This study examines the construction of Intrinsic Lyapunov functions to investigate the asymptotic stability of equilibrium states analyzed under specific conditions involving interaction coefficients and compartmenta...This study examines the construction of Intrinsic Lyapunov functions to investigate the asymptotic stability of equilibrium states analyzed under specific conditions involving interaction coefficients and compartmental transitions.It involves the qualitative properties of stratified compartmental models for drug user populations within heterogeneous communities using intrinsic Lyapunov methods.These models categorize populations into different compartments(e.g.,susceptible individuals,drug users,and those undergoing treatment)and account for interactions among these subpopulations.The system is governed by nonlinear ordinary differential equations,with parameters representing initiation,recovery,and relapse rates.Additionally,the boundedness of solutions is established,ensuring that population variables(e.g.the number of drug users)remain within biologically feasible limits over a period of time.These findings provide theoretical insights into the long-term dynamics of drug user populations,highlighting the impact of prevention,treatment,and socio-environmental factors.The results underscore the effectiveness of intrinsic Lyapunov methods in understanding stratified population dynamics and guiding targeted intervention strategies to control drug prevalence.展开更多
In this paper,we study the issue of controlling a rotating flexible body-beam system(RFBBS)which consists of a tip mass attached to the free-end and a rigid disk attached to the clamped-end of an Euler-Bernoulli beam....In this paper,we study the issue of controlling a rotating flexible body-beam system(RFBBS)which consists of a tip mass attached to the free-end and a rigid disk attached to the clamped-end of an Euler-Bernoulli beam.The boundary control input is affected by both unknown disturbance and nonlinear input backlash.First,the input backlash is considered as desired control input combined with a nonlinear input error,converting it to an external disturbance,and then,the control signal is designed through the energy-based control method.Next,the closed-loop system’s stability is analysed through Lyapunov direct method.Finally,the efficacy of the proposed control scheme is tested through numerical simulations utilizing the finite difference method.展开更多
This paper considers the mean square output containment control problem for heterogeneous multi-agent systems(MASs)with randomly switching topologies and nonuniform distributed delays.By modeling the switching topolog...This paper considers the mean square output containment control problem for heterogeneous multi-agent systems(MASs)with randomly switching topologies and nonuniform distributed delays.By modeling the switching topologies as a continuous-time Markov process and taking the distributed delays into consideration,a novel distributed containment observer is proposed to estimate the convex hull spanned by the leaders'states.A novel distributed output feedback containment controller is then designed without using the prior knowledge of distributed delays.By constructing a novel switching Lyapunov functional,the output containment control problem is then solved in the sense of mean square under an easily-verifiable sufficient condition.Finally,two numerical examples are given to show the effectiveness of the proposed controller.展开更多
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
The techniques to forecast available parking space(APS) are indispensable components for parking guidance systems(PGS). According to the data collected in Newcastle upon Tyne, England, the changing characteristics of ...The techniques to forecast available parking space(APS) are indispensable components for parking guidance systems(PGS). According to the data collected in Newcastle upon Tyne, England, the changing characteristics of APS were studied. Thereafter, aiming to build up a multi-step APS forecasting model that provides richer information than a conventional one-step model, the largest Lyapunov exponents(largest LEs) method was introduced into PGS. By experimental tests conducted using the same dataset, its prediction performance was compared with traditional wavelet neural network(WNN) method in both one-step and multi-step processes. Based on the results, a new multi-step forecasting model called WNN-LE method was proposed, where WNN, which enjoys a more accurate performance along with a better learning ability in short-term forecasting, was applied in the early forecast steps while the Lyapunov exponent prediction method in the latter steps precisely reflect the chaotic feature in latter forecast period. The MSE of APS forecasting for one hour time period can be reduced from 83.1 to 27.1(in a parking building with 492 berths) by using largest LEs method instead of WNN and further reduced to 19.0 by conducted the new method.展开更多
This paper focuses on the robust stability for time-delay systems of neutral type. A new complete Lyapunov-Krasovskii function (LKF) is developed. Based on this function and discretization, stability conditions in ter...This paper focuses on the robust stability for time-delay systems of neutral type. A new complete Lyapunov-Krasovskii function (LKF) is developed. Based on this function and discretization, stability conditions in terms of linear matrix inequalities are obtained. A class of time-varying uncertainty of system matrices can be studied by the method.展开更多
In this paper a new simplified method of stability study of dynamical nonlinear systems is proposed as an alternative to using Lyapunov’s method. Like the Lyapunov theorem, the new concept describes a sufficient cond...In this paper a new simplified method of stability study of dynamical nonlinear systems is proposed as an alternative to using Lyapunov’s method. Like the Lyapunov theorem, the new concept describes a sufficient condition for the systems to be globally stable. The proposed method is based on the assumption that, not only the state matrix contains information on the stability of the systems, but also the eigenvectors. So, first we will write the model of nonlinear systems in the state-space representation, then we use the eigenvectors of the state matrix as system stability indicators.展开更多
Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimati...Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimating settling-time function (STF) of the hybrid systems.When switching dynamics are FTS and impulsive dynamics involve destabilizing delay-dependent impulses, the FTS is retained if the impulses occur infrequently.展开更多
Switched linear parameter varying(LPV)systems have,in recent years,inspired a great number of research endeavors owing to their excellent ability to approximate nonlinear systems and handle complex hybrid dynamics in ...Switched linear parameter varying(LPV)systems have,in recent years,inspired a great number of research endeavors owing to their excellent ability to approximate nonlinear systems and handle complex hybrid dynamics in system analysis and synthesis.Nevertheless,numerous difficulties and challenges are also encountered due to the reciprocal effects of switching signals and scheduling parameters in the analysis and synthesis of switched LPV systems.In this paper,the standard description and specific characteristics of switched LPV systems are first introduced.Then,the main methodologies are proposed in the literature to cope with stability and performance analysis,control synthesis,as well as fault diagnosis and fault-tolerant control issues,and the typical applications in various fields are surveyed.Finally,several key open problems and current research activities are also discussed to elucidate the potential research directions in the future.展开更多
In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as...In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.展开更多
An optimal guidance law based on missile-target line-of-sight (LOS) angular rate is presented for intercepting a nonmaneuvering target. It is then integrated with sliding-mode control theory by using reaching-law of s...An optimal guidance law based on missile-target line-of-sight (LOS) angular rate is presented for intercepting a nonmaneuvering target. It is then integrated with sliding-mode control theory by using reaching-law of sliding-mode, in order to derive an optimal sliding-mode guidance law for intercepting a maneuvering target. The new guidance method's robustness against target maneuvers and good miss distance performance are proved by the second method of Lyapunov and simulation results. The presented guidance law is simple to implement in practical applications.展开更多
A new attitude controller is proposed for spacecraft whose actuator has variable input saturation limit. There are three identical flywheels orthogonally mounted on board. Each rotor is driven by a brushless DC motor ...A new attitude controller is proposed for spacecraft whose actuator has variable input saturation limit. There are three identical flywheels orthogonally mounted on board. Each rotor is driven by a brushless DC motor （BLDCM）. Models of spacecraft attitude dynamics and flywheel rotor driving motor electromechanics are discussed in detail. The controller design is similar to saturation limit linear assignment. An auxiliary parameter and a boundary coefficient are imported into the controller to guaran- tee system stability and improve control performance. A time-varying and state-dependent flywheel output torque saturation limit model is established. Stability of the closed-loop control system and asymptotic convergence of system states are proved via Lyapunov methods and LaSalle invariance principle. Boundedness of the auxiliary parameter ensures that the control objective can be achieved, while the boundary parameter＇s value makes a balance between system control performance and flywheel utilization efficiency. Compared with existing controllers, the newly developed controller with variable torque saturation limit can bring smoother control and faster system response. Numerical simulations validate the effectiveness of the controller.展开更多
The attitude tracking control problem for a satellite with parameter uncertainties and external disturbances is considered in this paper. For this class of multi-input multi-output uncertain nonlinear systems, a desig...The attitude tracking control problem for a satellite with parameter uncertainties and external disturbances is considered in this paper. For this class of multi-input multi-output uncertain nonlinear systems, a design method of robust output tracking controllers is proposed based on the upper-bounds of the uncertainties. Using the input/output feedback linearization approach and Lyapunov method, a control law is designed, which guarantees that the system output exponentially tracks the given desired output. The proposed controller is easy to compute and complement. Simulation results show that, in the closed-loop system, precise attitude control is accomplished in spite of the uncertainties in the system.展开更多
Conventional sliding mode controllers are based on the assumption of switching control, but a well-known drawback of such controllers is the chattering phenomenon. To overcome the undesirable chattering effects, the d...Conventional sliding mode controllers are based on the assumption of switching control, but a well-known drawback of such controllers is the chattering phenomenon. To overcome the undesirable chattering effects, the discontinuity in the control law can be smoothed out in a thin boundary layer neighboring the switching surface. In this paper, rigorous proofs of the boundedness and convergence properties of smooth sliding mode controllers are presented. This result corrects flawed conclusions previously reached in the literature. An illustrative example is also presented in order to confirm the convergence of the tracking error vector to the defined bounded region.展开更多
This paper investigates the robust H <SUB>∞</SUB> filtering problem for uncertain two-dimensional (2D) systems described by the Roesser model. The parameter uncertainties considered in this paper...This paper investigates the robust H <SUB>∞</SUB> filtering problem for uncertain two-dimensional (2D) systems described by the Roesser model. The parameter uncertainties considered in this paper are assumed to be of polytopic type. A new structured polynomially parameter-dependent method is utilized, which is based on homogeneous polynomially parameter-dependent matrices of arbitrary degree. The proposed method includes results in the quadratic framework and the linearly parameter-dependent framework as special cases for zeroth degree and first degree, respectively. A numerical example illustrates the feasibility and advantage of the proposed filter design methods.展开更多
This paper studies the robust stochastic stabilization and robust H∞ control for linear time-delay systems with both Markovian jump parameters and unknown norm-bounded parameter uncertainties. This problem can be sol...This paper studies the robust stochastic stabilization and robust H∞ control for linear time-delay systems with both Markovian jump parameters and unknown norm-bounded parameter uncertainties. This problem can be solved on the basis of stochastic Lyapunov approach and linear matrix inequality (LMI) technique. Sufficient conditions for the existence of stochastic stabilization and robust H∞ state feedback controller are presented in terms of a set of solutions of coupled LMIs. Finally, a numerical example is included to demonstrate the practicability of the proposed methods.展开更多
This paper proposes a novel nonlinear energy-based coupling control for an underactuated offshore ship-mounted crane,which guarantees both precise trolley positioning and payload swing suppressing performances under e...This paper proposes a novel nonlinear energy-based coupling control for an underactuated offshore ship-mounted crane,which guarantees both precise trolley positioning and payload swing suppressing performances under external sea wave disturbance. In addition to having such typical nonlinear underactuated property, as it is well known, an offshore ship-mounted crane also suffers from much unexpected persistent disturbances induced by sea waves or currents, which, essentially different from an overhead crane fixed on land, cause much difficulty in modeling and controller design. Inspired by the desire to achieve appropriate control performance against those challenging factors, in this paper, through carefully analyzing the inherent mechanism of the nonlinear dynamics, we first construct a new composite signal to enhance the coupling behavior of the trolley motion as well as the payload swing in the presence of ship′s roll motion disturbance. Based on which, an energy-based coupling control law is presented to achieve asymptotic stability of the crane control system′s equilibrium point. Without any linearization of the complex nonlinear dynamics, unlike traditional feedback controllers, the proposed control law takes a much simpler structure independent of the system parameters. To support the theoretical derivations and to further verify the actual control performance, Lyapunov-based mathematical analysis as well as numerical simulation/experimental results are carried out, which clarify the feasibility and superior performance of the proposed method over complicated disturbances.展开更多
The problem of robust stabilization for nonlinear systems with partially known uncertainties is considered in this paper. The required information about uncertainties in the system is merely that the uncertainties are...The problem of robust stabilization for nonlinear systems with partially known uncertainties is considered in this paper. The required information about uncertainties in the system is merely that the uncertainties are bounded, but the upper bounds are incompletely known. This paper can be viewed as an extension of the work in reference [1]. To compensate the uncertainties, an adaptive robust controller based on Lyapunov method is proposed and the design algorithm is also suggested. Compared with some previous controllers which can only ensure ultimate uniform boundedness of the systems, the controller given in the paper can make sure that the obtained closed-loop system is asymptotically stable in the large. Simulations show that the method presented is available and effective.展开更多
文摘This study examines the construction of Intrinsic Lyapunov functions to investigate the asymptotic stability of equilibrium states analyzed under specific conditions involving interaction coefficients and compartmental transitions.It involves the qualitative properties of stratified compartmental models for drug user populations within heterogeneous communities using intrinsic Lyapunov methods.These models categorize populations into different compartments(e.g.,susceptible individuals,drug users,and those undergoing treatment)and account for interactions among these subpopulations.The system is governed by nonlinear ordinary differential equations,with parameters representing initiation,recovery,and relapse rates.Additionally,the boundedness of solutions is established,ensuring that population variables(e.g.the number of drug users)remain within biologically feasible limits over a period of time.These findings provide theoretical insights into the long-term dynamics of drug user populations,highlighting the impact of prevention,treatment,and socio-environmental factors.The results underscore the effectiveness of intrinsic Lyapunov methods in understanding stratified population dynamics and guiding targeted intervention strategies to control drug prevalence.
基金supported in part by the National Natural Science Fundation of China under Grant Nos.62403263 and 62373207in part by the Natural Science Fundation of Qingdao,China under Grant No.24-4-4-zrjj-88-jch+1 种基金in part by the Team Plan for Youth Innovation of Universities in Shandong Province under Grant No.2024KJH148in part by the Foundation of Key Laboratory of Autonomous Systems and Networked Control(South China University of Technology),Ministry of Education under Grant No.2024A01.
文摘In this paper,we study the issue of controlling a rotating flexible body-beam system(RFBBS)which consists of a tip mass attached to the free-end and a rigid disk attached to the clamped-end of an Euler-Bernoulli beam.The boundary control input is affected by both unknown disturbance and nonlinear input backlash.First,the input backlash is considered as desired control input combined with a nonlinear input error,converting it to an external disturbance,and then,the control signal is designed through the energy-based control method.Next,the closed-loop system’s stability is analysed through Lyapunov direct method.Finally,the efficacy of the proposed control scheme is tested through numerical simulations utilizing the finite difference method.
文摘This paper considers the mean square output containment control problem for heterogeneous multi-agent systems(MASs)with randomly switching topologies and nonuniform distributed delays.By modeling the switching topologies as a continuous-time Markov process and taking the distributed delays into consideration,a novel distributed containment observer is proposed to estimate the convex hull spanned by the leaders'states.A novel distributed output feedback containment controller is then designed without using the prior knowledge of distributed delays.By constructing a novel switching Lyapunov functional,the output containment control problem is then solved in the sense of mean square under an easily-verifiable sufficient condition.Finally,two numerical examples are given to show the effectiveness of the proposed controller.
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Project(2012CB725402)supported by the National Key Basic Research Program of ChinaProjects(51338003,50908051)supported by the National Natural Science Foundation of China
文摘The techniques to forecast available parking space(APS) are indispensable components for parking guidance systems(PGS). According to the data collected in Newcastle upon Tyne, England, the changing characteristics of APS were studied. Thereafter, aiming to build up a multi-step APS forecasting model that provides richer information than a conventional one-step model, the largest Lyapunov exponents(largest LEs) method was introduced into PGS. By experimental tests conducted using the same dataset, its prediction performance was compared with traditional wavelet neural network(WNN) method in both one-step and multi-step processes. Based on the results, a new multi-step forecasting model called WNN-LE method was proposed, where WNN, which enjoys a more accurate performance along with a better learning ability in short-term forecasting, was applied in the early forecast steps while the Lyapunov exponent prediction method in the latter steps precisely reflect the chaotic feature in latter forecast period. The MSE of APS forecasting for one hour time period can be reduced from 83.1 to 27.1(in a parking building with 492 berths) by using largest LEs method instead of WNN and further reduced to 19.0 by conducted the new method.
基金the National High Technology Research and Development Program (863) of China(No. 2006AA05Z148)
文摘This paper focuses on the robust stability for time-delay systems of neutral type. A new complete Lyapunov-Krasovskii function (LKF) is developed. Based on this function and discretization, stability conditions in terms of linear matrix inequalities are obtained. A class of time-varying uncertainty of system matrices can be studied by the method.
文摘In this paper a new simplified method of stability study of dynamical nonlinear systems is proposed as an alternative to using Lyapunov’s method. Like the Lyapunov theorem, the new concept describes a sufficient condition for the systems to be globally stable. The proposed method is based on the assumption that, not only the state matrix contains information on the stability of the systems, but also the eigenvectors. So, first we will write the model of nonlinear systems in the state-space representation, then we use the eigenvectors of the state matrix as system stability indicators.
基金supported by the National Natural Science Foundation of China(61833005)
文摘Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimating settling-time function (STF) of the hybrid systems.When switching dynamics are FTS and impulsive dynamics involve destabilizing delay-dependent impulses, the FTS is retained if the impulses occur infrequently.
基金supported in part by the National Natural Science Foundation of China(62222310,61973131,62473379)the National Key Research and Develepment Program of China(2024YFB3310701)+1 种基金the Research Fund for the Taishan Scholar Project of Shandong Province of China,the Major Basic Research of Natural Science Foundation of Shandong Province(ZR2024ZD38,ZR2022ZD34)the Japan Society for the Promotion of Science(21K04129).
文摘Switched linear parameter varying(LPV)systems have,in recent years,inspired a great number of research endeavors owing to their excellent ability to approximate nonlinear systems and handle complex hybrid dynamics in system analysis and synthesis.Nevertheless,numerous difficulties and challenges are also encountered due to the reciprocal effects of switching signals and scheduling parameters in the analysis and synthesis of switched LPV systems.In this paper,the standard description and specific characteristics of switched LPV systems are first introduced.Then,the main methodologies are proposed in the literature to cope with stability and performance analysis,control synthesis,as well as fault diagnosis and fault-tolerant control issues,and the typical applications in various fields are surveyed.Finally,several key open problems and current research activities are also discussed to elucidate the potential research directions in the future.
基金Supported by the Innovation Platform Open Fund in Hunan Province Colleges and Universities of China(201485).
文摘In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.
文摘An optimal guidance law based on missile-target line-of-sight (LOS) angular rate is presented for intercepting a nonmaneuvering target. It is then integrated with sliding-mode control theory by using reaching-law of sliding-mode, in order to derive an optimal sliding-mode guidance law for intercepting a maneuvering target. The new guidance method's robustness against target maneuvers and good miss distance performance are proved by the second method of Lyapunov and simulation results. The presented guidance law is simple to implement in practical applications.
基金National Natural Science Foundation of China(10902003)
文摘A new attitude controller is proposed for spacecraft whose actuator has variable input saturation limit. There are three identical flywheels orthogonally mounted on board. Each rotor is driven by a brushless DC motor （BLDCM）. Models of spacecraft attitude dynamics and flywheel rotor driving motor electromechanics are discussed in detail. The controller design is similar to saturation limit linear assignment. An auxiliary parameter and a boundary coefficient are imported into the controller to guaran- tee system stability and improve control performance. A time-varying and state-dependent flywheel output torque saturation limit model is established. Stability of the closed-loop control system and asymptotic convergence of system states are proved via Lyapunov methods and LaSalle invariance principle. Boundedness of the auxiliary parameter ensures that the control objective can be achieved, while the boundary parameter＇s value makes a balance between system control performance and flywheel utilization efficiency. Compared with existing controllers, the newly developed controller with variable torque saturation limit can bring smoother control and faster system response. Numerical simulations validate the effectiveness of the controller.
文摘The attitude tracking control problem for a satellite with parameter uncertainties and external disturbances is considered in this paper. For this class of multi-input multi-output uncertain nonlinear systems, a design method of robust output tracking controllers is proposed based on the upper-bounds of the uncertainties. Using the input/output feedback linearization approach and Lyapunov method, a control law is designed, which guarantees that the system output exponentially tracks the given desired output. The proposed controller is easy to compute and complement. Simulation results show that, in the closed-loop system, precise attitude control is accomplished in spite of the uncertainties in the system.
基金supported by National Natural Science Foundation of China(31301080)China Postdoctoral Science Foundation Project(2015M582122,2016T90644)+2 种基金National Key Technology Support Program of China(2015BAF13B00)Natural Science Foundation of Shandong Province(ZR2015FL001)the Open Project of State Key Laboratory of Crop Biology(2013KF10)
基金supported by FAPERJ–State of Rio de JaneiroResearch Foundation (No. E-26/170.086/2006)
文摘Conventional sliding mode controllers are based on the assumption of switching control, but a well-known drawback of such controllers is the chattering phenomenon. To overcome the undesirable chattering effects, the discontinuity in the control law can be smoothed out in a thin boundary layer neighboring the switching surface. In this paper, rigorous proofs of the boundedness and convergence properties of smooth sliding mode controllers are presented. This result corrects flawed conclusions previously reached in the literature. An illustrative example is also presented in order to confirm the convergence of the tracking error vector to the defined bounded region.
基金Major Program of National Natural Science Foundation (No.60720106002)Program for Changjiang Scholars and Innovative Research Team in University
文摘This paper investigates the robust H <SUB>∞</SUB> filtering problem for uncertain two-dimensional (2D) systems described by the Roesser model. The parameter uncertainties considered in this paper are assumed to be of polytopic type. A new structured polynomially parameter-dependent method is utilized, which is based on homogeneous polynomially parameter-dependent matrices of arbitrary degree. The proposed method includes results in the quadratic framework and the linearly parameter-dependent framework as special cases for zeroth degree and first degree, respectively. A numerical example illustrates the feasibility and advantage of the proposed filter design methods.
文摘This paper studies the robust stochastic stabilization and robust H∞ control for linear time-delay systems with both Markovian jump parameters and unknown norm-bounded parameter uncertainties. This problem can be solved on the basis of stochastic Lyapunov approach and linear matrix inequality (LMI) technique. Sufficient conditions for the existence of stochastic stabilization and robust H∞ state feedback controller are presented in terms of a set of solutions of coupled LMIs. Finally, a numerical example is included to demonstrate the practicability of the proposed methods.
基金supported by National Natural Science Foundation of China (No. 11372144)National Science Fund for Distinguished Young Scholars of China (No. 61325017)National Science Foundation of Tianjin
文摘This paper proposes a novel nonlinear energy-based coupling control for an underactuated offshore ship-mounted crane,which guarantees both precise trolley positioning and payload swing suppressing performances under external sea wave disturbance. In addition to having such typical nonlinear underactuated property, as it is well known, an offshore ship-mounted crane also suffers from much unexpected persistent disturbances induced by sea waves or currents, which, essentially different from an overhead crane fixed on land, cause much difficulty in modeling and controller design. Inspired by the desire to achieve appropriate control performance against those challenging factors, in this paper, through carefully analyzing the inherent mechanism of the nonlinear dynamics, we first construct a new composite signal to enhance the coupling behavior of the trolley motion as well as the payload swing in the presence of ship′s roll motion disturbance. Based on which, an energy-based coupling control law is presented to achieve asymptotic stability of the crane control system′s equilibrium point. Without any linearization of the complex nonlinear dynamics, unlike traditional feedback controllers, the proposed control law takes a much simpler structure independent of the system parameters. To support the theoretical derivations and to further verify the actual control performance, Lyapunov-based mathematical analysis as well as numerical simulation/experimental results are carried out, which clarify the feasibility and superior performance of the proposed method over complicated disturbances.
文摘The problem of robust stabilization for nonlinear systems with partially known uncertainties is considered in this paper. The required information about uncertainties in the system is merely that the uncertainties are bounded, but the upper bounds are incompletely known. This paper can be viewed as an extension of the work in reference [1]. To compensate the uncertainties, an adaptive robust controller based on Lyapunov method is proposed and the design algorithm is also suggested. Compared with some previous controllers which can only ensure ultimate uniform boundedness of the systems, the controller given in the paper can make sure that the obtained closed-loop system is asymptotically stable in the large. Simulations show that the method presented is available and effective.
