Bell state can be achieved in a two qubit anisotropic Heisenberg XY chain via Lyapunov control. During the whole process, we only need to apply an external field along a given directio...We demonstrate that an arbitrary Bell state can be achieved in a two qubit anisotropic Heisenberg XY chain via Lyapunov control. During the whole process, we only need to apply an external field along a given direction to a single qubit. This control strategy is effective for all initial states in the four-dimensional Hilbert space where the target state is asymptotically stable. The effects of imperfections on the fidelity for the target state such as Gaussian leakage of local control and localized dephasing of individual spins are also considered.展开更多
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
A novel Lyapunov-based three-axis attitude intelligent control approach via allocation scheme is considered in the proposed research to deal with kinematics and dynamics regarding the unmanned aerial vehicle systems.T...A novel Lyapunov-based three-axis attitude intelligent control approach via allocation scheme is considered in the proposed research to deal with kinematics and dynamics regarding the unmanned aerial vehicle systems.There is a consensus among experts of this field that the new outcomes in the present complicated systems modeling and control are highly appreciated with respect to state-of-the-art.The control scheme presented here is organized in line with a new integration of the linear-nonlinear control approaches,as long as the angular velocities in the three axes of the system are accurately dealt with in the inner closed loop control.And the corresponding rotation angles are dealt with in the outer closed loop control.It should be noted that the linear control in the present outer loop is first designed through proportional based linear quadratic regulator(PD based LQR) approach under optimum coefficients,while the nonlinear control in the corresponding inner loop is then realized through Lyapunov-based approach in the presence of uncertainties and disturbances.In order to complete the inner closed loop control,there is a pulse-width pulse-frequency(PWPF) modulator to be able to handle on-off thrusters.Furthermore,the number of these on-off thrusters may be increased with respect to the investigated control efforts to provide the overall accurate performance of the system,where the control allocation scheme is realized in the proposed strategy.It may be shown that the dynamics and kinematics of the unmanned aerial vehicle systems have to be investigated through the quaternion matrix and its corresponding vector to avoid presenting singularity of the results.At the end,the investigated outcomes are presented in comparison with a number of potential benchmarks to verify the approach performance.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 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 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
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 analyses the issue of impact time control of super-cavitation weapons impact fixed targets which mainly refer to the ships or submarines who lost power, but still have combat capability. Control over impact...This paper analyses the issue of impact time control of super-cavitation weapons impact fixed targets which mainly refer to the ships or submarines who lost power, but still have combat capability. Control over impact time constraints of guidance law(ITCG) is derived by using sliding mode control(SMC) and Lyapunov stability theorem. The expected impact time is realized by using the notion of attack process and estimated time-to-go to design sliding mode surface(SMS). ITCG contains equivalent and discontinuous guidance laws, once state variables arrive at SMS,the equivalent guidance law keeps the state variables on SMS,then the discontinuous guidance law enforces state variables to move and reach SMS. The singularity problem of ITCG is also analyzed. Theoretical analysis and numerical simulation results are given to test the effectiveness of ITCG designed in this paper.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
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supported by National Natural Science Foundation of China(61573330)Chinese Academy of Sciences(CAS)the World Academy of Sciences(TWAS)
文摘In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First, the density matrix interested in quantum system is transferred to vector formation.Then, in order to obtain a controller with higher accuracy and faster convergence rate, a Lyapunov function based on the matrix logarithm function is designed. After that, a procedure for the controller design is derived based on the Lyapunov stability theorem. Finally, the numerical simulation experiments for an amplitude damping Markovian open quantum system are performed to prepare the desired quantum gate. The simulation results show that the preparation of Hadamard gate based on the proposed control laws can achieve the fidelity up to 0.9985 for the different coupling strengths.
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.
文摘We demonstrate that an arbitrary Bell state can be achieved in a two qubit anisotropic Heisenberg XY chain via Lyapunov control. During the whole process, we only need to apply an external field along a given direction to a single qubit. This control strategy is effective for all initial states in the four-dimensional Hilbert space where the target state is asymptotically stable. The effects of imperfections on the fidelity for the target state such as Gaussian leakage of local control and localized dephasing of individual spins are also considered.
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 Islamic Azad University (IAU),South Tehran Branch,Tehran,Iran in support of the present research
文摘A novel Lyapunov-based three-axis attitude intelligent control approach via allocation scheme is considered in the proposed research to deal with kinematics and dynamics regarding the unmanned aerial vehicle systems.There is a consensus among experts of this field that the new outcomes in the present complicated systems modeling and control are highly appreciated with respect to state-of-the-art.The control scheme presented here is organized in line with a new integration of the linear-nonlinear control approaches,as long as the angular velocities in the three axes of the system are accurately dealt with in the inner closed loop control.And the corresponding rotation angles are dealt with in the outer closed loop control.It should be noted that the linear control in the present outer loop is first designed through proportional based linear quadratic regulator(PD based LQR) approach under optimum coefficients,while the nonlinear control in the corresponding inner loop is then realized through Lyapunov-based approach in the presence of uncertainties and disturbances.In order to complete the inner closed loop control,there is a pulse-width pulse-frequency(PWPF) modulator to be able to handle on-off thrusters.Furthermore,the number of these on-off thrusters may be increased with respect to the investigated control efforts to provide the overall accurate performance of the system,where the control allocation scheme is realized in the proposed strategy.It may be shown that the dynamics and kinematics of the unmanned aerial vehicle systems have to be investigated through the quaternion matrix and its corresponding vector to avoid presenting singularity of the results.At the end,the investigated outcomes are presented in comparison with a number of potential benchmarks to verify the approach performance.
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.
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.
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 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 National Natural Science Foundation of China(5137917651679201)
文摘This paper analyses the issue of impact time control of super-cavitation weapons impact fixed targets which mainly refer to the ships or submarines who lost power, but still have combat capability. Control over impact time constraints of guidance law(ITCG) is derived by using sliding mode control(SMC) and Lyapunov stability theorem. The expected impact time is realized by using the notion of attack process and estimated time-to-go to design sliding mode surface(SMS). ITCG contains equivalent and discontinuous guidance laws, once state variables arrive at SMS,the equivalent guidance law keeps the state variables on SMS,then the discontinuous guidance law enforces state variables to move and reach SMS. The singularity problem of ITCG is also analyzed. Theoretical analysis and numerical simulation results are given to test the effectiveness of ITCG designed in this paper.
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.
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.
