This work presents an anticipatory terminal iterative learning control scheme for a class of batch proc- esses, where only the final system output is measurable and the control input is constant in each operations. Th...This work presents an anticipatory terminal iterative learning control scheme for a class of batch proc- esses, where only the final system output is measurable and the control input is constant in each operations. The propgsed approach works well with input constraints provided that the desired control input with respect to the desired trajectory is within the samratiorl bound. The tracking error convergence is established with rigorous mathe- matical analysis. Simulation results .are provided to showthe effectiveness, of the proposed approach.展开更多
In this paper, the stability of iterative learning control with data dropouts is discussed. By the super vector formulation, an iterative learning control （ILC） system with data dropouts can be modeled as an asynchr...In this paper, the stability of iterative learning control with data dropouts is discussed. By the super vector formulation, an iterative learning control （ILC） system with data dropouts can be modeled as an asynchronous dynamical system with rate constraints on events in the iteration domain. The stability condition is provided in the form of linear matrix inequalities （LMIS） depending on the stability of asynchronous dynamical systems. The analysis is supported by simulations.展开更多
Abstract--This paper conducts a survey on iterative learn- ing control （ILC） with incomplete information and associated control system design, which is a frontier of the ILC field. The incomplete information, includ...Abstract--This paper conducts a survey on iterative learn- ing control （ILC） with incomplete information and associated control system design, which is a frontier of the ILC field. The incomplete information, including passive and active types, can cause data loss or fragment due to various factors. Passive incomplete information refers to incomplete data and information caused by practical system limitations during data collection, storage, transmission, and processing, such as data dropouts, delays, disordering, and limited transmission bandwidth. Active incomplete information refers to incomplete data and information caused by man-made reduction of data quantity and quality on the premise that the given objective is satisfied, such as sampling and quantization. This survey emphasizes two aspects： the first one is how to guarantee good learning performance and tracking performance with passive incomplete data, and the second is how to balance the control performance index and data demand by active means. The promising research directions along this topic are also addressed, where data robustness is highly emphasized. This survey is expected to improve understanding of the restrictive relationship and trade-off between incomplete data and tracking performance, quantitatively, and promote further developments of ILC theory. Index Terms--Data dropout, data robustness, incomplete in- formation, iterative learning controi（ILC）, quantized control, sampled control, varying lengths.展开更多
The iterative learning control （ILC） has been demon-strated to be capable of considerably improving the tracking perfor-mance of systems which are affected by the iteration-independent disturbance. However, the achi...The iterative learning control （ILC） has been demon-strated to be capable of considerably improving the tracking perfor-mance of systems which are affected by the iteration-independent disturbance. However, the achievable performance is greatly degraded when iteration-dependent, stochastic disturbances are pre-sented. This paper considers the robustness of the ILC algorithm for the nonlinear system in presence of stochastic measurement disturbances. The robust convergence of the P-type ILC algorithm is firstly addressed, and then an improved ILC algorithm with a decreasing gain is proposed. Theoretical analyses show that the proposed algorithm can guarantee that the tracking error of the nonlinear system tends to zero in presence of measurement dis-turbances. The analysis is also supported by a numerical example.展开更多
In this paper, the iterative learning control problem is considered for a class of remote control system over wireless network communication channel. The control performance of remote iterative learning control （R-IL...In this paper, the iterative learning control problem is considered for a class of remote control system over wireless network communication channel. The control performance of remote iterative learning control （R-ILC） system is analyzed and an error boundary of the stable output of the R-ILC system is obtained for the boundary stochastic noise channel. Finally, we obtain some rules to reduce the fluctuation caused by wireless channel noise through the analysis results for fluctuation boundary. The simulation results prove the proposed rule is correct.展开更多
An adaptive iterative learning control scheme is presented for a class of strict-feedback nonlinear time-delay systems, with unknown nonlinearly parameterised and time-varying disturbed functions of known periods. Rad...An adaptive iterative learning control scheme is presented for a class of strict-feedback nonlinear time-delay systems, with unknown nonlinearly parameterised and time-varying disturbed functions of known periods. Radial basis function neural network and Fourier series expansion （FSE） are combined into a new function approximator to model each suitable disturbed function in systems. The requirement of the traditional iterative learning control algorithm on the nonlinear functions （such as global Lipschitz condition） is relaxed. Furthermore, by using appropriate Lyapunov-Krasovskii functionals, all signs in the closed loop system are guaranteed to be semiglobally uniformly ultimately bounded, and the output of the system is proved to converge to the desired trajectory. A simulation example is provided to illustrate the effectiveness of the control scheme.展开更多
In this paper, an open-loop PD-type iterative learning control(ILC) scheme is first proposed for two kinds of distributed parameter systems(DPSs) which are described by parabolic partial differential equations using n...In this paper, an open-loop PD-type iterative learning control(ILC) scheme is first proposed for two kinds of distributed parameter systems(DPSs) which are described by parabolic partial differential equations using non-collocated sensors and actuators. Then, a closed-loop PD-type ILC algorithm is extended to a class of distributed parameter systems with a non-collocated single sensor and m actuators when the initial states of the system exist some errors. Under some given assumptions, the convergence conditions of output errors for the systems can be obtained. Finally, one numerical example for a distributed parameter system with a single sensor and two actuators is presented to illustrate the effectiveness of the proposed ILC schemes.展开更多
This paper presents an Iterative Learning Control design applied to homing guidance of missiles against maneuvering targets. According to numerical experiments, although an increase of the control energies is apprecia...This paper presents an Iterative Learning Control design applied to homing guidance of missiles against maneuvering targets. According to numerical experiments, although an increase of the control energies is appreciated with respect to a previous published base controller for comparison, this strategy, which is simple to realize, is able to reduce the time to reach the head-on condition to target destruction. This fact is important to minimize the missile lateral force-level to fulfill engaging in hyper-sonic target persecutions.展开更多
Stochastic iterative learning control(ILC) is designed for solving the tracking problem of stochastic linear systems through fading channels. Consequently, the signals used in learning control algorithms are faded in ...Stochastic iterative learning control(ILC) is designed for solving the tracking problem of stochastic linear systems through fading channels. Consequently, the signals used in learning control algorithms are faded in the sense that a random variable is multiplied by the original signal. To achieve the tracking objective, a two-dimensional Kalman filtering method is used in this study to derive a learning gain matrix varying along both time and iteration axes. The learning gain matrix minimizes the trace of input error covariance. The asymptotic convergence of the generated input sequence to the desired input value is strictly proved in the mean-square sense. Both output and input fading are accounted for separately in turn, followed by a general formulation that both input and output fading coexists.Illustrative examples are provided to verify the effectiveness of the proposed schemes.展开更多
In this paper, both output-feedback iterative learning control(ILC) and repetitive learning control(RLC) schemes are proposed for trajectory tracking of nonlinear systems with state-dependent time-varying uncertaintie...In this paper, both output-feedback iterative learning control(ILC) and repetitive learning control(RLC) schemes are proposed for trajectory tracking of nonlinear systems with state-dependent time-varying uncertainties. An iterative learning controller, together with a state observer and a fully-saturated learning mechanism, through Lyapunov-like synthesis, is designed to deal with time-varying parametric uncertainties. The estimations for outputs, instead of system outputs themselves, are applied to form the error equation, which helps to establish convergence of the system outputs to the desired ones. This method is then extended to repetitive learning controller design. The boundedness of all the signals in the closed-loop is guaranteed and asymptotic convergence of both the state estimation error and the tracking error is established in both cases of ILC and RLC. Numerical results are presented to verify the effectiveness of the proposed methods.展开更多
This paper aims to solve the robust iterative learning control(ILC)problems for nonlinear time-varying systems in the presence of nonrepetitive uncertainties.A new optimization-based method is proposed to design and a...This paper aims to solve the robust iterative learning control(ILC)problems for nonlinear time-varying systems in the presence of nonrepetitive uncertainties.A new optimization-based method is proposed to design and analyze adaptive ILC,for which robust convergence analysis via a contraction mapping approach is realized by leveraging properties of substochastic matrices.It is shown that robust tracking tasks can be realized for optimization-based adaptive ILC,where the boundedness of system trajectories and estimated parameters can be ensured,regardless of unknown time-varying nonlinearities and nonrepetitive uncertainties.Two simulation tests,especially implemented for an injection molding process,demonstrate the effectiveness of our robust optimization-based ILC results.展开更多
In order to accelerate the convergence speed of iterative learning control(ILC), taking the P-type learning algorithm as an example, a correction algorithm with kernel-based autoassociative is proposed for the linear ...In order to accelerate the convergence speed of iterative learning control(ILC), taking the P-type learning algorithm as an example, a correction algorithm with kernel-based autoassociative is proposed for the linear system. The learning mechanism of human brain associative memory is introduced to the traditional ILC. The control value of the subsequent time is precorrected with the current time information by association in each iterative learning process. The learning efficiency of the whole system is improved significantly with the proposed algorithm. Through the rigorous analysis, it shows that under this new designed ILC scheme, the uniform convergence of the state tracking error is guaranteed. Numerical simulations illustrate the effectiveness of the proposed associative control scheme and the validity of the conclusion.展开更多
Generally, the classic iterative learning control(ILC)methods focus on finding design conditions for repetitive systems to achieve the perfect tracking of any specified trajectory,whereas they ignore a fundamental pro...Generally, the classic iterative learning control(ILC)methods focus on finding design conditions for repetitive systems to achieve the perfect tracking of any specified trajectory,whereas they ignore a fundamental problem of ILC: whether the specified trajectory is trackable, or equivalently, whether there exist some inputs for the repetitive systems under consideration to generate the specified trajectory? The current paper contributes to dealing with this problem. Not only is a concept of trackability introduced formally for any specified trajectory in ILC, but also some related trackability criteria are established. Further, the relation between the trackability and the perfect tracking tasks for ILC is bridged, based on which a new convergence analysis approach is developed for ILC by leveraging properties of a functional Cauchy sequence(FCS). Simulation examples are given to verify the effectiveness of the presented trackability criteria and FCS-induced convergence analysis method for ILC.展开更多
This work proposes a novel proportional-derivative(PD)-type state-dependent Riccati equation(SDRE)approach with iterative learning control(ILC)augmentation.On the one hand,the PD-type control gains could adopt many us...This work proposes a novel proportional-derivative(PD)-type state-dependent Riccati equation(SDRE)approach with iterative learning control(ILC)augmentation.On the one hand,the PD-type control gains could adopt many useful available criteria and tools of conventional PD controllers.On the other hand,the SDRE adds nonlinear and optimality characteristics to the controller,i.e.,increasing the stability margins.These advantages with the ILC correction part deliver a precise control law with the capability of error reduction by learning.The SDRE provides a symmetric-positive-definite distributed nonlinear suboptimal gain K(x)for the control input law u=–R–1(x)BT(x)K(x)x.The sub-blocks of the overall gain R–1(x)BT(x)K(x),are not necessarily symmetric positive definite.A new design is proposed to transform the optimal gain into two symmetric-positive-definite gains like PD-type controllers as u=–KSP(x)e–KSD(x)?.The new form allows us to analytically prove the stability of the proposed learning-based controller for mechanical systems;and presents guaranteed uniform boundedness in finite-time between learning loops.The symmetric PD-type controller is also developed for the state-dependent differential Riccati equation(SDDRE)to manipulate the final time.The SDDRE expresses a differential equation with a final boundary condition,which imposes a constraint on time that could be used for finitetime control.So,the availability of PD-type finite-time control is an asset for enhancing the conventional classical linear controllers with this tool.The learning rules benefit from the gradient descent method for both regulation and tracking cases.One of the advantages of this approach is a guaranteed-stability even from the first loop of learning.A mechanical manipulator,as an illustrative example,was simulated for both regulation and tracking problems.Successful experimental validation was done to show the capability of the system in practice by the implementation of the proposed method on a variable-pitch rotor benchmark.展开更多
Terminal iterative learning control(TILC) is developed to reduce the error between system output and a fixed desired point at the terminal end of operation interval over iterations under strictly identical initial con...Terminal iterative learning control(TILC) is developed to reduce the error between system output and a fixed desired point at the terminal end of operation interval over iterations under strictly identical initial conditions. In this work, the initial states are not required to be identical further but can be varying from iteration to iteration. In addition, the desired terminal point is not fixed any more but is allowed to change run-to-run. Consequently, a new adaptive TILC is proposed with a neural network initial state learning mechanism to achieve the learning objective over iterations. The neural network is used to approximate the effect of iteration-varying initial states on the terminal output and the neural network weights are identified iteratively along the iteration axis.A dead-zone scheme is developed such that both learning and adaptation are performed only if the terminal tracking error is outside a designated error bound. It is shown that the proposed approach is able to track run-varying terminal desired points fast with a specified tracking accuracy beyond the initial state variance.展开更多
Although standard iterative learning control(ILC) approaches can achieve perfect tracking for active magnetic bearing(AMB) systems under external disturbances, the disturbances are required to be iteration-invariant.I...Although standard iterative learning control(ILC) approaches can achieve perfect tracking for active magnetic bearing(AMB) systems under external disturbances, the disturbances are required to be iteration-invariant.In contrast to existing approaches, we address the tracking control problem of AMB systems under iteration-variant disturbances that are in different channels from the control inputs. A disturbance observer based ILC scheme is proposed that consists of a universal extended state observer(ESO) and a classical ILC law. Using only output feedback, the proposed control approach estimates and attenuates the disturbances in every iteration. The convergence of the closed-loop system is guaranteed by analyzing the contraction behavior of the tracking error.Simulation and comparison studies demonstrate the superior tracking performance of the proposed control approach.展开更多
基金Supported by the National Natural Science Foundation of China （60974040, 61120106009）, the Research Award Foundation for the Excellent Youth Scientists of Shandong Province of China （BS2011DX010）, and the High School Science ＆ Technol- ogy Fund Planning Project of Shandong Province of China （J 10LG32）.
文摘This work presents an anticipatory terminal iterative learning control scheme for a class of batch proc- esses, where only the final system output is measurable and the control input is constant in each operations. The propgsed approach works well with input constraints provided that the desired control input with respect to the desired trajectory is within the samratiorl bound. The tracking error convergence is established with rigorous mathe- matical analysis. Simulation results .are provided to showthe effectiveness, of the proposed approach.
基金supported by General Program (No. 60774022)State Key Program (No. 60834001) of National Natural Science Foundation of China
文摘In this paper, the stability of iterative learning control with data dropouts is discussed. By the super vector formulation, an iterative learning control （ILC） system with data dropouts can be modeled as an asynchronous dynamical system with rate constraints on events in the iteration domain. The stability condition is provided in the form of linear matrix inequalities （LMIS） depending on the stability of asynchronous dynamical systems. The analysis is supported by simulations.
基金supported by the National Natural Science Foundation of China(61673045)Beijing Natural Science Foundation(4152040)
文摘Abstract--This paper conducts a survey on iterative learn- ing control （ILC） with incomplete information and associated control system design, which is a frontier of the ILC field. The incomplete information, including passive and active types, can cause data loss or fragment due to various factors. Passive incomplete information refers to incomplete data and information caused by practical system limitations during data collection, storage, transmission, and processing, such as data dropouts, delays, disordering, and limited transmission bandwidth. Active incomplete information refers to incomplete data and information caused by man-made reduction of data quantity and quality on the premise that the given objective is satisfied, such as sampling and quantization. This survey emphasizes two aspects： the first one is how to guarantee good learning performance and tracking performance with passive incomplete data, and the second is how to balance the control performance index and data demand by active means. The promising research directions along this topic are also addressed, where data robustness is highly emphasized. This survey is expected to improve understanding of the restrictive relationship and trade-off between incomplete data and tracking performance, quantitatively, and promote further developments of ILC theory. Index Terms--Data dropout, data robustness, incomplete in- formation, iterative learning controi（ILC）, quantized control, sampled control, varying lengths.
基金supported by the National Natural Science Foundation of China (61203065 60834001)the Program of Open Laboratory Foundation of Control Engineering Key Discipline of Henan Provincial High Education (KG 2011-10)
文摘The iterative learning control （ILC） has been demon-strated to be capable of considerably improving the tracking perfor-mance of systems which are affected by the iteration-independent disturbance. However, the achievable performance is greatly degraded when iteration-dependent, stochastic disturbances are pre-sented. This paper considers the robustness of the ILC algorithm for the nonlinear system in presence of stochastic measurement disturbances. The robust convergence of the P-type ILC algorithm is firstly addressed, and then an improved ILC algorithm with a decreasing gain is proposed. Theoretical analyses show that the proposed algorithm can guarantee that the tracking error of the nonlinear system tends to zero in presence of measurement dis-turbances. The analysis is also supported by a numerical example.
基金Project supported by the Innovation Foundation of the Education Commission of Shanghai Municipality (Grant No.09ZZ89)the Shanghai Leading Academic Discipline Project (Grant No.S30108)the Science and Technology Commission of Shanghai Municipality (Grant No.08DZ223110)
文摘In this paper, the iterative learning control problem is considered for a class of remote control system over wireless network communication channel. The control performance of remote iterative learning control （R-ILC） system is analyzed and an error boundary of the stable output of the R-ILC system is obtained for the boundary stochastic noise channel. Finally, we obtain some rules to reduce the fluctuation caused by wireless channel noise through the analysis results for fluctuation boundary. The simulation results prove the proposed rule is correct.
基金supported by National Natural Science Foundation of China (No. 72103676)partially supported by the Fundamental Research Funds for the Central Universities
文摘An adaptive iterative learning control scheme is presented for a class of strict-feedback nonlinear time-delay systems, with unknown nonlinearly parameterised and time-varying disturbed functions of known periods. Radial basis function neural network and Fourier series expansion （FSE） are combined into a new function approximator to model each suitable disturbed function in systems. The requirement of the traditional iterative learning control algorithm on the nonlinear functions （such as global Lipschitz condition） is relaxed. Furthermore, by using appropriate Lyapunov-Krasovskii functionals, all signs in the closed loop system are guaranteed to be semiglobally uniformly ultimately bounded, and the output of the system is proved to converge to the desired trajectory. A simulation example is provided to illustrate the effectiveness of the control scheme.
基金supported by National Natural Science Foundation of China(61807016)Postgraduate Research and Practice Innovation Program of Jiangsu Province(KYCX18-1859)。
文摘In this paper, an open-loop PD-type iterative learning control(ILC) scheme is first proposed for two kinds of distributed parameter systems(DPSs) which are described by parabolic partial differential equations using non-collocated sensors and actuators. Then, a closed-loop PD-type ILC algorithm is extended to a class of distributed parameter systems with a non-collocated single sensor and m actuators when the initial states of the system exist some errors. Under some given assumptions, the convergence conditions of output errors for the systems can be obtained. Finally, one numerical example for a distributed parameter system with a single sensor and two actuators is presented to illustrate the effectiveness of the proposed ILC schemes.
基金partially supported by the Spanish Ministry of Economy and Competitiveness under grant number DPI2015-64170-R(MINECO/FEDER)
文摘This paper presents an Iterative Learning Control design applied to homing guidance of missiles against maneuvering targets. According to numerical experiments, although an increase of the control energies is appreciated with respect to a previous published base controller for comparison, this strategy, which is simple to realize, is able to reduce the time to reach the head-on condition to target destruction. This fact is important to minimize the missile lateral force-level to fulfill engaging in hyper-sonic target persecutions.
基金supported by the National Natural Science Foundation of China(61673045)the Fundamental Research Funds for the Central Universities(XK1802-4)
文摘Stochastic iterative learning control(ILC) is designed for solving the tracking problem of stochastic linear systems through fading channels. Consequently, the signals used in learning control algorithms are faded in the sense that a random variable is multiplied by the original signal. To achieve the tracking objective, a two-dimensional Kalman filtering method is used in this study to derive a learning gain matrix varying along both time and iteration axes. The learning gain matrix minimizes the trace of input error covariance. The asymptotic convergence of the generated input sequence to the desired input value is strictly proved in the mean-square sense. Both output and input fading are accounted for separately in turn, followed by a general formulation that both input and output fading coexists.Illustrative examples are provided to verify the effectiveness of the proposed schemes.
基金supported by the Third Level of Hangzhou 131 Young Talent Cultivation Plan Funding2018 Soft Science Research Project of Zhejiang Provincial Science and Technology Department Zhejiang Province Construction and participate in the“The Belt and Road”Technology Innovation Community Path Research(2018C35029)
文摘In this paper, both output-feedback iterative learning control(ILC) and repetitive learning control(RLC) schemes are proposed for trajectory tracking of nonlinear systems with state-dependent time-varying uncertainties. An iterative learning controller, together with a state observer and a fully-saturated learning mechanism, through Lyapunov-like synthesis, is designed to deal with time-varying parametric uncertainties. The estimations for outputs, instead of system outputs themselves, are applied to form the error equation, which helps to establish convergence of the system outputs to the desired ones. This method is then extended to repetitive learning controller design. The boundedness of all the signals in the closed-loop is guaranteed and asymptotic convergence of both the state estimation error and the tracking error is established in both cases of ILC and RLC. Numerical results are presented to verify the effectiveness of the proposed methods.
基金supported by the National Natural Science Foundation of China(61873013,61922007)。
文摘This paper aims to solve the robust iterative learning control(ILC)problems for nonlinear time-varying systems in the presence of nonrepetitive uncertainties.A new optimization-based method is proposed to design and analyze adaptive ILC,for which robust convergence analysis via a contraction mapping approach is realized by leveraging properties of substochastic matrices.It is shown that robust tracking tasks can be realized for optimization-based adaptive ILC,where the boundedness of system trajectories and estimated parameters can be ensured,regardless of unknown time-varying nonlinearities and nonrepetitive uncertainties.Two simulation tests,especially implemented for an injection molding process,demonstrate the effectiveness of our robust optimization-based ILC results.
基金Supported by National Natural Science Foundation ot China （61203065, 61120106009）, the Program of Natural Science of Henan Provincial Education Department （12A510013）, and the Program of Open Laboratory Foundation of Control Engineering Key Discipline of Henan Provincial High Education （KG 2011-10）
文摘在这份报纸，反复的学习控制(ILC ) 与任意的切换的信号为线性分离时间的交换系统的一个类被考虑。交换系统重复地在有限时间间隔期间被操作，这被假定，然后第一个顺序 P 类型 ILC 计划能被用来完成完美的追踪在上自始至终间隔。由超级向量途径，为在重复领域的如此的 ILC 系统的一个集中条件能被给。理论分析被模拟支持。
基金Supported by National Basic Research Program of China （973 Program） （2005CB321902） National Natural Science Foundation of China （60727002 60774003 60921001 90916024）+2 种基金 the Commission on Science Technology and Industry for National Defense （A2120061303） the Doctoral Program Foundation of Ministry of Education of China （20030006003） the Innovation Foundation of BUAA for Ph.D. Graduates
基金supported by the National Natural Science Foundation of China(51777170)the Aeronautical Science Foundation of China(20162853026)the Project Supported by Natural Science Basic Research Plan in Shannxi Province of China(2019JM-462,2020JM-151)。
文摘In order to accelerate the convergence speed of iterative learning control(ILC), taking the P-type learning algorithm as an example, a correction algorithm with kernel-based autoassociative is proposed for the linear system. The learning mechanism of human brain associative memory is introduced to the traditional ILC. The control value of the subsequent time is precorrected with the current time information by association in each iterative learning process. The learning efficiency of the whole system is improved significantly with the proposed algorithm. Through the rigorous analysis, it shows that under this new designed ILC scheme, the uniform convergence of the state tracking error is guaranteed. Numerical simulations illustrate the effectiveness of the proposed associative control scheme and the validity of the conclusion.
基金supported in part by the National Natural Science Foundation of China (62273018)in part by the Science and Technology on Space Intelligent Control Laboratory (HTKJ2022KL502006)。
文摘Generally, the classic iterative learning control(ILC)methods focus on finding design conditions for repetitive systems to achieve the perfect tracking of any specified trajectory,whereas they ignore a fundamental problem of ILC: whether the specified trajectory is trackable, or equivalently, whether there exist some inputs for the repetitive systems under consideration to generate the specified trajectory? The current paper contributes to dealing with this problem. Not only is a concept of trackability introduced formally for any specified trajectory in ILC, but also some related trackability criteria are established. Further, the relation between the trackability and the perfect tracking tasks for ILC is bridged, based on which a new convergence analysis approach is developed for ILC by leveraging properties of a functional Cauchy sequence(FCS). Simulation examples are given to verify the effectiveness of the presented trackability criteria and FCS-induced convergence analysis method for ILC.
基金supported by the European Commission H2020 Programme under HYFLIERS project contract 779411AERIAL-CORE project contract number 871479 and the ARTIC(RTI2018-102224-B-I00)projectfunded by the Spanish Agencia Estatal de Investigación。
文摘This work proposes a novel proportional-derivative(PD)-type state-dependent Riccati equation(SDRE)approach with iterative learning control(ILC)augmentation.On the one hand,the PD-type control gains could adopt many useful available criteria and tools of conventional PD controllers.On the other hand,the SDRE adds nonlinear and optimality characteristics to the controller,i.e.,increasing the stability margins.These advantages with the ILC correction part deliver a precise control law with the capability of error reduction by learning.The SDRE provides a symmetric-positive-definite distributed nonlinear suboptimal gain K(x)for the control input law u=–R–1(x)BT(x)K(x)x.The sub-blocks of the overall gain R–1(x)BT(x)K(x),are not necessarily symmetric positive definite.A new design is proposed to transform the optimal gain into two symmetric-positive-definite gains like PD-type controllers as u=–KSP(x)e–KSD(x)?.The new form allows us to analytically prove the stability of the proposed learning-based controller for mechanical systems;and presents guaranteed uniform boundedness in finite-time between learning loops.The symmetric PD-type controller is also developed for the state-dependent differential Riccati equation(SDDRE)to manipulate the final time.The SDDRE expresses a differential equation with a final boundary condition,which imposes a constraint on time that could be used for finitetime control.So,the availability of PD-type finite-time control is an asset for enhancing the conventional classical linear controllers with this tool.The learning rules benefit from the gradient descent method for both regulation and tracking cases.One of the advantages of this approach is a guaranteed-stability even from the first loop of learning.A mechanical manipulator,as an illustrative example,was simulated for both regulation and tracking problems.Successful experimental validation was done to show the capability of the system in practice by the implementation of the proposed method on a variable-pitch rotor benchmark.
基金supported by National Natural Science Foundation of China(Nos.61374102,61433002 and 61120106009)High Education Science&Technology Fund Planning Project of Shandong Province of China(No.J14LN30)
文摘Terminal iterative learning control(TILC) is developed to reduce the error between system output and a fixed desired point at the terminal end of operation interval over iterations under strictly identical initial conditions. In this work, the initial states are not required to be identical further but can be varying from iteration to iteration. In addition, the desired terminal point is not fixed any more but is allowed to change run-to-run. Consequently, a new adaptive TILC is proposed with a neural network initial state learning mechanism to achieve the learning objective over iterations. The neural network is used to approximate the effect of iteration-varying initial states on the terminal output and the neural network weights are identified iteratively along the iteration axis.A dead-zone scheme is developed such that both learning and adaptation are performed only if the terminal tracking error is outside a designated error bound. It is shown that the proposed approach is able to track run-varying terminal desired points fast with a specified tracking accuracy beyond the initial state variance.
文摘Although standard iterative learning control(ILC) approaches can achieve perfect tracking for active magnetic bearing(AMB) systems under external disturbances, the disturbances are required to be iteration-invariant.In contrast to existing approaches, we address the tracking control problem of AMB systems under iteration-variant disturbances that are in different channels from the control inputs. A disturbance observer based ILC scheme is proposed that consists of a universal extended state observer(ESO) and a classical ILC law. Using only output feedback, the proposed control approach estimates and attenuates the disturbances in every iteration. The convergence of the closed-loop system is guaranteed by analyzing the contraction behavior of the tracking error.Simulation and comparison studies demonstrate the superior tracking performance of the proposed control approach.
