基于神经网络的复杂非线性系统鲁棒控制与滤波研究
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摘要
本论文针对两大类型的复杂非线性系统,即非线性不确定Markov跳变系统和温室气候控制系统,借助于神经网络这一智能工具,分两大部分分别研究和探讨了其鲁棒控制和非线性滤波问题。
第一部分,以一类非线性Markov跳变系统的鲁棒控制和滤波为引线,逐步深入地分析和探讨了跳变转移概率未知条件下的非线性Markov跳变系统的稳态性能和暂态性能。
首先,针对一类含有不确定项和有界外部干扰的非线性Markov跳变系统,用智能方法研究其鲁棒性能分析与综合问题。将神经网络与鲁棒控制相结合,运用线性微分包含方法,对近似非线性项的神经网络进行分段线性化设计,再将线性微分包含方法表示的神经网络代入到这类非线性系统中,使得对允许的不确定性、外部干扰以及神经网络建模误差,相应的闭环控制系统或闭环误差系统鲁棒随机稳定且满足H∞性能指标。
接着,考虑实际工程中跳变转移概率的难以获得性,深入分析跳变转移概率未知条件下的非线性Markov跳变系统的稳态性能,研究其鲁棒H∞控制及鲁棒H∞滤波问题。考虑建模误差带来的系统不确定项,在过程激励噪声和测量噪声统计特性无法获知的情况下,给出鲁棒H∞控制器和鲁棒H∞滤波器设计方法。基于Lyapunov稳定性理论,给出相应控制器和滤波器的存在条件。
然后,根据实际工程需要,深入探讨了非线性Markov跳变系统的暂态性能问题,即在给定的有限时间区限内,对所有允许的参数不确定性、外部干扰以及神经网络建模误差,闭环系统的轨迹不超过某一给定的界限。在跳变转移概率完全已知和部分已知两种情况下,讨论了系统的鲁棒有限时间镇定及滤波问题,并给出了最优有限时间控制器和最优有限时间滤波器的具体设计方案。
第二部分,以提高温室气候系统的控制精确度为目的,分别从提高控制决策策略的自适应能力和滤波精度两个角度出发,深入而系统的研究了提高温室气候控制精度的关键技术。
首先,从提高控制决策策略的自适应能力方面考虑,研究外界干扰时变条件下的温室气候控制系统的神经网络鲁棒自适应控制策略,不仅分析了其稳定性、收敛性、鲁棒性,而且所提出的神经网络和反馈线性化控制相结合的鲁棒自适应控制策略,对提高温室气候的控制质量具有重要意义。
其次,从滤波器角度出发,当系统过程激励噪声和测量噪声为互不相干的高斯白噪声时,提出了利用扩展卡尔曼滤波器对温室室内气候控制系统进行精确参数估计的方法。仿真结果表明,经过扩展卡尔曼滤波器估计后的系统的控制精度得到了明显的提高。
接着,为了减少线性化误差对非线性温室气候系统控制精度的影响,采用不敏卡尔曼滤波方法对非线性系统进行高精度的滤波。不敏卡尔曼滤波器可以通过本身的自适应调整来减轻模型误差的影响,且不需要对非线性系统进行线性化,实现相对简单。
最后,为了减小对真实噪声的高斯性假设误差对滤波性能的影响,进而提高温室气候系统的控制精度,研究了能在非高斯噪声下具有较高估计精度的非线性粒子滤波方法,解决了长期以来工业过程控制中对非线性非高斯噪声干扰较难控制的问题。
This thesis is concerned with the problem of robust control and nonlinear filtering for two kinds of complex nonlinear systems with the help of neural networks, i. e., stochastic complex nonlinear systems with Markov jump parameters and deterministic complex systems of greenhouse climate control, which falls into two major parts.
In the first part, based on the robust control and filtering of a class of nonlinear Markov jump systems (MJSs), the steady-state behavior and the transient performance of nonlinear MJSs with partially known transition jump rates are further analyzed and discussed.
First of all, the analysis and synthesis problem of performance robustness is studied for a class of nonlinear MJSs with uncertainties and external disturbances with the aid of intelligent control method. Incorporating neural network with robust control, the nonlinearities are initially approximated by multilayer feedback neural networks. Subsequently, the neural networks are piecewisely interpolated to generate a linear differential inclusion (LDI) model. Then, substituting the neural network with the representation of LDI into nonlinear systems, the resulting closed-loop control systems or the closed-loop error systems are robustly stochastic stable and satisfy the H∞performance index for all admissible uncertainties, the external disturbances and approximation errors of the networks.
Subsequently, in real physical systems, not all the transition probabilities of the jumps are easy to measure, and even part of the elements in the desired transition rate matrix is not available. Therefore, it is necessary to study the steady-state behavior for more general nonlinear MJSs with partially known transition probabilities, i. e., the robust H∞control and the robust H∞filtering. Considering the uncertainties produced by modeling errors and the situation involving unknown statistic characteristics of the processor noise and the measurement noise, the robust H∞controller and filter design methodology is presented. Based on the Lyapunov theory, sufficient conditions for the existence of the desired controller and filter are derived.
Then, in terms of practical engineering, transient performance of nonlinear MJSs is further studied, i. e., in a fixed time interval, the trajectories of the system stay within a given bound for all admissible uncertainties, the norm bounded external disturbances and approximation errors of the networks. In both situation of partially known transition probabilities and complete access to transition probabilities, the robust finite-time stabilization and filtering criteria for the underlying systems is discussed. What is more, the detailed design proposal is given for optimal finite-time controller and optimal finite-time filter.
In the second part, with the view of improving the control accuracy of greenhouse climate systems, the relevant key technique has been further explored from two aspects:one is the adaptive capability of control policy, the other is the accuracy of filter.
Firstly, in order to improve the adaptive capability of control policy, a general framework of robust adaptive neural network-based controller design for greenhouse climate system with time-varying external disturbances is presented, in which not only the stability, convergence property and the robustness are discussed, but also the robust adaptive control method, which combines the well-known feedback linearization with radial basis function neural networks, makes great sense to the control quality of greenhouse climate system.
Secondly, from filter point of view and assuming the process noises and sensor noises are uncorrelated white Gaussian random process, the extended Kalman filter (EKF) is proposed to estimate the greenhouse climate system. The simulation results show that the control accuracy of EKF observer-controller combination is much better than that of controller alone.
Thirdly, the ability of the unscented Kalman filter (UKF) to accurately estimate nonlinearities makes it attractive for implementation on greenhouse climate control systems. The unscented transformation coupled with certain parts of the classic Kalman filter, provides a more accurate method than the EKF for estimating the greenhouse states and filtering out the noises. What's more, the UKF is far easier to implement because it does not involve any linearization steps.
Finally, to reduce the influence of filtering ability caused by Gaussian assumption of real noises and further improve the control accuracy, the nonlinear particle filter is derived in an attempt to solve the state estimation problem of the greenhouse climate control systems with non-Gaussian process and measurement noises, which solves the trouble controlling of nonlinear and non-Gaussian noises in industrial process control for a long time.
第一部分,以一类非线性Markov跳变系统的鲁棒控制和滤波为引线,逐步深入地分析和探讨了跳变转移概率未知条件下的非线性Markov跳变系统的稳态性能和暂态性能。
首先,针对一类含有不确定项和有界外部干扰的非线性Markov跳变系统,用智能方法研究其鲁棒性能分析与综合问题。将神经网络与鲁棒控制相结合,运用线性微分包含方法,对近似非线性项的神经网络进行分段线性化设计,再将线性微分包含方法表示的神经网络代入到这类非线性系统中,使得对允许的不确定性、外部干扰以及神经网络建模误差,相应的闭环控制系统或闭环误差系统鲁棒随机稳定且满足H∞性能指标。
接着,考虑实际工程中跳变转移概率的难以获得性,深入分析跳变转移概率未知条件下的非线性Markov跳变系统的稳态性能,研究其鲁棒H∞控制及鲁棒H∞滤波问题。考虑建模误差带来的系统不确定项,在过程激励噪声和测量噪声统计特性无法获知的情况下,给出鲁棒H∞控制器和鲁棒H∞滤波器设计方法。基于Lyapunov稳定性理论,给出相应控制器和滤波器的存在条件。
然后,根据实际工程需要,深入探讨了非线性Markov跳变系统的暂态性能问题,即在给定的有限时间区限内,对所有允许的参数不确定性、外部干扰以及神经网络建模误差,闭环系统的轨迹不超过某一给定的界限。在跳变转移概率完全已知和部分已知两种情况下,讨论了系统的鲁棒有限时间镇定及滤波问题,并给出了最优有限时间控制器和最优有限时间滤波器的具体设计方案。
第二部分,以提高温室气候系统的控制精确度为目的,分别从提高控制决策策略的自适应能力和滤波精度两个角度出发,深入而系统的研究了提高温室气候控制精度的关键技术。
首先,从提高控制决策策略的自适应能力方面考虑,研究外界干扰时变条件下的温室气候控制系统的神经网络鲁棒自适应控制策略,不仅分析了其稳定性、收敛性、鲁棒性,而且所提出的神经网络和反馈线性化控制相结合的鲁棒自适应控制策略,对提高温室气候的控制质量具有重要意义。
其次,从滤波器角度出发,当系统过程激励噪声和测量噪声为互不相干的高斯白噪声时,提出了利用扩展卡尔曼滤波器对温室室内气候控制系统进行精确参数估计的方法。仿真结果表明,经过扩展卡尔曼滤波器估计后的系统的控制精度得到了明显的提高。
接着,为了减少线性化误差对非线性温室气候系统控制精度的影响,采用不敏卡尔曼滤波方法对非线性系统进行高精度的滤波。不敏卡尔曼滤波器可以通过本身的自适应调整来减轻模型误差的影响,且不需要对非线性系统进行线性化,实现相对简单。
最后,为了减小对真实噪声的高斯性假设误差对滤波性能的影响,进而提高温室气候系统的控制精度,研究了能在非高斯噪声下具有较高估计精度的非线性粒子滤波方法,解决了长期以来工业过程控制中对非线性非高斯噪声干扰较难控制的问题。
This thesis is concerned with the problem of robust control and nonlinear filtering for two kinds of complex nonlinear systems with the help of neural networks, i. e., stochastic complex nonlinear systems with Markov jump parameters and deterministic complex systems of greenhouse climate control, which falls into two major parts.
In the first part, based on the robust control and filtering of a class of nonlinear Markov jump systems (MJSs), the steady-state behavior and the transient performance of nonlinear MJSs with partially known transition jump rates are further analyzed and discussed.
First of all, the analysis and synthesis problem of performance robustness is studied for a class of nonlinear MJSs with uncertainties and external disturbances with the aid of intelligent control method. Incorporating neural network with robust control, the nonlinearities are initially approximated by multilayer feedback neural networks. Subsequently, the neural networks are piecewisely interpolated to generate a linear differential inclusion (LDI) model. Then, substituting the neural network with the representation of LDI into nonlinear systems, the resulting closed-loop control systems or the closed-loop error systems are robustly stochastic stable and satisfy the H∞performance index for all admissible uncertainties, the external disturbances and approximation errors of the networks.
Subsequently, in real physical systems, not all the transition probabilities of the jumps are easy to measure, and even part of the elements in the desired transition rate matrix is not available. Therefore, it is necessary to study the steady-state behavior for more general nonlinear MJSs with partially known transition probabilities, i. e., the robust H∞control and the robust H∞filtering. Considering the uncertainties produced by modeling errors and the situation involving unknown statistic characteristics of the processor noise and the measurement noise, the robust H∞controller and filter design methodology is presented. Based on the Lyapunov theory, sufficient conditions for the existence of the desired controller and filter are derived.
Then, in terms of practical engineering, transient performance of nonlinear MJSs is further studied, i. e., in a fixed time interval, the trajectories of the system stay within a given bound for all admissible uncertainties, the norm bounded external disturbances and approximation errors of the networks. In both situation of partially known transition probabilities and complete access to transition probabilities, the robust finite-time stabilization and filtering criteria for the underlying systems is discussed. What is more, the detailed design proposal is given for optimal finite-time controller and optimal finite-time filter.
In the second part, with the view of improving the control accuracy of greenhouse climate systems, the relevant key technique has been further explored from two aspects:one is the adaptive capability of control policy, the other is the accuracy of filter.
Firstly, in order to improve the adaptive capability of control policy, a general framework of robust adaptive neural network-based controller design for greenhouse climate system with time-varying external disturbances is presented, in which not only the stability, convergence property and the robustness are discussed, but also the robust adaptive control method, which combines the well-known feedback linearization with radial basis function neural networks, makes great sense to the control quality of greenhouse climate system.
Secondly, from filter point of view and assuming the process noises and sensor noises are uncorrelated white Gaussian random process, the extended Kalman filter (EKF) is proposed to estimate the greenhouse climate system. The simulation results show that the control accuracy of EKF observer-controller combination is much better than that of controller alone.
Thirdly, the ability of the unscented Kalman filter (UKF) to accurately estimate nonlinearities makes it attractive for implementation on greenhouse climate control systems. The unscented transformation coupled with certain parts of the classic Kalman filter, provides a more accurate method than the EKF for estimating the greenhouse states and filtering out the noises. What's more, the UKF is far easier to implement because it does not involve any linearization steps.
Finally, to reduce the influence of filtering ability caused by Gaussian assumption of real noises and further improve the control accuracy, the nonlinear particle filter is derived in an attempt to solve the state estimation problem of the greenhouse climate control systems with non-Gaussian process and measurement noises, which solves the trouble controlling of nonlinear and non-Gaussian noises in industrial process control for a long time.
引文
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