基于RBF-ARX模型的复杂系统建模、优化与控制研究
摘要
RBF-ARX模型是一种便于局部线性化的全局非线性时间序列模型,全称为具有径向基函数神经网络型系数的带外生变量的自回归模型。它有时变线性ARX模型的基本结构,用RBF神经网络逼近非线性ARX模型的依存于系统状态的函数型系数,就得到了RBF-ARX模型。因此,RBF-ARX模型兼具状态依赖的ARX模型对非线性动态特性的描述能力,以及RBF神经网络的函数逼近能力和对过程局部变化的学习能力。
RBF-ARX模型的参数可由一种结构化的非线性参数优化方法离线辨识得到。此方法将线性参数和非线性参数分开辨识,不但避免了模型参数在线辨识失败带来的潜在风险,而且提高了建模精度和参数优化过程的收敛速度。此外,模型的复杂性被分散到了RBF-ARX模型的自回归滞后结构中,所以与单纯的RBF模型相比,它不需要太多的中心。
本论文对基于RBF-ARX模型的建模、优化及控制方法进行了较为深入的研究,主要研究成果包括：
(1)在以往众多相关研究成果的基础上,提出了多变量RBF-ARX模型结构及其建模、参数优化方法,以及基于多变量RBF-ARX模型的非线性预测控制器的设计方法。该方法基于一个统一的框架,可用于一类快速变化或慢速变化的多变量非线性系统的建模和优化控制。分别在一个快速变化对象(四旋翼飞行器)和一个慢速变化对象(日本海洋大学实验船舶)上,对本文提出的建模、优化及控制方法进行了应用研究并作了深入的探讨。
(2)四旋翼飞行器是一个具有多变量、强耦合、不确定性等复杂非线性特性的快速对象(控制周期为0.1秒)。本文介绍了该对象的物理模型,及基于物理模型的LQR控制策略。然后将四旋翼直升机的工作空间平均划分为16个工作区,在每个工作区分别辨识出一个线性ARX模型,并设计了一个综合16个局部线性ARX模型的增益调度LQR控制策略。本文建立了四旋翼飞行器的4输入3输出RBF-ARX模型,并设计了基于多变量RBF-ARX模型的全局LQR控制器(一种基于局部线性化模型的无限时域预测控制器),以控制四旋翼直升机的俯仰、翻转和巡航姿态。
(3)海洋船舶是一个具有典型复杂非线性特性的欠驱动慢速对象(控制周期为1秒)。本论文首先以船舶舵角为输入,首摇角偏差为输出,建立了单输入单输出的RBF-ARX模型,然后综合船舶运动学方程模型,构造出了单输入双输出的混合状态空问模型。将基于RBF-ARX模型的混合模型作为预测控制器的内部模型,设计了基于该模型的预测控制策略,并给出了详细的理论推导和分析过程。
(4)为提高船舶航迹跟踪过程的控制性能,本论文设计了一种船舶航迹跟踪导航策略和多步提前预报策略,该策略可以有效抑制船舶在拐点处位置跟踪误差的超调,并减小曲线航迹跟踪过程的位置跟踪误差。
(5)对船舶航迹跟踪过程的建模方法进行了进一步的研究,建立了渐近稳定的基于RBF-ARX模型的混合模型,弥补了原不稳定模型长期预测结果不理想的缺点。通过与船舶转弯实验的真实航迹对比,证明该渐近稳定混合模型的动态特性与真实船舶的动态特性更接近。
(6)针对混合模型船舶位置跟踪误差的一步预测输出存在偏移的缺点,建立了多变量RBF-ARX模型综合描述船舶舵角、首摇角偏差和位置跟踪误差三者间的动态关系。该模型解决了混合模型位置跟踪误差的一步预测输出存在偏移的问题,而且在有限时域内的长期预测性能更好。
(7)除建模外,外在不可抗拒自然力的干扰,也会造成船舶位置跟踪误差的偏移。本文设计了一个带输出补偿的预测控制器,可以有效地消除各种因素引起的位置跟踪误差偏移。在船舶的直线航迹跟踪控制实船实验中,验证了该控制策略的有效性。
本文提出的基于多变量RBF-ARX模型的建模、优化方法,不但可以很好地描述一类多变量慢速变化控制过程的全局复杂非线性特性,而且对一些多变量快速变化对象也有优越的全局非线性描述能力。本文中的两个成功的实际应用,验证了基于多变量RBF-ARX模型的建模、优化和控制策略是一种较为通用的、安全的、使用方便的、性能优越的先进建模与控制策略,不但在工业控制领域有重要的应用价值,对我国的国防建设也有一定的积极意义。
The RBF-ARX model is a global nonlinear time serious model which can be locally linearized at each state-dependent working point. Using radial basis function (RBF) networks to approximate the functional coefficients of a state-dependent AutoRegressive model with eXogenous variable (SD-ARX) yields the RBF-ARX model. Therefore, it incorporates the advantages of SD-ARX models in nonlinear dynamics description and the RBF network in function approximation.
The parameters of the RBF-ARX model are identified offline by a structured nonlinear parameter optimization method which can avoid the potential problems of online parameter estimation. The parameter search space is divided into the linear weight subspace and the nonlinear parameter space, and therefore the computational convergence speed and the modeling accuracy are improved. Besides, compared with the single RBF network model it does not need too many RBF centers, because the model's complexity is dispersed into the lags of the autoregressive parts.
The main research works and achievements are summarized as follows.
(1) On the basis of a large amount of existing research results, this dissertation presents the multi-input multi-output (MIMO) RBF-ARX model together with its parameter optimization method. Based-on the MIMO RBF-ARX model, a predictive control strategy is designed to control the multivariable nonlinear system.
The state-space form of the MIMO RBF-ARX model can be easily obtained, thus it is convenient to apply the RBF-ARX model to the industry control field. In this dissertation, the MIMO RBF-ARX modeling method is for the first time applied to a fast multivariable control plant (the quadrotor helicopter); a hybrid model based-on the RBF-ARX model is presented for the first time to characterize a slow control process (the ship's trajectory tracking process). In the two real control applications, the RBF-ARX model-based modeling method, optimization method and controller design approaches are discussed deeply.
(2) The referenced quadrotor in this dissertation is a fast system (sampling period:0.1s) and has a unique configuration which is different from the classic quadrotor in cross configuration. It is a typical complex multi-input and multi-output control system with strong coupling and uncertain nonlinearities. Firstly, the physical model-based LQR control strategy is introduced. Secondly, the working space of the quadrotor is divided into16working areas averagely, then16linear ARX models are identified in each area and the ARX model-set-based LQR gain scheduling controller is designed. At last, a global RBF-ARX model-based LQR control strategy is proposed to realize the attitude control of the quadrotor.
(3) Ship tracking control process is a typical slow complex under-actuated system with1input and2outputs (sampling period:Is). A single input single output RBF-ARX model is built to describe the nonlinear relation between the ship heading angle deviation and the ship ruder. Then a single input dual outputs state space model combined with the relationship between the heading angle deviation and the cross track errors is proposed to represent the tracking dynamic behavior. Based on the hybrid state space model a model predictive controller is designed to steer the ship tracking a predefined reference trajectory with a constant velocity.
(4) A navigation strategy together with a multistep forecast strategy is designed for the ship tracking predictive controller, which could suppress the overshot at the switching points of the curve trajectory, and reduce the cross track error during the curve tracking segments.
(5) For improving the long-term prediction performance of the hybrid model, an RBF-ARX model-based critical stable hybrid model was proposed. It is verified by comparing the turning test trajectory that the dynamic behavior of the new hybrid model is much better.
(6) A pure single input dual outputs RBF-ARX model was built for more detailed representation of a ship's dynamic tracking behavior. The modeling results showed that the pure RBF-ARX model has a better modeling accuracy not only in the one-step-ahead prediction but also in a finite horizon long-term prediction.
(7) Apart from the modeling, external natural force will also result in the large offset of the cross track. For overcoming the influence introduced by the irresistible natural force, a novel RBF-ARX model-based predictive controller with output compensation was proposed. The real-time control result of the straight-line tracking verified the effectiveness of the compensation strategy.
The two successful applications verified the effectiveness and the superiority of the multivariable RBF-ARX model-based modeling and control method in handling multivariable nonlinear systems modeling and control problem, not only for the slow control processes but also for some fast systems. It is also verified that the multivariable RBF-ARX model-based modeling, optimization and control method is a general, reliable, convenient and advanced method, which has the significance in both the industry field and national defense.
RBF-ARX模型的参数可由一种结构化的非线性参数优化方法离线辨识得到。此方法将线性参数和非线性参数分开辨识,不但避免了模型参数在线辨识失败带来的潜在风险,而且提高了建模精度和参数优化过程的收敛速度。此外,模型的复杂性被分散到了RBF-ARX模型的自回归滞后结构中,所以与单纯的RBF模型相比,它不需要太多的中心。
本论文对基于RBF-ARX模型的建模、优化及控制方法进行了较为深入的研究,主要研究成果包括：
(1)在以往众多相关研究成果的基础上,提出了多变量RBF-ARX模型结构及其建模、参数优化方法,以及基于多变量RBF-ARX模型的非线性预测控制器的设计方法。该方法基于一个统一的框架,可用于一类快速变化或慢速变化的多变量非线性系统的建模和优化控制。分别在一个快速变化对象(四旋翼飞行器)和一个慢速变化对象(日本海洋大学实验船舶)上,对本文提出的建模、优化及控制方法进行了应用研究并作了深入的探讨。
(2)四旋翼飞行器是一个具有多变量、强耦合、不确定性等复杂非线性特性的快速对象(控制周期为0.1秒)。本文介绍了该对象的物理模型,及基于物理模型的LQR控制策略。然后将四旋翼直升机的工作空间平均划分为16个工作区,在每个工作区分别辨识出一个线性ARX模型,并设计了一个综合16个局部线性ARX模型的增益调度LQR控制策略。本文建立了四旋翼飞行器的4输入3输出RBF-ARX模型,并设计了基于多变量RBF-ARX模型的全局LQR控制器(一种基于局部线性化模型的无限时域预测控制器),以控制四旋翼直升机的俯仰、翻转和巡航姿态。
(3)海洋船舶是一个具有典型复杂非线性特性的欠驱动慢速对象(控制周期为1秒)。本论文首先以船舶舵角为输入,首摇角偏差为输出,建立了单输入单输出的RBF-ARX模型,然后综合船舶运动学方程模型,构造出了单输入双输出的混合状态空问模型。将基于RBF-ARX模型的混合模型作为预测控制器的内部模型,设计了基于该模型的预测控制策略,并给出了详细的理论推导和分析过程。
(4)为提高船舶航迹跟踪过程的控制性能,本论文设计了一种船舶航迹跟踪导航策略和多步提前预报策略,该策略可以有效抑制船舶在拐点处位置跟踪误差的超调,并减小曲线航迹跟踪过程的位置跟踪误差。
(5)对船舶航迹跟踪过程的建模方法进行了进一步的研究,建立了渐近稳定的基于RBF-ARX模型的混合模型,弥补了原不稳定模型长期预测结果不理想的缺点。通过与船舶转弯实验的真实航迹对比,证明该渐近稳定混合模型的动态特性与真实船舶的动态特性更接近。
(6)针对混合模型船舶位置跟踪误差的一步预测输出存在偏移的缺点,建立了多变量RBF-ARX模型综合描述船舶舵角、首摇角偏差和位置跟踪误差三者间的动态关系。该模型解决了混合模型位置跟踪误差的一步预测输出存在偏移的问题,而且在有限时域内的长期预测性能更好。
(7)除建模外,外在不可抗拒自然力的干扰,也会造成船舶位置跟踪误差的偏移。本文设计了一个带输出补偿的预测控制器,可以有效地消除各种因素引起的位置跟踪误差偏移。在船舶的直线航迹跟踪控制实船实验中,验证了该控制策略的有效性。
本文提出的基于多变量RBF-ARX模型的建模、优化方法,不但可以很好地描述一类多变量慢速变化控制过程的全局复杂非线性特性,而且对一些多变量快速变化对象也有优越的全局非线性描述能力。本文中的两个成功的实际应用,验证了基于多变量RBF-ARX模型的建模、优化和控制策略是一种较为通用的、安全的、使用方便的、性能优越的先进建模与控制策略,不但在工业控制领域有重要的应用价值,对我国的国防建设也有一定的积极意义。
The RBF-ARX model is a global nonlinear time serious model which can be locally linearized at each state-dependent working point. Using radial basis function (RBF) networks to approximate the functional coefficients of a state-dependent AutoRegressive model with eXogenous variable (SD-ARX) yields the RBF-ARX model. Therefore, it incorporates the advantages of SD-ARX models in nonlinear dynamics description and the RBF network in function approximation.
The parameters of the RBF-ARX model are identified offline by a structured nonlinear parameter optimization method which can avoid the potential problems of online parameter estimation. The parameter search space is divided into the linear weight subspace and the nonlinear parameter space, and therefore the computational convergence speed and the modeling accuracy are improved. Besides, compared with the single RBF network model it does not need too many RBF centers, because the model's complexity is dispersed into the lags of the autoregressive parts.
The main research works and achievements are summarized as follows.
(1) On the basis of a large amount of existing research results, this dissertation presents the multi-input multi-output (MIMO) RBF-ARX model together with its parameter optimization method. Based-on the MIMO RBF-ARX model, a predictive control strategy is designed to control the multivariable nonlinear system.
The state-space form of the MIMO RBF-ARX model can be easily obtained, thus it is convenient to apply the RBF-ARX model to the industry control field. In this dissertation, the MIMO RBF-ARX modeling method is for the first time applied to a fast multivariable control plant (the quadrotor helicopter); a hybrid model based-on the RBF-ARX model is presented for the first time to characterize a slow control process (the ship's trajectory tracking process). In the two real control applications, the RBF-ARX model-based modeling method, optimization method and controller design approaches are discussed deeply.
(2) The referenced quadrotor in this dissertation is a fast system (sampling period:0.1s) and has a unique configuration which is different from the classic quadrotor in cross configuration. It is a typical complex multi-input and multi-output control system with strong coupling and uncertain nonlinearities. Firstly, the physical model-based LQR control strategy is introduced. Secondly, the working space of the quadrotor is divided into16working areas averagely, then16linear ARX models are identified in each area and the ARX model-set-based LQR gain scheduling controller is designed. At last, a global RBF-ARX model-based LQR control strategy is proposed to realize the attitude control of the quadrotor.
(3) Ship tracking control process is a typical slow complex under-actuated system with1input and2outputs (sampling period:Is). A single input single output RBF-ARX model is built to describe the nonlinear relation between the ship heading angle deviation and the ship ruder. Then a single input dual outputs state space model combined with the relationship between the heading angle deviation and the cross track errors is proposed to represent the tracking dynamic behavior. Based on the hybrid state space model a model predictive controller is designed to steer the ship tracking a predefined reference trajectory with a constant velocity.
(4) A navigation strategy together with a multistep forecast strategy is designed for the ship tracking predictive controller, which could suppress the overshot at the switching points of the curve trajectory, and reduce the cross track error during the curve tracking segments.
(5) For improving the long-term prediction performance of the hybrid model, an RBF-ARX model-based critical stable hybrid model was proposed. It is verified by comparing the turning test trajectory that the dynamic behavior of the new hybrid model is much better.
(6) A pure single input dual outputs RBF-ARX model was built for more detailed representation of a ship's dynamic tracking behavior. The modeling results showed that the pure RBF-ARX model has a better modeling accuracy not only in the one-step-ahead prediction but also in a finite horizon long-term prediction.
(7) Apart from the modeling, external natural force will also result in the large offset of the cross track. For overcoming the influence introduced by the irresistible natural force, a novel RBF-ARX model-based predictive controller with output compensation was proposed. The real-time control result of the straight-line tracking verified the effectiveness of the compensation strategy.
The two successful applications verified the effectiveness and the superiority of the multivariable RBF-ARX model-based modeling and control method in handling multivariable nonlinear systems modeling and control problem, not only for the slow control processes but also for some fast systems. It is also verified that the multivariable RBF-ARX model-based modeling, optimization and control method is a general, reliable, convenient and advanced method, which has the significance in both the industry field and national defense.
引文
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