复杂非线性系统的自适应学习控制
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摘要
学习控制理论包括迭代学习控制和重复控制,是处理具有重复性或者周期性系统的有力工具。迭代学习控制主要针对定义在有限时间区间上的重复系统,通过之前迭代周期的控制信息,对当前的系统控制输入进行更新,以使系统输出收敛于给定的期望轨迹。重复控制主要用于在无限时间区间上对周期轨迹的跟踪或者对周期干扰的抑除。两者之间既存在区别也有着广泛的联系,本质上可以当作一类系统来处理。
为了克服传统学习控制在处理非线性动态系统问题中的局限性,同时也为了将学习控制和控制界的主流研究工具Lyapunov理论结合起来,结合了自适应控制方法和学习控制理念的自适应学习控制得到了提出和发展。本文在回顾自适应学习控制理论的同时,重点解决了其中控制方向未知和信号周期未知的问题。
具体来说,本文的主要工作包括：
(1)利用连续Nussbaum增益方法解决了连续非线性系统的重复学习控制中存在的控制方向未知的问题。提出了Nussbaum增益方法在Lyapunov理论分析中应用的重要引理,并将其引入到一类带有未知时变参数的连续非线性系统的重复学习控制。进而利用连续Nussbaum增益方法解决了具有严格反馈形式和输出反馈形式的高阶连续非线性系统的重复学习控制中的控制方向未知问题。
(2)利用离散Nussbaum增益方法解决了离散非线性系统的迭代学习控制中存在的控制方向未知的问题。研究了一类带有未知时变参数和输入增益的离散非线性系统的迭代学习控制问题。进而利用离散Nussbaum增益方法解决了带有严格反馈形式和输出反馈形式的高阶离散非线性系统的迭代学习控制中的控制方向未知问题。
(3)将切换控制与自适应学习控制结合起来,解决了非线性动态系统中信号周期未知的问题。在信号周期可以表达为一个已知常数和一个未知整数乘积的假设下,通过在自适应学习控制律的基础上设置合理的切换逻辑,使信号周期的估计值不断更新,最终达到合理的估计值,以使系统跟踪误差最终收敛到零。利用切换自适应学习控制律解决了一类带有周期未知时变参数的非线性系统的轨迹跟踪问题。
(4)利用切换自适应学习控制方法研究了一类带有周期未知干扰的非线性参数化系统的抗干扰问题。去除了非线性参数化系统的自适应控制中对未知变量的限制,利用切换机制同时对干扰周期以及干扰和未知变量共有边界的估计值进行更新,以达到对周期干扰的完全抑制。
Learning control theory, including iterative learning control (ILC) and repetitive control (RC), is a powerful tool to handle the systems with repetitiveness or periodic signals. ILC mainly focuses on repeatable systems defined in the finite time interval. In ILC, the system control input of current trial is updated by the control information of past trials, so that the system output converges to the given desired trajectory. RC, which is defined in the infinite time domain, mainly deals with the tracking of periodic trajectory or the rejection of periodic disturbance. There are both differences and extensive links between ILC and RC. Thus they are able to be treated as the same type of systems essentially.
In order to overcome the limitations of the traditional learning control in dealing with the problems associated with nonlinear dynamic systems, also to incorporate the learning control theory with the popular Lyapunov theory, adaptive learning control, which combines both the design methods of adaptive control and the concept of learning control, has been proposed and developed. After reviewing the adaptive learning control theory, this paper mainly tackles the problems of unknown control directions and unknown periods in nonlinear systems.
Specifically speaking, the main work of this paper is as follows:
(1) The continuous Nussbaum gain method is employed to tackle the problems associated with unknown control directions in the repetitive learning control (RLC) for continuous-time nonlinear systems. An important lemma, which facilitates the application of Nussbaum gain method in the Lyapunov theory based control design, is developed and introduced into RLC for a class of continuous nonlinear systems with unknown time-varying parameters. Then the continuous Nussbaum gain method is exploited to deal with the problems associated with unknown control directions in the RLC for high-order continuous-time nonlinear systems with strict feedback form and output feedback form.
(2) The discrete Nussbaum gain method is employed to tackle the problems associated with unknown control directions in the ILC for discrete-time nonlinear systems. First we focus on ILC for a class of discrete nonlinear systems with unknown time-varying parameters and time-varying input gain. Then the discrete Nussbaum gain method is exploited to deal with the problems associated with unknown control directions in the ILC for high-order discrete-time nonlinear systems with strict feedback form and output feedback form.
(3) Switching control is plugged into the adaptive learning control to tackle the problems of unknown period. The signal period is assumed to be the product of a known constant and an unknown integer. Thus, based on the adaptive learning control scheme, we can tune the estimate of period by appropriate switching logic. After the period estimate has reached a proper value, the tracking error can converge to zero asymptotically. The switching adaptive learning scheme is exploited to handle the trajectory tracking for a class of linearly parameterized systems with time-vary ing parameters of unknown periods.
(4) The switching adaptive learning control method is employed to deal with the problem of disturbance rejection for a class of nonlinearly parameterized systems with disturbance of unknown period. The restrictions on the unknown parameters in the adaptive control for nonlinearly parameterized systems are removed. The estimates of period of disturbance and upper bound of both the disturbance and the unknown parameters are tuned by the proposed switching logic, so that the periodic disturbance can be rejected completely.
为了克服传统学习控制在处理非线性动态系统问题中的局限性,同时也为了将学习控制和控制界的主流研究工具Lyapunov理论结合起来,结合了自适应控制方法和学习控制理念的自适应学习控制得到了提出和发展。本文在回顾自适应学习控制理论的同时,重点解决了其中控制方向未知和信号周期未知的问题。
具体来说,本文的主要工作包括：
(1)利用连续Nussbaum增益方法解决了连续非线性系统的重复学习控制中存在的控制方向未知的问题。提出了Nussbaum增益方法在Lyapunov理论分析中应用的重要引理,并将其引入到一类带有未知时变参数的连续非线性系统的重复学习控制。进而利用连续Nussbaum增益方法解决了具有严格反馈形式和输出反馈形式的高阶连续非线性系统的重复学习控制中的控制方向未知问题。
(2)利用离散Nussbaum增益方法解决了离散非线性系统的迭代学习控制中存在的控制方向未知的问题。研究了一类带有未知时变参数和输入增益的离散非线性系统的迭代学习控制问题。进而利用离散Nussbaum增益方法解决了带有严格反馈形式和输出反馈形式的高阶离散非线性系统的迭代学习控制中的控制方向未知问题。
(3)将切换控制与自适应学习控制结合起来,解决了非线性动态系统中信号周期未知的问题。在信号周期可以表达为一个已知常数和一个未知整数乘积的假设下,通过在自适应学习控制律的基础上设置合理的切换逻辑,使信号周期的估计值不断更新,最终达到合理的估计值,以使系统跟踪误差最终收敛到零。利用切换自适应学习控制律解决了一类带有周期未知时变参数的非线性系统的轨迹跟踪问题。
(4)利用切换自适应学习控制方法研究了一类带有周期未知干扰的非线性参数化系统的抗干扰问题。去除了非线性参数化系统的自适应控制中对未知变量的限制,利用切换机制同时对干扰周期以及干扰和未知变量共有边界的估计值进行更新,以达到对周期干扰的完全抑制。
Learning control theory, including iterative learning control (ILC) and repetitive control (RC), is a powerful tool to handle the systems with repetitiveness or periodic signals. ILC mainly focuses on repeatable systems defined in the finite time interval. In ILC, the system control input of current trial is updated by the control information of past trials, so that the system output converges to the given desired trajectory. RC, which is defined in the infinite time domain, mainly deals with the tracking of periodic trajectory or the rejection of periodic disturbance. There are both differences and extensive links between ILC and RC. Thus they are able to be treated as the same type of systems essentially.
In order to overcome the limitations of the traditional learning control in dealing with the problems associated with nonlinear dynamic systems, also to incorporate the learning control theory with the popular Lyapunov theory, adaptive learning control, which combines both the design methods of adaptive control and the concept of learning control, has been proposed and developed. After reviewing the adaptive learning control theory, this paper mainly tackles the problems of unknown control directions and unknown periods in nonlinear systems.
Specifically speaking, the main work of this paper is as follows:
(1) The continuous Nussbaum gain method is employed to tackle the problems associated with unknown control directions in the repetitive learning control (RLC) for continuous-time nonlinear systems. An important lemma, which facilitates the application of Nussbaum gain method in the Lyapunov theory based control design, is developed and introduced into RLC for a class of continuous nonlinear systems with unknown time-varying parameters. Then the continuous Nussbaum gain method is exploited to deal with the problems associated with unknown control directions in the RLC for high-order continuous-time nonlinear systems with strict feedback form and output feedback form.
(2) The discrete Nussbaum gain method is employed to tackle the problems associated with unknown control directions in the ILC for discrete-time nonlinear systems. First we focus on ILC for a class of discrete nonlinear systems with unknown time-varying parameters and time-varying input gain. Then the discrete Nussbaum gain method is exploited to deal with the problems associated with unknown control directions in the ILC for high-order discrete-time nonlinear systems with strict feedback form and output feedback form.
(3) Switching control is plugged into the adaptive learning control to tackle the problems of unknown period. The signal period is assumed to be the product of a known constant and an unknown integer. Thus, based on the adaptive learning control scheme, we can tune the estimate of period by appropriate switching logic. After the period estimate has reached a proper value, the tracking error can converge to zero asymptotically. The switching adaptive learning scheme is exploited to handle the trajectory tracking for a class of linearly parameterized systems with time-vary ing parameters of unknown periods.
(4) The switching adaptive learning control method is employed to deal with the problem of disturbance rejection for a class of nonlinearly parameterized systems with disturbance of unknown period. The restrictions on the unknown parameters in the adaptive control for nonlinearly parameterized systems are removed. The estimates of period of disturbance and upper bound of both the disturbance and the unknown parameters are tuned by the proposed switching logic, so that the periodic disturbance can be rejected completely.
引文
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