互联系统的分散式自适应迭代学习控制及应用研究
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摘要
随着现代工业的高速发展,互联系统越来越多地出现在各种实际的控制系统中,近年来,关于互联大系统分散式控制理论的研究引起了学术界和工程界的广泛关注。由于在互联系统中各个子系统之间的信息交换有时在物理上难以实现,并且由于缺少与集中控制器相应的足够计算能力,在这种复杂情况之下分散控制技术需要优先使用。本文以几类非线性互联系统为研究对象,分析系统特性,分别设计分散式自适应迭代学习控制,对算法进行收敛性分析,同时运用算法的数值仿真来验证算法的有效性。本文通过系统性地结合自适应迭代学习控制和分散式控制技术,以求在一定程度上促进非线性互联系统控制科学的深入发展并为一类实际工程问题提供更好的解决方案。
本文研究内容有以下几方面：
1.针对一类具有不确定性的非线性互联系统,其互联项满足多项式有界条件,提出分散式模型参考自适应迭代学习控制,该算法包括2部分,一部分为反馈控制,用于保证子系统的闭环稳定性,另一部分为互联估计参数自适应迭代学习控制,用于消除各个子系统之间的互联项影响。进行了该分散式迭代学习控制算法的收敛性分析,仿真结果表明该算法的有效性。
2.针对一类具有不确定性的状态非线性时滞互联系统,给出分散式模型参考自适应迭代学习控制,该控制器为非记忆型控制器,只应用了跟踪误差项的实时信息,通过额外引入自适应迭代更新参数,来消除由于时滞互联项给互联系统带来的影响。对控制算法的收敛性进行详细推导,得到有效的仿真结果。由于各子系统之间普遍存在着信息传输的滞后性,对非线性互联系统而言,研究存在时滞情况下控制器设计问题更具有实际应用价值。
3.针对一类具有严格反馈形式的非线性互联系统,分2种情况进行分析,一类为互联项为子系统输出的单项式有界,一类为互联项为子系统输出的高阶多项式有界。当互联项为子系统输出的单项式有界时,引入了自适应更新参数岔,用以消除互联项的影响；当互联项为子系统输出的高阶多项式有界时,同时引入了自适应更新参数(?)ik和βik,消除子系统输出的高阶多项式有界影响。给出了控制器收敛性分析的理论推导,仿真结果验证了这种分散式自适应迭代学习控制的有效性。
4.将提出的理论与方法在互联机械系统上进行应用。分析了互联机械系统的特点,针对互联机械系统设计了分散式自适应迭代学习控制算法。同时基于Lyapunov方法对其进行算法收敛性分析,通过对子系统中未知参数和互联参数的迭代更新,可使得由跟踪误差和参数估计误差构成的Laypunov函数沿着迭代方向上单调递减。仿真结果显示了所给出的分散式自适应迭代学习控制算法有效性。
With the rapid development of modern science and technology, many practical control systems can be seen as nonlinear interconnected large-scale systems, so the decentralized control theory of interconnected large-scale systems has attracted great attentions in both academic research and industrial applications. Owing to the unrealized information exchanges between subsystems physically and the lack of computing power corresponding to the centralized controllers, the decentralized control technique usually has priority in usage under these complicated circumstances. The dissertation focuses on the certain kinds of nonlinear interconnected systems and analyses the systems characteristics. Then the decentralized adaptive learning control algorithms are designed correspondingly. The convergence analysis is provided for the proposed algorithms in this paper. Simulation results demonstrate that, utilizing the proposed controllers, the tracking error for each subsystem converges along the iteration axis. By systematically combining adaptive iterative learning control and decentralized control techniques, an attempt was made in this dissertation not only to forward deep development of interconnected system control science but also to provide better approaches to practical engineering problems to a certain degree.
The main contents are composed of the following four parts.
(1) An decentralized model reference adaptive iterative learning controller is designed for a class of nonlinear interconnected system with uncertainties. There are two parts in the controller, one is the feed-back controller which is used to stabilize the closed subsystem, the other is the adaptive iterative learning controller which eliminates the effects of the interconnections among subsystems. The convergence of the proposed algorithm is proved based on a Lyapunov-like method, guaranteeing the tracking error of each subsystem approaches to zero along with control iterations. A simulation example is given to show the effectiveness of the proposed method.
(2) Base on the nonlinear interconnected systems with state delay and model uncertainties, a decentralized model reference adaptive iterative learning control is proposed in this paper. The proposed controller of each subsystem is delay-independent which utilize only the current closed-loop local state variables. In order to eliminate the effects of interconnections and state delay, the extra adaptive parameters are updated along iteration axis. The algorithm convergence is proved carefully and the effectiveness of the proposed scheme is shown through computer simulation. Time delays, due to the information transmission between subsystems, naturally exist in interconnected systems and hence the control problem becomes more important than those interconnected systems without time delays.
(3) A decentralized backstepping adaptive iterative learning control schemes is proposed for a class of interconnected nonlinear systems of strict feedback form. The interconnections among subsystems are assumed to be bounded by an unknown1st-order or Pth-order polynomial in sub-outputs. A time-vary adaptive iterative learning control gain ζik is introduced to counteract the effect of the interconnections which are linear bounded in sub-output. As for the Pth-order polynomial sub-outputs bounded interconnections, two adaptive updated parameters ζik and βik are utilized. All the adaptive parameters are updated along both iteration axis and time one to counter the effects of the interconnections. It is shown that by using the proposed decentralized controller, the outputs of the subsystems can track the desired reference outputs iteratively. The simulation results show that the output tracking error of each subsystem converges along the iterative axis.
(4) A decentralized robust adaptive iterative learning control scheme for trajectory tracking of interconnected manipulators is developed. The proof of convergences based on the Lyapunov method. Through the iterative update of subsystem unknown parameters and interconnected parameters, the Lyapunov function composed of tracking errors and estimated parameter errors is monotonically decreased in iteration domain. The simulation results show that this method can guarantee the tracking error convergence of each subsystem.
本文研究内容有以下几方面：
1.针对一类具有不确定性的非线性互联系统,其互联项满足多项式有界条件,提出分散式模型参考自适应迭代学习控制,该算法包括2部分,一部分为反馈控制,用于保证子系统的闭环稳定性,另一部分为互联估计参数自适应迭代学习控制,用于消除各个子系统之间的互联项影响。进行了该分散式迭代学习控制算法的收敛性分析,仿真结果表明该算法的有效性。
2.针对一类具有不确定性的状态非线性时滞互联系统,给出分散式模型参考自适应迭代学习控制,该控制器为非记忆型控制器,只应用了跟踪误差项的实时信息,通过额外引入自适应迭代更新参数,来消除由于时滞互联项给互联系统带来的影响。对控制算法的收敛性进行详细推导,得到有效的仿真结果。由于各子系统之间普遍存在着信息传输的滞后性,对非线性互联系统而言,研究存在时滞情况下控制器设计问题更具有实际应用价值。
3.针对一类具有严格反馈形式的非线性互联系统,分2种情况进行分析,一类为互联项为子系统输出的单项式有界,一类为互联项为子系统输出的高阶多项式有界。当互联项为子系统输出的单项式有界时,引入了自适应更新参数岔,用以消除互联项的影响；当互联项为子系统输出的高阶多项式有界时,同时引入了自适应更新参数(?)ik和βik,消除子系统输出的高阶多项式有界影响。给出了控制器收敛性分析的理论推导,仿真结果验证了这种分散式自适应迭代学习控制的有效性。
4.将提出的理论与方法在互联机械系统上进行应用。分析了互联机械系统的特点,针对互联机械系统设计了分散式自适应迭代学习控制算法。同时基于Lyapunov方法对其进行算法收敛性分析,通过对子系统中未知参数和互联参数的迭代更新,可使得由跟踪误差和参数估计误差构成的Laypunov函数沿着迭代方向上单调递减。仿真结果显示了所给出的分散式自适应迭代学习控制算法有效性。
With the rapid development of modern science and technology, many practical control systems can be seen as nonlinear interconnected large-scale systems, so the decentralized control theory of interconnected large-scale systems has attracted great attentions in both academic research and industrial applications. Owing to the unrealized information exchanges between subsystems physically and the lack of computing power corresponding to the centralized controllers, the decentralized control technique usually has priority in usage under these complicated circumstances. The dissertation focuses on the certain kinds of nonlinear interconnected systems and analyses the systems characteristics. Then the decentralized adaptive learning control algorithms are designed correspondingly. The convergence analysis is provided for the proposed algorithms in this paper. Simulation results demonstrate that, utilizing the proposed controllers, the tracking error for each subsystem converges along the iteration axis. By systematically combining adaptive iterative learning control and decentralized control techniques, an attempt was made in this dissertation not only to forward deep development of interconnected system control science but also to provide better approaches to practical engineering problems to a certain degree.
The main contents are composed of the following four parts.
(1) An decentralized model reference adaptive iterative learning controller is designed for a class of nonlinear interconnected system with uncertainties. There are two parts in the controller, one is the feed-back controller which is used to stabilize the closed subsystem, the other is the adaptive iterative learning controller which eliminates the effects of the interconnections among subsystems. The convergence of the proposed algorithm is proved based on a Lyapunov-like method, guaranteeing the tracking error of each subsystem approaches to zero along with control iterations. A simulation example is given to show the effectiveness of the proposed method.
(2) Base on the nonlinear interconnected systems with state delay and model uncertainties, a decentralized model reference adaptive iterative learning control is proposed in this paper. The proposed controller of each subsystem is delay-independent which utilize only the current closed-loop local state variables. In order to eliminate the effects of interconnections and state delay, the extra adaptive parameters are updated along iteration axis. The algorithm convergence is proved carefully and the effectiveness of the proposed scheme is shown through computer simulation. Time delays, due to the information transmission between subsystems, naturally exist in interconnected systems and hence the control problem becomes more important than those interconnected systems without time delays.
(3) A decentralized backstepping adaptive iterative learning control schemes is proposed for a class of interconnected nonlinear systems of strict feedback form. The interconnections among subsystems are assumed to be bounded by an unknown1st-order or Pth-order polynomial in sub-outputs. A time-vary adaptive iterative learning control gain ζik is introduced to counteract the effect of the interconnections which are linear bounded in sub-output. As for the Pth-order polynomial sub-outputs bounded interconnections, two adaptive updated parameters ζik and βik are utilized. All the adaptive parameters are updated along both iteration axis and time one to counter the effects of the interconnections. It is shown that by using the proposed decentralized controller, the outputs of the subsystems can track the desired reference outputs iteratively. The simulation results show that the output tracking error of each subsystem converges along the iterative axis.
(4) A decentralized robust adaptive iterative learning control scheme for trajectory tracking of interconnected manipulators is developed. The proof of convergences based on the Lyapunov method. Through the iterative update of subsystem unknown parameters and interconnected parameters, the Lyapunov function composed of tracking errors and estimated parameter errors is monotonically decreased in iteration domain. The simulation results show that this method can guarantee the tracking error convergence of each subsystem.
引文
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