The separation of the Lyapunov matrices and system matrices plays an important role when one uses parameter-dependent Lyapunov functional handling systems with polytopic type uncertainties. The delay-dependent robust ...The separation of the Lyapunov matrices and system matrices plays an important role when one uses parameter-dependent Lyapunov functional handling systems with polytopic type uncertainties. The delay-dependent robust stability problem for systems with polytopic type uncertainties is discussed by using parameter-dependent Lyapunov functional. The derivative term in the derivative of Lyapunov functional is reserved and the free weighting matrices are employed to express the relationship between die terms in the system equation such that the Lyapunov matrices are not involved in any product terms with the system matrices. In addition, the relationships between the terms in the Leibniz Newton formula are also described by some free weighting matrices and some delay-dependent stability conditions are derived. Numerical examples demonstrate that the proposed criteria are more effective than the previous results.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
The problem of robust L 1 filtering with pole constraint in a disk for linear continuous polytopic uncertain systems is discussed. The attention is focused on design a linear asymptotically stable filter such that th...The problem of robust L 1 filtering with pole constraint in a disk for linear continuous polytopic uncertain systems is discussed. The attention is focused on design a linear asymptotically stable filter such that the filtering error system remains robustly stable, and has a L 1 performance constraint and pole constraint in a disk. The new robust L 1 performance criteria and regional pole placement condition are obtained via parameter-dependent Lyapunov functions method. Upon the proposed multiobjective performance criteria and by means of LMI technique, both full-order and reduced-order robust L 1 filter with suitable dynamic behavior can be obtained from the solution of convex optimization problems. Compared with earlier result in the quadratic framework, this approach turns out to be less conservative. The efficiency of the proposed technique is demonstrated by a numerical example.展开更多
Addresses the design problems of robust L2-L∞ filters with pole constraint in a disk for uncertain continuous-time linear systems. The uncertain parameters are assumed to belong to convex bounded domains. The aim is ...Addresses the design problems of robust L2-L∞ filters with pole constraint in a disk for uncertain continuous-time linear systems. The uncertain parameters are assumed to belong to convex bounded domains. The aim is to determine a stable linear filter such that the filtering error system possesses a prescribed L2-L∞ noise attenuation level and expected poles location. The filtering strategies are based on parameter-dependent Lyapunov stability results to derive new robust L2-L∞ performance criteria and the regional pole placement conditions. From the proposed multi-objective performance criteria, we derive sufficient conditions for the existence of robust L2-L∞ filters with pole constraint in a disk, and cast the filter design into a convex optimization problem subject to a set of linear matrix inequality constraints. This filtering method exhibits less conservativeness than previous results in the quadratic framework. The advantages of the filter design procedures are demonstrated by means of numerical examples.展开更多
For discrete-time T-S fuzzy systems, the stability and controller design method are in-vestigated based on parameter-dependent Lyapunov function (PDLF). T-S fuzzy systems di?er fromnon-fuzzy systems with polytopic des...For discrete-time T-S fuzzy systems, the stability and controller design method are in-vestigated based on parameter-dependent Lyapunov function (PDLF). T-S fuzzy systems di?er fromnon-fuzzy systems with polytopic description or multi-model description in that the weighting coef-ficients have respective meanings. They, however, have stability aspect in common. By adopting astability condition for polytopic systems obtained via PDLF, and combining the properties of T-Sfuzzy systems, new results are given in this paper. An example shows that by applying the newresults, the stability conditions that can be distinguished are less conservative.展开更多
The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain syst...The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.展开更多
This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors.In this paper, the specific control laws under the three forms are given.S...This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors.In this paper, the specific control laws under the three forms are given.Stability is analyzed by the La Salle invariance principle and the numerical simulation is carried out in a 2D test system.The calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing algorithm.Finally, a unified form of the control laws under the three forms is given.展开更多
In this paper, we investigate one kind of complex-valued systems with an impulsive control field, where the complex-valued system is governed by the Schrödinger equation, which is used for quantum systems, etc. W...In this paper, we investigate one kind of complex-valued systems with an impulsive control field, where the complex-valued system is governed by the Schrödinger equation, which is used for quantum systems, etc. We study the convergence of the complex-valued system with impulsive control fields by one Lyapunov function based on the state distance and the invariant principle of impulsive systems. We propose new results for the mentioned complex-valued systems in the form of sufficient conditions and also present one numerical simulation to illustrate the effectiveness of the proposed control method.展开更多
Stability criteria for the complex-valued impulsive system are applied widely in many fields, such as quantum systems, which have been studied in recent decades. In this paper, I investigate the Lyapunov control of fi...Stability criteria for the complex-valued impulsive system are applied widely in many fields, such as quantum systems, which have been studied in recent decades. In this paper, I investigate the Lyapunov control of finite dimensional complex-valued systems with impulsive control fields, where the studied complex-valued systems are governed by the Schrödinger equation and can be used in quantum systems. By one Lyapunov function based on state error and the invariant principle of impulsive systems, I study the convergence of complex-valued systems with impulsive control fields and propose new results for the mentioned complex-valued systems in the form of sufficient conditions. A numerical simulation to validate the proposed control method is provided.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
This paper presents a predefined-time controller for Multiple Space transportation Robots System (MSRS), which can be applied in on-orbit assembly tasks to transport modules to pre-assembly configuration quickly. Firs...This paper presents a predefined-time controller for Multiple Space transportation Robots System (MSRS), which can be applied in on-orbit assembly tasks to transport modules to pre-assembly configuration quickly. Firstly, to simplify the analysis and design of predefined-time controller, a Predefined-time Stability Criterion is proposed in the form of Composite Lyapunov Function (CLF-PSC). Besides simplicity, the CLF-PSC also has the advantage of less conservativeness due to utilization of initial state information. Secondly, a concept of Lp-Norm-Normalized Sign Function (LPNNSF) is proposed based on the CLF-PSC. Different from traditional norm-normalized sign function, the Lp-norm of LPNNSF can be selected arbitrarily according to practical control task requirements, which means that the proposed LPNNSF is more generalized and more convenient for calculation. Thirdly, a predefined-time disturbance observer and predefined-time controller are designed based on the LPNNSF. The observer has the property of predefined-time convergence to achieve quicker and more accurate estimation of the lumped disturbance. The controller has less control input and chattering phenomenon than traditional predefined-time controller. In addition, by introducing the observer into the controller, the closed-loop system enjoys high precision and strong robustness. Finally, the effectiveness of the proposed controller is verified by numerical simulations. By employing the controller, the MSRS can carry assembly modules to the desired pre-assembly configuration accurately within predefined time.展开更多
Disability is defined as a condition that makes it difficult for a person to perform certain vital activities.In recent years,the integration of the concepts of intelligence in solving various problems for disabled pe...Disability is defined as a condition that makes it difficult for a person to perform certain vital activities.In recent years,the integration of the concepts of intelligence in solving various problems for disabled persons has become more frequent.However,controlling an exoskeleton for rehabilitation presents challenges due to their nonlinear characteristics and external disturbances caused by the structure itself or the patient wearing the exoskeleton.To remedy these problems,this paper presents a novel adaptive control strategy for upper-limb rehabilitation exoskeletons,addressing the challenges of nonlinear dynamics and external disturbances.The proposed controller integrated a Radial Basis Function Neural Network(RBFNN)with a disturbance observer and employed a high-dimensional integral Lyapunov function to guarantee system stability and trajectory tracking performance.In the control system,the role of the RBFNN was to estimate uncertain signals in the dynamic model,while the disturbance observer tackled external disturbances during trajectory tracking.Artificially created scenarios for Human-Robot interactive experiments and periodically repeated reference trajectory experiments validated the controller’s performance,demonstrating efficient tracking.The proposed controller is found to achieve superior tracking accuracy with Root-Mean-Squared(RMS)errors of 0.022-0.026 rad for all joints,outperforming conventional Proportional-Integral-Derivative(PID)by 73%and Neural-Fuzzy Adaptive Control(NFAC)by 389.47%lower error.These results suggested that the RBFNN adaptive controller,coupled with disturbance compensation,could serve as an effective rehabilitation tool for upper-limb exoskeletons.These results demonstrate the superiority of the proposed method in enhancing rehabilitation accuracy and robustness,offering a promising solution for the control of upper-limb assistive devices.Based on the obtained results and due to their high robustness,the proposed control schemes can be extended to other motor disabilities,including lower limb exoskeletons.展开更多
An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local ...An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.展开更多
The robust admissibility analysis of a class of uncertain discrete-time switched linear singular（SLS） systems for arbitrary switching laws is addressed. The parameter uncertainty is assumed to be norm-bounded. First...The robust admissibility analysis of a class of uncertain discrete-time switched linear singular（SLS） systems for arbitrary switching laws is addressed. The parameter uncertainty is assumed to be norm-bounded. First, by using the switched Lyapunov function approach, some new sufficient conditions ensuring the nominal discrete-time SLS system to be regular, casual and asymptotically stable for arbitrary switching laws are derived in terms of linear matrix inequalities. Then, the robust admissibility condition for the uncertain discrete-time SLS systems is presented. The obtained results can be viewed as an extension of previous works on the switched Lyapunov function approach from the regular switched linear systems to the switched linear singular cases. Numerical examples show the reduced conservatism and effectiveness of the proposed conditions.展开更多
文摘The separation of the Lyapunov matrices and system matrices plays an important role when one uses parameter-dependent Lyapunov functional handling systems with polytopic type uncertainties. The delay-dependent robust stability problem for systems with polytopic type uncertainties is discussed by using parameter-dependent Lyapunov functional. The derivative term in the derivative of Lyapunov functional is reserved and the free weighting matrices are employed to express the relationship between die terms in the system equation such that the Lyapunov matrices are not involved in any product terms with the system matrices. In addition, the relationships between the terms in the Leibniz Newton formula are also described by some free weighting matrices and some delay-dependent stability conditions are derived. Numerical examples demonstrate that the proposed criteria are more effective than the previous results.
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The problem of robust L 1 filtering with pole constraint in a disk for linear continuous polytopic uncertain systems is discussed. The attention is focused on design a linear asymptotically stable filter such that the filtering error system remains robustly stable, and has a L 1 performance constraint and pole constraint in a disk. The new robust L 1 performance criteria and regional pole placement condition are obtained via parameter-dependent Lyapunov functions method. Upon the proposed multiobjective performance criteria and by means of LMI technique, both full-order and reduced-order robust L 1 filter with suitable dynamic behavior can be obtained from the solution of convex optimization problems. Compared with earlier result in the quadratic framework, this approach turns out to be less conservative. The efficiency of the proposed technique is demonstrated by a numerical example.
文摘Addresses the design problems of robust L2-L∞ filters with pole constraint in a disk for uncertain continuous-time linear systems. The uncertain parameters are assumed to belong to convex bounded domains. The aim is to determine a stable linear filter such that the filtering error system possesses a prescribed L2-L∞ noise attenuation level and expected poles location. The filtering strategies are based on parameter-dependent Lyapunov stability results to derive new robust L2-L∞ performance criteria and the regional pole placement conditions. From the proposed multi-objective performance criteria, we derive sufficient conditions for the existence of robust L2-L∞ filters with pole constraint in a disk, and cast the filter design into a convex optimization problem subject to a set of linear matrix inequality constraints. This filtering method exhibits less conservativeness than previous results in the quadratic framework. The advantages of the filter design procedures are demonstrated by means of numerical examples.
文摘For discrete-time T-S fuzzy systems, the stability and controller design method are in-vestigated based on parameter-dependent Lyapunov function (PDLF). T-S fuzzy systems di?er fromnon-fuzzy systems with polytopic description or multi-model description in that the weighting coef-ficients have respective meanings. They, however, have stability aspect in common. By adopting astability condition for polytopic systems obtained via PDLF, and combining the properties of T-Sfuzzy systems, new results are given in this paper. An example shows that by applying the newresults, the stability conditions that can be distinguished are less conservative.
基金supported by the National Natural Science Foundation of China (6090405161021002)
文摘The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.
基金Project supported by the National Natural Science Foundation of China (Grant No.62176140)。
文摘This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors.In this paper, the specific control laws under the three forms are given.Stability is analyzed by the La Salle invariance principle and the numerical simulation is carried out in a 2D test system.The calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing algorithm.Finally, a unified form of the control laws under the three forms is given.
文摘In this paper, we investigate one kind of complex-valued systems with an impulsive control field, where the complex-valued system is governed by the Schrödinger equation, which is used for quantum systems, etc. We study the convergence of the complex-valued system with impulsive control fields by one Lyapunov function based on the state distance and the invariant principle of impulsive systems. We propose new results for the mentioned complex-valued systems in the form of sufficient conditions and also present one numerical simulation to illustrate the effectiveness of the proposed control method.
文摘Stability criteria for the complex-valued impulsive system are applied widely in many fields, such as quantum systems, which have been studied in recent decades. In this paper, I investigate the Lyapunov control of finite dimensional complex-valued systems with impulsive control fields, where the studied complex-valued systems are governed by the Schrödinger equation and can be used in quantum systems. By one Lyapunov function based on state error and the invariant principle of impulsive systems, I study the convergence of complex-valued systems with impulsive control fields and propose new results for the mentioned complex-valued systems in the form of sufficient conditions. A numerical simulation to validate the proposed control method is provided.
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.
基金co-supported by the National Natural Science Foundation of China(Nos.12372048,12102343)the Key Program of the National Natural Science Foundation of China(No.U2013206)+1 种基金the China Postdoctoral Science Foundation(No.2023M742835)the Guangdong Basic and Applied Basic Research Foundation,China(No.2023A1515011421).
文摘This paper presents a predefined-time controller for Multiple Space transportation Robots System (MSRS), which can be applied in on-orbit assembly tasks to transport modules to pre-assembly configuration quickly. Firstly, to simplify the analysis and design of predefined-time controller, a Predefined-time Stability Criterion is proposed in the form of Composite Lyapunov Function (CLF-PSC). Besides simplicity, the CLF-PSC also has the advantage of less conservativeness due to utilization of initial state information. Secondly, a concept of Lp-Norm-Normalized Sign Function (LPNNSF) is proposed based on the CLF-PSC. Different from traditional norm-normalized sign function, the Lp-norm of LPNNSF can be selected arbitrarily according to practical control task requirements, which means that the proposed LPNNSF is more generalized and more convenient for calculation. Thirdly, a predefined-time disturbance observer and predefined-time controller are designed based on the LPNNSF. The observer has the property of predefined-time convergence to achieve quicker and more accurate estimation of the lumped disturbance. The controller has less control input and chattering phenomenon than traditional predefined-time controller. In addition, by introducing the observer into the controller, the closed-loop system enjoys high precision and strong robustness. Finally, the effectiveness of the proposed controller is verified by numerical simulations. By employing the controller, the MSRS can carry assembly modules to the desired pre-assembly configuration accurately within predefined time.
基金funded by the King Salman Center For Disability Research,through Research Group No.KSRG-2024-468。
文摘Disability is defined as a condition that makes it difficult for a person to perform certain vital activities.In recent years,the integration of the concepts of intelligence in solving various problems for disabled persons has become more frequent.However,controlling an exoskeleton for rehabilitation presents challenges due to their nonlinear characteristics and external disturbances caused by the structure itself or the patient wearing the exoskeleton.To remedy these problems,this paper presents a novel adaptive control strategy for upper-limb rehabilitation exoskeletons,addressing the challenges of nonlinear dynamics and external disturbances.The proposed controller integrated a Radial Basis Function Neural Network(RBFNN)with a disturbance observer and employed a high-dimensional integral Lyapunov function to guarantee system stability and trajectory tracking performance.In the control system,the role of the RBFNN was to estimate uncertain signals in the dynamic model,while the disturbance observer tackled external disturbances during trajectory tracking.Artificially created scenarios for Human-Robot interactive experiments and periodically repeated reference trajectory experiments validated the controller’s performance,demonstrating efficient tracking.The proposed controller is found to achieve superior tracking accuracy with Root-Mean-Squared(RMS)errors of 0.022-0.026 rad for all joints,outperforming conventional Proportional-Integral-Derivative(PID)by 73%and Neural-Fuzzy Adaptive Control(NFAC)by 389.47%lower error.These results suggested that the RBFNN adaptive controller,coupled with disturbance compensation,could serve as an effective rehabilitation tool for upper-limb exoskeletons.These results demonstrate the superiority of the proposed method in enhancing rehabilitation accuracy and robustness,offering a promising solution for the control of upper-limb assistive devices.Based on the obtained results and due to their high robustness,the proposed control schemes can be extended to other motor disabilities,including lower limb exoskeletons.
基金Specialized Research Fund for the Doctoral Program of Higher Education ( No. 20090092110051)the Key Project of Chinese Ministry of Education ( No. 108060)the National Natural Science Foundation of China ( No. 51076027, 51036002, 51106024)
文摘An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.
基金The National Natural Science Foundation of China(No.60835001)the Key Project of Ministry of Education of China (No.108060)
文摘The robust admissibility analysis of a class of uncertain discrete-time switched linear singular（SLS） systems for arbitrary switching laws is addressed. The parameter uncertainty is assumed to be norm-bounded. First, by using the switched Lyapunov function approach, some new sufficient conditions ensuring the nominal discrete-time SLS system to be regular, casual and asymptotically stable for arbitrary switching laws are derived in terms of linear matrix inequalities. Then, the robust admissibility condition for the uncertain discrete-time SLS systems is presented. The obtained results can be viewed as an extension of previous works on the switched Lyapunov function approach from the regular switched linear systems to the switched linear singular cases. Numerical examples show the reduced conservatism and effectiveness of the proposed conditions.
