一类随机非线性系统控制设计算法及应用
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摘要
在实际控制工程中，由于建模误差、环境干扰等因素的影响，完全的确定性系统是不存在的，研究不确定非线性系统的控制问题具有重要的理论意义和实际应用价值。随机非线性系统是一类带有随机动态特征的非线性系统，是近年来非线性控制理论研究的热点方向之一。本文基于自适应鲁棒控制理论、神经网络逼近理论、随机微分方程稳定性理论、时滞泛函微分方程稳定性理论，探讨了一类随机非线性系统的控制问题。主要研究工作如下：
第一，针对带随机扰动和内动态的不确定非仿射非线性系统，提出一种基于高增益观测器和神经网络的自适应输出反馈控制器。在假设系统零动态稳定的条件下，将确定性系统控制方法扩展到随机系统，并利用神经网络的泛化学习能力，对非仿射非线性系统进行了自适应估计和鲁棒控制器设计。应用Lyapunov稳定性及随机系统稳定性理论证明闭环系统信号是依概率有界的，且跟踪误差收敛于原点的可调节邻域内。
第二，针对一类含有不确定非线性函数的随机系统，提出一种自适应观测器设计算法。所讨论的系统的不确定非线性函数包含未知状态而非仅仅包含系统输出，是一类更加宽泛的不确定随机系统。通过构建一个含有参数自适应律的观测器来重构状态，有效地解决具有非仿射不确定性的随机系统的状态估计问题。应用Lyapunov稳定性理论和Ito随机微分理论给出严格的稳定性分析，证明该观测器是依概率有界的，并且它的界可以通过选取适当的参数进行调节。
第三，研究一类带有未知时滞的不确定随机非线性系统控制设计问题。针对带未知时滞的非参数不确定随机非线性系统，提出一种与时滞无关的自适应控制算法；进一步，针对同时带有未知时滞、不确定参数和不确定非线性函数的随机非线性系统，提出一种基于神经网络的自适应滤波反步控制算法。利用滤波反步法代替传统反步法，以避免传统反步法设计中固有的“explosion of complexity”问题。控制结果使得闭环系统信号是依概率有界的，且跟踪误差均方收敛于原点的小的可调节邻域内。
第四，针对高速、高精度宏/微定位平台的动态特性，提出基于自适应Kalman滤波器的非线性输出反馈控制设计算法。自适应Kalman滤波器用于补偿宏动定位平台的系统振动及外界噪声干扰。针对压电陶瓷驱动的微动平台系统固有的迟滞非线性特性，提出基于高增益观测器的智能自适应输出反馈控制设计算法。该算法利用神经网络模拟不确定非线性迟滞特性，同时包含一个鲁棒控制项，用于补偿神经网络逼近误差及观测器的观测误差。
第五，针对多AUV协作作业时相互通信中不可避免的信息包丢失问题，提出一种基于观测预报器的最优估值器。观测预报器设计为所有已知历史观测信息的加权值，改进了传统的利用最近接收到的信息代替当前丢失信息的方法，可以充分有效地利用有用的历史信息来补偿通信过程中随机丢失的信息。进而基于补偿后的观测信息值，应用新息分析方法来设计AUV通信预报器、滤波器及平滑器。
Because of the influence of environmental interference and the modeling error, thecompletely deterministic system is not exist in the real word. Hence, the researches on thecontrol of uncertain nonlinear systems have both theoretical and practical interests. Stochasticnonlinear systems are a class of nonlinear systems with stochastic dynamic characterstics, andthe one of the hot research direction of nonlinear control theory. In this paper, based on theadaptive robust nonlinear control theory, the neural network approximation theory, thestability of stochastic differential equation and the stability of delay differential equation, theproblems of control for a class of stochastic nonlinear systems are investigate. The maincontributions of are outlined as follows:
Firstly, based on the high gain observer and neural-network(NN), an adaptiveoutput-feedback control is addressed for a class of nonaffine uncertain nonlinear systems withstochastic disturbance and internal dynamics. Under the assumption that zero dynamics of thesystem is stable, the obtained results extend the existing methodology from deterministicsystems to stochastic systems. Using the generalization learn ability of the neural network, anadaptive estimation and robust control law are addressed for the nonaffine nonlinear systems.Using Lyapunov theorem, it is shown that all the signals of the closed-loop system arebounded in probability, and the tracking error converges to an adjustable neighborhood of theorigin.
Secondly, the problem of adaptive observer design is investigated for a class ofstochastic nonlinear systems with nonparametric uncertainties. Different from the existingresults, the uncertain parameters of the systems not only contain output variable. Through thedesign of a nonlinear observer with an adaptive law of parameters to reconstruct the systemstates, the adaptive observer can solve the state estimation problem of the uncertaintynonaffine stochastic nonlinear systems effectively. Application of Lyapunov theorem andIto stochastic differential theory show that the observation error convergences toneighborhood of the origin, whose size can be adjusted by observer parameters.
Thirdly, the control design problem is studied for a class of uncertain stochasticnonlinear system with unknown time delays. For a class of uncertain stochastic nonlinearsystem with unknown time delays and uncertain nonlinear function, a delay-independentadaptive control is proposed. Furthermore, for a class of uncertain stochastic nonlinear system with unknown time delays, uncertain parameters and uncertain nonlinear functions, anadaptive filtered backstepping controller is designed based on neural network. Using thefiltered backstepping instead of the traditional backstepping to avoid the inherent problem of“explosion of complexity” in the traditional baskstepping design. It is proved that theproposed adaptive control is able to guarantee boundedness in probability of all the signals inthe closed-loop system and the tracking error is proven to converge to a small adjustableneighborhood.
Fourthly, based on the adaptive Kalman filter (AKF), a nonlinear output-feedbackcontrol scheme is proposed for macro-micro dual-drive positioning stage with highacceleration and high precision. AKF is used to compensate VCM vibration and the externalnoise. For the inherent hysteresis of Piezoactuator-driven stage, an adaptive output-feedbackcontrol is proposed based on the high-gain observer. The control scheme uses a neuralnetwork to simulate the uncertain nonlinear hysteresis, and a robust control is designed tocompensate the neural network approximation error and observer error.
Fifthly, for the problem of the inevitable stochastic communication packet dropouts in themulti-AUV cooperation, an optimal estimation is proposed based on a measurement predictor.The estimated measurement values for the lost information are obtained by using all theweighted known measurement values instead of the latest one, improved the traditionalmethods. Based on the estimated measurement values, the optimal estimators including filter,predictor and smoother are developed via an innovation analysis approach for multiple packetdropouts systems.
第一，针对带随机扰动和内动态的不确定非仿射非线性系统，提出一种基于高增益观测器和神经网络的自适应输出反馈控制器。在假设系统零动态稳定的条件下，将确定性系统控制方法扩展到随机系统，并利用神经网络的泛化学习能力，对非仿射非线性系统进行了自适应估计和鲁棒控制器设计。应用Lyapunov稳定性及随机系统稳定性理论证明闭环系统信号是依概率有界的，且跟踪误差收敛于原点的可调节邻域内。
第二，针对一类含有不确定非线性函数的随机系统，提出一种自适应观测器设计算法。所讨论的系统的不确定非线性函数包含未知状态而非仅仅包含系统输出，是一类更加宽泛的不确定随机系统。通过构建一个含有参数自适应律的观测器来重构状态，有效地解决具有非仿射不确定性的随机系统的状态估计问题。应用Lyapunov稳定性理论和Ito随机微分理论给出严格的稳定性分析，证明该观测器是依概率有界的，并且它的界可以通过选取适当的参数进行调节。
第三，研究一类带有未知时滞的不确定随机非线性系统控制设计问题。针对带未知时滞的非参数不确定随机非线性系统，提出一种与时滞无关的自适应控制算法；进一步，针对同时带有未知时滞、不确定参数和不确定非线性函数的随机非线性系统，提出一种基于神经网络的自适应滤波反步控制算法。利用滤波反步法代替传统反步法，以避免传统反步法设计中固有的“explosion of complexity”问题。控制结果使得闭环系统信号是依概率有界的，且跟踪误差均方收敛于原点的小的可调节邻域内。
第四，针对高速、高精度宏/微定位平台的动态特性，提出基于自适应Kalman滤波器的非线性输出反馈控制设计算法。自适应Kalman滤波器用于补偿宏动定位平台的系统振动及外界噪声干扰。针对压电陶瓷驱动的微动平台系统固有的迟滞非线性特性，提出基于高增益观测器的智能自适应输出反馈控制设计算法。该算法利用神经网络模拟不确定非线性迟滞特性，同时包含一个鲁棒控制项，用于补偿神经网络逼近误差及观测器的观测误差。
第五，针对多AUV协作作业时相互通信中不可避免的信息包丢失问题，提出一种基于观测预报器的最优估值器。观测预报器设计为所有已知历史观测信息的加权值，改进了传统的利用最近接收到的信息代替当前丢失信息的方法，可以充分有效地利用有用的历史信息来补偿通信过程中随机丢失的信息。进而基于补偿后的观测信息值，应用新息分析方法来设计AUV通信预报器、滤波器及平滑器。
Because of the influence of environmental interference and the modeling error, thecompletely deterministic system is not exist in the real word. Hence, the researches on thecontrol of uncertain nonlinear systems have both theoretical and practical interests. Stochasticnonlinear systems are a class of nonlinear systems with stochastic dynamic characterstics, andthe one of the hot research direction of nonlinear control theory. In this paper, based on theadaptive robust nonlinear control theory, the neural network approximation theory, thestability of stochastic differential equation and the stability of delay differential equation, theproblems of control for a class of stochastic nonlinear systems are investigate. The maincontributions of are outlined as follows:
Firstly, based on the high gain observer and neural-network(NN), an adaptiveoutput-feedback control is addressed for a class of nonaffine uncertain nonlinear systems withstochastic disturbance and internal dynamics. Under the assumption that zero dynamics of thesystem is stable, the obtained results extend the existing methodology from deterministicsystems to stochastic systems. Using the generalization learn ability of the neural network, anadaptive estimation and robust control law are addressed for the nonaffine nonlinear systems.Using Lyapunov theorem, it is shown that all the signals of the closed-loop system arebounded in probability, and the tracking error converges to an adjustable neighborhood of theorigin.
Secondly, the problem of adaptive observer design is investigated for a class ofstochastic nonlinear systems with nonparametric uncertainties. Different from the existingresults, the uncertain parameters of the systems not only contain output variable. Through thedesign of a nonlinear observer with an adaptive law of parameters to reconstruct the systemstates, the adaptive observer can solve the state estimation problem of the uncertaintynonaffine stochastic nonlinear systems effectively. Application of Lyapunov theorem andIto stochastic differential theory show that the observation error convergences toneighborhood of the origin, whose size can be adjusted by observer parameters.
Thirdly, the control design problem is studied for a class of uncertain stochasticnonlinear system with unknown time delays. For a class of uncertain stochastic nonlinearsystem with unknown time delays and uncertain nonlinear function, a delay-independentadaptive control is proposed. Furthermore, for a class of uncertain stochastic nonlinear system with unknown time delays, uncertain parameters and uncertain nonlinear functions, anadaptive filtered backstepping controller is designed based on neural network. Using thefiltered backstepping instead of the traditional backstepping to avoid the inherent problem of“explosion of complexity” in the traditional baskstepping design. It is proved that theproposed adaptive control is able to guarantee boundedness in probability of all the signals inthe closed-loop system and the tracking error is proven to converge to a small adjustableneighborhood.
Fourthly, based on the adaptive Kalman filter (AKF), a nonlinear output-feedbackcontrol scheme is proposed for macro-micro dual-drive positioning stage with highacceleration and high precision. AKF is used to compensate VCM vibration and the externalnoise. For the inherent hysteresis of Piezoactuator-driven stage, an adaptive output-feedbackcontrol is proposed based on the high-gain observer. The control scheme uses a neuralnetwork to simulate the uncertain nonlinear hysteresis, and a robust control is designed tocompensate the neural network approximation error and observer error.
Fifthly, for the problem of the inevitable stochastic communication packet dropouts in themulti-AUV cooperation, an optimal estimation is proposed based on a measurement predictor.The estimated measurement values for the lost information are obtained by using all theweighted known measurement values instead of the latest one, improved the traditionalmethods. Based on the estimated measurement values, the optimal estimators including filter,predictor and smoother are developed via an innovation analysis approach for multiple packetdropouts systems.
引文
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