CN118034269B - An adaptive control method for ship intelligent maneuvering - Google Patents
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Abstract
本发明公开了一种用于船舶智能机动的自适应控制方法,对具有外部干扰和输入饱和效应的船舶智能机动系统设计一种有限时间预定性能的约束控制策略。针对船舶智能机动时需要保持的约束条件和所产生的输入饱和问题分别设计出时变的障碍李亚普诺夫函数和辅助系统,以此提升船舶航向角、输入舵令等参数的稳定性,利用神经网络技术和新的复合非线性干扰观测器去解决由未知外部干扰、高度不确定性未知函数对控制器递推设计的影响,结合有限时间控制技术和预定性能控制技术来保证包含航向角、偏航率、舵令等所有参数的有限时间稳定,保证船舶航向角与规定航向角的误差在预定时间内缩小到预定范围里,提高船舶航行时的平衡性和精度。
The present invention discloses an adaptive control method for ship intelligent maneuvering, and designs a constraint control strategy with finite time predetermined performance for a ship intelligent maneuvering system with external interference and input saturation effects. Time-varying obstacle Lyapunov functions and auxiliary systems are designed for the constraint conditions that need to be maintained during ship intelligent maneuvers and the input saturation problem generated, so as to improve the stability of parameters such as ship heading angle and input steering command, and use neural network technology and new composite nonlinear disturbance observer to solve the influence of unknown external interference and highly uncertain unknown functions on the recursive design of the controller. Finite time control technology and predetermined performance control technology are combined to ensure the finite time stability of all parameters including heading angle, yaw rate, steering command, etc., to ensure that the error between the ship heading angle and the specified heading angle is reduced to a predetermined range within a predetermined time, and to improve the balance and accuracy of the ship during navigation.
Description
技术领域Technical Field
本发明涉及自适应控制技术领域,具体涉及一种针对具有外部干扰和输入饱和效应的船舶智能机动系统有限时间预定性能的约束控制策略。The present invention relates to the field of adaptive control technology, and in particular to a constraint control strategy for the finite time predetermined performance of a ship intelligent maneuvering system with external disturbance and input saturation effects.
背景技术Background Art
古往今来,在众多交通运输工具当中,船一直占据着重要位置,在智能化越来越普及的今天,船舶的智能机动也在快速的发展中。由于在船舶的运行中会受到诸如外部干扰、环境参数的不确定、舵令饱和现象等多种不利因素的影响,所以在船舶的智能机动的研究中,如何使船舶在各种不利因素的影响下按照给定的线路行驶并且保证其平衡是此研究中的关键问题。Throughout the ages, ships have always occupied an important position among many means of transportation. Today, as intelligence becomes more and more popular, the intelligent maneuverability of ships is also developing rapidly. Since the operation of ships is affected by many unfavorable factors such as external interference, uncertainty of environmental parameters, rudder command saturation, etc., in the study of intelligent maneuverability of ships, how to make the ship travel along a given route and ensure its balance under the influence of various unfavorable factors is a key issue in this study.
在近几年的研究中,以递推法为基础的跟踪控制策略为上述问题提供了解决思路,加上神经网络、预定性能、干扰观测器等技术,一类具有干扰抑制能力的预定性能控制策略应运而生。然而,大多数情况下,船舶的机动具有高度的不确定性,同时,为改善其平衡性,需要对船舶机动时的相关参数进行约束,因此,亟需一种改善的控制策略来解决上述问题。In recent years, the tracking control strategy based on the recursive method has provided a solution to the above problems. Combined with technologies such as neural networks, predetermined performance, and disturbance observers, a type of predetermined performance control strategy with interference suppression capability has emerged. However, in most cases, the maneuvering of ships is highly uncertain. At the same time, in order to improve its balance, it is necessary to constrain the relevant parameters of the ship during maneuvering. Therefore, an improved control strategy is urgently needed to solve the above problems.
由于船舶的机动系统未知函数的自变量包含所有状态量,所以系统是一个高度不确定性的系统,常规的递推方法将不再适用,已有的控制方案多数是假设未知函数单调递增有界或者利用变量分离法,假设未知函数单调递增有界会降低所设计控制策略的适用性,变量分离法会加大系统的收敛域。Since the independent variables of the unknown functions of the ship's maneuvering system include all state quantities, the system is a highly uncertain system, and the conventional recursive method will no longer be applicable. Most of the existing control schemes assume that the unknown function is monotonically increasing and bounded or use the variable separation method. Assuming that the unknown function is monotonically increasing and bounded will reduce the applicability of the designed control strategy, and the variable separation method will increase the convergence domain of the system.
为了克服已有相关研究的不足,本发明提出了一种用于船舶智能机动的自适应控制方法,具体是针对具有外部干扰和输入饱和效应的船舶智能机动系统设计一种有限时间预定性能的约束控制策略,解决了现有方法不能适用于具有高不确定性船舶智能机动系统问题的,同时,提升船舶智能机动的跟踪性能以及平衡性。In order to overcome the shortcomings of existing related research, the present invention proposes an adaptive control method for ship intelligent maneuvering, specifically, a constrained control strategy with finite time predetermined performance is designed for a ship intelligent maneuvering system with external interference and input saturation effects, which solves the problem that the existing methods cannot be applied to ship intelligent maneuvering systems with high uncertainty, and at the same time, improves the tracking performance and balance of ship intelligent maneuvering.
发明内容Summary of the invention
发明目的:为了克服已有技术性能上的不足,本发明提供一种用于船舶智能机动的自适应控制方法,利用非线性干扰观测器去估计新的复合干扰,即构造新的复合干扰观测器,既能保证系统航向角与参考航向角之间的误差在预定时间内收敛到预定范围内,又能保证系统的航向角、偏航率等状态参数自始至终满足约束条件,实现系统内所有的信号的有限时间稳定,同时还具有抗干扰和抗饱和的功能,加强了船舶智能机动的可靠性和平衡性。Purpose of the invention: In order to overcome the shortcomings of the existing technical performance, the present invention provides an adaptive control method for ship intelligent maneuvering, which uses a nonlinear disturbance observer to estimate a new composite disturbance, that is, constructs a new composite disturbance observer, which can not only ensure that the error between the system heading angle and the reference heading angle converges to a predetermined range within a predetermined time, but also ensure that the system's heading angle, yaw rate and other state parameters meet the constraints from beginning to end, and realize the finite time stability of all signals in the system. At the same time, it also has anti-interference and anti-saturation functions, thereby enhancing the reliability and balance of the ship's intelligent maneuvering.
技术方案:本发明公开了一种用于船舶智能机动的自适应控制方法,针对具有外部干扰和输入饱和效应的船舶智能机动系统设计一种有限时间预定性能的约束控制策略,包括以下步骤:Technical solution: The present invention discloses an adaptive control method for ship intelligent maneuvering, and designs a constrained control strategy with limited time predetermined performance for a ship intelligent maneuvering system with external interference and input saturation effect, including the following steps:
步骤1:构造船舶智能机动的模型并结合神经网络技术将所述模型的方程进行转化;Step 1: construct a model of ship intelligent maneuvering and transform the equations of the model by combining neural network technology;
其中,为船舶航向角,代表偏航率,是偏航率的变化率,T是一个时间常数,K,w分别代表诺宾系数、方向增益、方向舵角和r维独立标准布朗运动,表示未知函数;in, is the ship heading angle, represents the yaw rate, is the rate of change of the yaw rate, T is a time constant, K, w represents the Nobin coefficient, directional gain, rudder angle and r-dimensional independent standard Brownian motion, respectively. Represents an unknown function;
定义将式(1)写成状态方程的形式,得到:definition Writing equation (1) in the form of a state equation yields:
其中,TE是船舶时间常数,KE是船舶的控制增益,代表舵令,f函数是一个未知函数,y为系统输出,是系统外部干扰,表示该系统受到外部非匹配干扰的影响;f函数的自变量包含为了保持船舶行驶的平衡性,船舶的航向角以及偏航率状态参数需要满足一定的约束条件,即状态参数需要满足 为约束条件;u为系统输入,sat(u)表示舵令的饱和输入,由下式表示:in, TE is the ship time constant, KE is the ship control gain, represents the steering command, f function is an unknown function, y is the system output, is the external disturbance of the system, indicating that the system is affected by external non-matching disturbance; the independent variables of the f function include In order to maintain the balance of the ship, the ship's heading angle and yaw rate state parameters need to meet certain constraints, that is, the state parameters need to meet is the constraint condition; u is the system input, sat(u) represents the saturated input of the steering command, which is expressed by the following formula:
其中,u1>0,u2<0代表已知常数,根据实际控制的需要,控制输入u是有界的,由于饱和输入sat(u)是有界的,所以饱和误差Δu=sat(u)-u也是有界的;Among them, u 1 > 0, u 2 < 0 represent known constants. According to the actual control needs, the control input u is bounded. Since the saturation input sat(u) is bounded, the saturation error Δu = sat(u) -u is also bounded;
结合神经网络逼近技术,未知函数和用神经网络进行逼近,即:同时,定义有界函数式(2)重写为:Combined with neural network approximation technology, unknown function and Use neural network to approximate, that is: At the same time, define the bounded function Formula (2) can be rewritten as:
其中, 为神经网络逼近的最优权值,是基函数,代表神经网络最小逼近误差;in, is the optimal weight of the neural network approximation, is the basis function, Represents the minimum approximation error of the neural network;
步骤2:针对约束条件以及输入饱和分别设计出时变的障碍李雅普诺夫函数和辅助系统以分别确保约束条件的成立和抗饱和的实现;Step 2: Design time-varying barrier Lyapunov functions and auxiliary systems for constraints and input saturation to ensure the establishment of constraints and the realization of anti-saturation respectively;
步骤3:结合命令滤波递推和复合非线性干扰观测器设计出虚拟控制、实际控制和自适应更新率;并构造合适的李雅普诺夫函数L,验证所设计的虚拟控制、实际控制和自适应更新率是否满足闭环系统有限时间稳定判别条件其中,M为设计参数,M2为一个正数,两者比值影响L的收敛域,若不能满足,则重新设计虚拟控制、实际控制和自适应更新率直至满足 Step 3: Combine command filter recursion and composite nonlinear disturbance observer to design virtual control, actual control and adaptive update rate; and construct a suitable Lyapunov function L to verify whether the designed virtual control, actual control and adaptive update rate meet the finite time stability judgment condition of the closed-loop system. Among them, M is the design parameter, M2 is a positive number, and the ratio of the two is If the convergence domain of L is not satisfied, redesign the virtual control, actual control and adaptive update rate until it is satisfied.
步骤4:对所设计的虚拟控制、实际控制和自适应更新率进行稳定性和性能分析,验证其能够保证船舶智能机动系统内包含航向角、偏航率、舵令参数的有限时间稳定,保证船舶航向角与规定航向角的误差在预定时间内缩小到预定范围里,确保系统状态量在约束条件内。Step 4: Conduct stability and performance analysis on the designed virtual control, actual control and adaptive update rate to verify that they can ensure the finite time stability of the ship's intelligent maneuvering system including the heading angle, yaw rate and steering command parameters, ensure that the error between the ship's heading angle and the specified heading angle is reduced to a predetermined range within a predetermined time, and ensure that the system state quantity is within the constraints.
进一步地,所述步骤2中设计出时变的障碍李雅普诺夫函数和辅助系统具体如下:Furthermore, the time-varying obstacle Lyapunov function and auxiliary system designed in step 2 are specifically as follows:
1)构建有限时间性能函数为:1) Construct the finite time performance function as:
其中,ar,br,是正参数,代表预定义的收敛时间,整个函数会在Tr,s时间内从初值收敛到内,r=1,2,3;in, a r , b r , is a positive parameter, Represents the predefined convergence time. The entire function will converge from the initial value within T r,s . Converge to Inner, r = 1, 2, 3;
设计如下形式的时变障碍李亚普诺夫函数:Design a time-varying barrier Lyapunov function of the following form:
其中,是被约束变量,是约束的上下界,r=1,2,3;in, is the bound variable, are the upper and lower bounds of the constraints, r = 1, 2, 3;
针对输入饱和效应构造的辅助系统具体如下:The auxiliary system constructed for input saturation effect is as follows:
其中,和是辅助系统的状态变量,l1,l2和l3是辅助系统的增益参数,Δu=sat(u)-u表示饱和输入和正常输入之间的误差,状态变量的初值都为0。in, and is the state variable of the auxiliary system, l 1 , l 2 and l 3 are the gain parameters of the auxiliary system, Δu = sat(u) -u represents the error between the saturated input and the normal input, and the initial values of the state variables are all 0.
进一步地,所述步骤3中具体包括:Furthermore, the step 3 specifically includes:
1)设计一系列误差变量表示为:1) Design a series of error variables expressed as:
其中,和表示系统状态误差,yf是参考航向角,满足 是yf的一阶时间导数,是一阶滤波器的输出,代表补偿信号,代表补偿误差,和分别代表神经网络权值估计值和复合干扰估计值,是神经网络权值估计误差,是复合干扰估计误差,复合干扰的估计值将会通过后续设计的复合非线性干扰观测器给出;in, and represents the system state error, y f is the reference heading angle, and satisfies is the first-order time derivative of y f , is the output of the first-order filter, represents the compensation signal, represents the compensation error, and Represent the neural network weight estimate and the composite interference estimate, respectively. is the neural network weight estimation error, is the composite interference estimation error, the estimated value of the composite interference It will be given by the composite nonlinear disturbance observer designed subsequently;
2)设计满足控制目标的虚拟控制、实际输入和自适应更新律,包括:2) Design virtual control, actual input and adaptive update law that meet the control objectives, including:
其中,是虚拟控制,u是实际输入,是自适应更新率,mr,1,mr,2,m2,a,m3,a表示待设计参数,变量和是设计过程中引入的辅助变量,常数r=1,2,3。in, is the virtual control, u is the actual input, is the adaptive update rate, m r,1 ,m r,2 ,m 2,a ,m 3,a represent the parameters to be designed, and the variables and It is an auxiliary variable introduced in the design process, and the constant r=1,2,3.
进一步地,所述步骤3中结合命令滤波递推和复合非线性干扰观测器设计出虚拟控制、实际控制和自适应更新率的具体设计过程及构造的李雅普诺夫函数L如下:Furthermore, in step 3, the specific design process of virtual control, actual control and adaptive update rate and the constructed Lyapunov function L are designed by combining command filtering recursion and composite nonlinear disturbance observer as follows:
步骤3.1:根据具有外部干扰和输入饱和效应的船舶智能机动系统的状态方程式(4)和误差变量(8),对误差变量进行求导,计算得到:Step 3.1: According to the state equation (4) and error variable (8) of the ship intelligent maneuvering system with external disturbance and input saturation effect, the error variable Taking the derivative, we get:
其中,假设复合干扰及其一阶导数是有界的,即 和代表正的常数,r=1,2,3;in, Assuming composite interference and its first-order derivative is bounded, i.e. and Represents a positive constant, r = 1, 2, 3;
为了把未知干扰对系统的影响补偿掉,设计一个如下形式的非线性干扰观测器:In order to compensate for the impact of unknown disturbances on the system, a nonlinear disturbance observer is designed in the following form:
其中,m1,d为正的设计参数,是干扰观测器中的辅助变量;根据式(11),对干扰误差进行求导,得到:Among them, m 1,d is a positive design parameter, is the auxiliary variable in the disturbance observer; according to formula (11), the disturbance error Taking the derivative, we get:
为实现控制目标,设计如下虚拟控制:In order to achieve the control goal, the following virtual control is designed:
其中,和都是辅助变量,m1,1,m1,2是待设计的正常数,常数 in, and are auxiliary variables, m 1,1 and m 1,2 are normal numbers to be designed, and constants
设计一个时间常数为的一阶滤波器,该滤波器的输入为虚拟控制输出为具体形式为:Design a time constant of A first-order filter whose input is a virtual control The output is The specific form is:
其中,和是滤波器输入输出的初值;in, and is the initial value of the filter input and output;
为了减小滤波误差对控制系统的影响,设计一个新的补偿信号 In order to reduce the filtering error Impact on the control system, design a new compensation signal
其中,是补偿信号的初值,m1,2是正的设计参数;in, is the initial value of the compensation signal, m 1,2 is a positive design parameter;
设计如下正定Lyapunov函数Design the following positive definite Lyapunov function
对L1求其关于时间的导数,得到:Taking the derivative of L1 with respect to time, we get:
结合杨氏不等式,得到如下不等式:Combining Young's inequality, we get the following inequality:
将式(18)代入式(17)中去,放缩得到:Substituting formula (18) into formula (17) and scaling it up, we get:
步骤3.2:参考步骤3.1,根据状态方程式(4)和误差变量(8),得到状态误差的时间导数,设计如下形式的复合非线性干扰观测器来得到复合干扰的估计值:Step 3.2: Referring to step 3.1, according to the state equation (4) and the error variable (8), the state error is obtained The time derivative of , design the following composite nonlinear disturbance observer to obtain the composite disturbance Estimated value:
其中,是复合干扰,复合干扰满足是正的常数,是一个中间变量,m2,d>0是待设计参数;依此构造第2个虚拟控制和神经网络自适应更新律为:in, It is a composite interference, composite interference satisfy is a positive constant, is an intermediate variable, m 2,d >0 is the parameter to be designed; based on this, the second virtual control and neural network adaptive update law are constructed as follows:
其中m2,1,m2,2和m2,a都是设计参数,是辅助变量,常数构造第2个Lyapunov函数:Among them, m 2,1 ,m 2,2 and m 2,a are design parameters. is an auxiliary variable, a constant Construct the second Lyapunov function:
计算李雅普诺夫函数L2关于时间的导数并且进行放缩运算,可得:Calculating the derivative of the Lyapunov function L2 with respect to time and scaling it, we can get:
其中,mc,1,m2,a,m2,d,mc,2,c=1,2均是正的设计参数,和是辅助变量,常数 Among them, m c,1 ,m 2,a ,m 2,d ,m c,2 , c=1,2 are all positive design parameters. and is an auxiliary variable, a constant
步骤3.3:根据状态方程式(4)和误差变量(8),得到状态误差的时间导数,设计非线性干扰观测器并计算干扰估计误差时间导数,设计实际的控制器u和神经网络自适应更新律为:Step 3.3: According to the state equation (4) and the error variable (8), the state error is obtained The time derivative of is used to design a nonlinear disturbance observer and calculate the time derivative of the disturbance estimation error. The actual controller u and the neural network adaptive update law are designed as follows:
其中m3,1,m3,2和m3,a都是设计参数,是辅助变量,常数 Among them, m 3,1 ,m 3,2 and m 3,a are design parameters. is an auxiliary variable, a constant
设计第3个正定的Lyapunov函数为:Design the third positive definite Lyapunov function as:
对L3求关于时间导数并且进行放缩运算,可得:Taking the time derivative of L3 and scaling it, we get:
其中,mc,1,mc,a,mc,d,mc,2均是正的设计参数,和是辅助变量,常数 Among them, m c,1 ,m c,a ,m c,d ,m c,2 are all positive design parameters. and is an auxiliary variable, a constant
进一步地,所述步骤4具体包括:Furthermore, the step 4 specifically includes:
整合闭环系统的Lyapunov函数为如下形式:The Lyapunov function of the integrated closed-loop system is as follows:
对L求关于时间的导数并且整合计算,可得:Taking the time derivative of L and integrating the calculations, we get:
其中,设计参数需满足mr,1,mr,a-mr,d,mr,d-2,m1,d-1,mr,2都大于0;Among them, the design parameters must satisfy that m r,1 ,m r,a -m r,d ,m r,d -2,m 1,d -1,m r,2 are all greater than 0;
定义:definition:
因此,式(23)可以转化为:Therefore, formula (23) can be transformed into:
根据以下不等式According to the following inequality
将式(26)代入到式(25)中,得到:Substituting formula (26) into formula (25), we get:
其中, in,
易得:Easy to get:
计算式(28),得到对所有的t≥td时,成立,其中,是一个常数且满足得到的收敛时间td用下式表示:Calculate formula (28) and get that for all t≥td , Established, among which, is a constant and satisfies The obtained convergence time td is expressed as follows:
有益效果:Beneficial effects:
1、本发明提出的控制策略是针对具有外部干扰和输入饱和效应的船舶智能机动系统设计的有限时间预定性能的约束控制策略,使用神经网络技术和复合非线性干扰观测器技术来解决船舶智能机动模型中高度不确定性函数在递推中的影响,同时,复合干扰估计值的嵌入减小了输入舵令的幅值,除此之外,使用预定性能控制、有限时间控制和约束控制等技术设计出来的控制器能够保证本系统的航向角与参考航向角之间的误差在预定时间内收敛到预定范围内,保证系统的航向角、偏航率等状态参数自始至终满足约束条件,实现闭环系统内所有的信号都的有限时间稳定性,这些特性极大程度上提升了船舶智能机动的精度和平衡性。1. The control strategy proposed in the present invention is a finite-time predetermined performance constraint control strategy designed for a ship intelligent maneuvering system with external interference and input saturation effects. Neural network technology and composite nonlinear disturbance observer technology are used to solve the influence of highly uncertain functions in the ship intelligent maneuvering model in the recursion. At the same time, the embedding of the composite interference estimate reduces the amplitude of the input steering command. In addition, the controller designed using technologies such as predetermined performance control, finite-time control and constraint control can ensure that the error between the heading angle of the system and the reference heading angle converges to a predetermined range within a predetermined time, and ensures that the system's heading angle, yaw rate and other state parameters meet the constraints from beginning to end, and achieves finite-time stability of all signals in the closed-loop system. These characteristics greatly improve the accuracy and balance of ship intelligent maneuvers.
2、本发明所使用的递推法结合了命令滤波技术,与传统的滤波方法不同,一组补偿信号的引入显著降低了滤波误差对控制性能的影响,提升了本发明控制策略的控制效果;另一方面,辅助系统的设计很好的补偿掉了输入饱和效应对船舶智能机动系统的影响,与近似函数逼近饱和函数的方法不同,辅助系统方法拥有更小的饱和误差,这样一来,闭环系统的鲁棒性进一步的得到了提高。需要注意的是,本发明的控制策略可以扩展到状态量更多的实际应用模型中,加上抗饱和和抗干扰的特性,使得本发明的控制策略的适用性和有效性得到了极大的提升,能够应用于实际生产的多个场景中。2. The recursive method used in the present invention is combined with command filtering technology. Unlike traditional filtering methods, the introduction of a set of compensation signals significantly reduces the impact of filtering errors on control performance, and improves the control effect of the control strategy of the present invention. On the other hand, the design of the auxiliary system well compensates for the impact of input saturation effects on the ship's intelligent maneuvering system. Unlike the method of approximating a saturated function with an approximate function, the auxiliary system method has a smaller saturation error, so that the robustness of the closed-loop system is further improved. It should be noted that the control strategy of the present invention can be extended to practical application models with more state quantities. Coupled with the anti-saturation and anti-interference characteristics, the applicability and effectiveness of the control strategy of the present invention are greatly improved, and can be applied to multiple scenarios in actual production.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为本发明实施例所述的自适应控制策略流程图。FIG1 is a flow chart of an adaptive control strategy according to an embodiment of the present invention.
具体实施方式DETAILED DESCRIPTION
下面对本发明技术方案进行详细说明。The technical solution of the present invention is described in detail below.
本发明针对船舶机动系统来进行控制策略的设计,该船舶机动模型的方程为:The present invention designs a control strategy for a ship maneuvering system, and the equation of the ship maneuvering model is:
式(1)中,为船舶航向角,代表偏航率,是偏航率的变化率,T是一个时间常数,K,w分别代表诺宾系数、方向增益、方向舵角和r维的独立标准布朗运动,表示未知函数。In formula (1), is the ship heading angle, represents the yaw rate, is the rate of change of the yaw rate, T is a time constant, K, w represents the Nobin coefficient, directional gain, rudder angle and r-dimensional independent standard Brownian motion, Represents an unknown function.
定义将式(1)写成状态方程的形式,得到:definition Writing equation (1) in the form of a state equation yields:
其中,TE是船舶时间常数,KE是船舶的控制增益,代表舵令,f函数是一个未知函数,y为系统输出,是系统外部干扰,表示该系统受到外部非匹配干扰的影响。需要注意的是,f函数的自变量包含因此,式(2)所表示的船舶智能机动模型是一个具有高度不确定性的非线性系统模型。为了保持船舶行时的平衡性,船舶的航向角以及偏航率等状态参数需要满足一定的约束条件,即状态参数需要满足 为约束条件。u为系统输入,sat(u)表示舵令的饱和输入,由下式表示:in, TE is the ship time constant, KE is the ship control gain, represents the steering command, f function is an unknown function, y is the system output, is the external disturbance of the system, indicating that the system is affected by external non-matching disturbance. It should be noted that the independent variable of the f function contains Therefore, the ship intelligent maneuvering model represented by formula (2) is a nonlinear system model with high uncertainty. In order to maintain the balance of the ship during navigation, the state parameters of the ship such as heading angle and yaw rate need to meet certain constraints, that is, the state parameters need to meet is the constraint condition. u is the system input, and sat(u) represents the saturated input of the steering command, which is expressed by the following formula:
其中,u1>0,u2<0代表已知常数。根据实际控制的需要,控制输入u理应是有界的,如果u趋于无穷大,那么系统很可能会变得不可控,因此,u是有界的,由于饱和输入sat(u)是有界的,所以饱和误差Δu=sat(u)-u也是有界的。Among them, u 1 > 0, u 2 < 0 represent known constants. According to the needs of actual control, the control input u should be bounded. If u tends to infinity, the system is likely to become uncontrollable. Therefore, u is bounded. Since the saturation input sat(u) is bounded, the saturation error Δu = sat(u)-u is also bounded.
结合神经网络逼近技术,未知函数和可以用神经网络进行逼近,即:同时,定义有界函数b=g2,这样,系统函数(2)可以重写为:Combined with neural network approximation technology, unknown function and It can be approximated by a neural network, namely: At the same time, define the bounded function b = g 2 , In this way, the system function (2) can be rewritten as:
其中, 为神经网络逼近的最优权值,是基函数,代表神经网络最小逼近误差。in, is the optimal weight of the neural network approximation, is the basis function, Represents the minimum approximation error of the neural network.
本发明提出的控制策略是具有外部干扰和输入饱和效应的船舶智能机动系统有限时间预定性能约束控制策略,针对受非匹配外部干扰和输入饱和影响的船舶智能机动系统,结合命令滤波递推技术、有限时间控制技术、复合非线性干扰观测器技术、约束控制方法和神经网络逼近技术来设计控制策略以实现控制目标。本发明的控制策略要使船舶智能机动系统在有外部干扰和输入饱和效应的影响下实现以下控制目标:The control strategy proposed in the present invention is a finite time predetermined performance constraint control strategy for a ship intelligent maneuvering system with external disturbance and input saturation effects. For a ship intelligent maneuvering system affected by non-matching external disturbance and input saturation, a control strategy is designed by combining command filtering recursion technology, finite time control technology, composite nonlinear disturbance observer technology, constraint control method and neural network approximation technology to achieve the control target. The control strategy of the present invention enables the ship intelligent maneuvering system to achieve the following control targets under the influence of external disturbance and input saturation effects:
目标1:闭环系统内所有的信号都是有限时间稳定的。Goal 1: All signals in the closed-loop system are finite-time stable.
目标2:系统的航向角、偏航率等状态参数自始至终满足约束条件。Goal 2: The system's heading angle, yaw rate and other state parameters meet the constraints from beginning to end.
目标3:系统航向角与参考航向角之间的误差在预定时间内收敛到预定范围内。Objective 3: The error between the system heading angle and the reference heading angle converges to a predetermined range within a predetermined time.
目标4:外部干扰和输入饱和效应对系统的影响得到很好的抑制。Objective 4: The impact of external interference and input saturation effects on the system is well suppressed.
采用本发明所述的控制策略实现具有外部干扰和输入饱和效应的船舶智能机动系统有限时间预定性能约束控制,详细的步骤如下:The control strategy of the present invention is used to realize the finite time predetermined performance constraint control of the ship intelligent maneuvering system with external disturbance and input saturation effect. The detailed steps are as follows:
(1)构建时变障碍李亚普诺夫函数和辅助系统。(1) Construct time-varying barrier Lyapunov function and auxiliary system.
设计如下有限时间性能函数:Design the following finite-time performance function:
其中,ar,br,是正参数,代表预定义的收敛时间,整个函数会在Tr,s时间内从初值收敛到内,r=1,2,3。in, a r , b r , is a positive parameter, Represents the predefined convergence time. The entire function will converge from the initial value within T r,s . Converge to Inside, r=1,2,3.
基于上述有限时间性能函数,设计如下形式的时变障碍李亚普诺夫函数:Based on the above finite-time performance function, the following time-varying barrier Lyapunov function is designed:
其中,是被约束变量,后面会对其进行定义,是约束的上下界,r=1,2,3。in, is a constrained variable, which will be defined later. are the upper and lower bounds of the constraints, r=1,2,3.
为了消除输入饱和对系统的影响,设计如下的辅助系统:In order to eliminate the influence of input saturation on the system, the following auxiliary system is designed:
其中,和是辅助系统的状态变量,l1,l2和l3是辅助系统的增益参数,Δu=sat(u)-u表示饱和输入和正常输入之间的误差,状态变量的初值都为0。in, and is the state variable of the auxiliary system, l 1 , l 2 and l 3 are the gain parameters of the auxiliary system, Δu = sat(u) -u represents the error between the saturated input and the normal input, and the initial values of the state variables are all 0.
(2)结合神经网络的万能逼近原理、命令滤波递推法、有限时间控制、约束控制和复合非线性干扰观测器的方法来设计虚拟控制、实际控制输入、神经网络自适应更新律来满足控制目标;所设计一系列误差变量表示为:(2) Combining the universal approximation principle of neural network, command filtering recursion method, finite time control, constrained control and composite nonlinear disturbance observer method to design virtual control, actual control input, neural network adaptive update law to meet the control objectives; the designed series of error variables are expressed as:
其中,和表示系统状态误差,yf是参考航向角,满足 是yf的一阶时间导数,是一阶滤波器的输出,代表补偿信号,滤波器和补偿信号的设计会在后续给出,代表补偿误差,和分别代表神经网络权值估计值和复合干扰估计值,是神经网络权值估计误差,是复合干扰估计误差,复合干扰的估计值将会通过后续设计的复合非线性干扰观测器给出。in, and represents the system state error, y f is the reference heading angle, and satisfies is the first-order time derivative of y f , is the output of the first-order filter, represents the compensation signal. The design of the filter and compensation signal will be given later. represents the compensation error, and Represent the neural network weight estimate and the composite interference estimate, respectively. is the neural network weight estimation error, is the composite interference estimation error, the estimated value of the composite interference It will be given through the composite nonlinear disturbance observer designed subsequently.
设计满足控制目标的虚拟控制、实际输入和自适应更新律,包括:Design virtual control, actual input, and adaptive update laws that meet control objectives, including:
其中,是虚拟控制,u是实际输入,是自适应更新率,mr,1,mr,2,m2,a,m3,a表示一些待设计参数,变量和是设计过程中引入的辅助变量,常数r=1,2,3。in, is the virtual control, u is the actual input, is the adaptive update rate, m r,1 ,m r,2 ,m 2,a ,m 3,a represent some parameters to be designed, variables and It is an auxiliary variable introduced in the design process, and the constant r=1,2,3.
(3)构造合适的李雅普诺夫函数L,对L进行求导运算得到将设计的虚拟控制、实际控制和自适应更新率代入到求导运算当中,经过不等式放缩,验证所设计的虚拟控制、实际控制和自适应更新率是否满足闭环系统有限时间稳定判别条件其中,M为设计参数,M2为一个正数,两者比值影响L的收敛域,若不能满足,则重新设计虚拟控制、实际控制和自适应更新率直至满足若能够满足,则证明所设计的虚拟控制、实际控制和自适应更新率可以保证闭环系统有限时间稳定。(3) Construct a suitable Lyapunov function L and perform a derivative operation on L to obtain Substitute the designed virtual control, actual control and adaptive update rate into the derivative operation, and after scaling the inequality, verify whether the designed virtual control, actual control and adaptive update rate meet the finite time stability judgment condition of the closed-loop system. Among them, M is the design parameter, M2 is a positive number, and the ratio of the two is If the convergence domain of L is not satisfied, redesign the virtual control, actual control and adaptive update rate until it is satisfied. If it can be satisfied, it proves that the designed virtual control, actual control and adaptive update rate can ensure the finite time stability of the closed-loop system.
下面将给出具有外部干扰和输入饱和效应的船舶智能机动系统有限时间预定性能约束控制策略设计的具体步骤,设计步骤被分为3步:The following is a detailed design procedure for the finite time performance constraint control strategy of the ship intelligent maneuvering system with external disturbance and input saturation effects. The design procedure is divided into three steps:
第1步:根据具有外部干扰和输入饱和效应的船舶智能机动系统的状态方程式(4)误差变量(8)对误差变量进行求导,计算得到:Step 1: According to the state equation (4) of the ship intelligent maneuvering system with external disturbance and input saturation effect, the error variable (8) is Taking the derivative, we get:
其中,假设及其一阶导数是有界的,即 和代表正的常数。in, Assumptions and its first-order derivative is bounded, i.e. and Represents a positive constant.
为了把未知干扰对系统的影响补偿掉,设计一个如下形式的非线性干扰观测器:In order to compensate for the impact of unknown disturbances on the system, a nonlinear disturbance observer is designed in the following form:
其中,m1,d为正的设计参数,是干扰观测器中的辅助变量。Among them, m 1,d is a positive design parameter, is the auxiliary variable in the disturbance observer.
根据式(11),对进行求导,得到:According to formula (11), Taking the derivative, we get:
为实现控制目标,设计如下虚拟控制:In order to achieve the control goal, the following virtual control is designed:
其中,和都是辅助变量,m1,1,m1,2是待设计的正常数,常数 in, and are auxiliary variables, m 1,1 and m 1,2 are normal numbers to be designed, and constants
为了解决传统递推方法中对虚拟控制重复微分导致计算量过大的问题,设计一个时间常数为的一阶滤波器,该滤波器的输入为输出为具体形式为:In order to solve the problem of excessive calculation caused by repeated differentiation of virtual control in the traditional recursive method, a time constant is designed. The first-order filter has an input of The output is The specific form is:
其中,和是滤波器输入输出的初值。in, and is the initial value of the filter input and output.
为了减小滤波误差对控制系统的影响,设计一个新的补偿信号 In order to reduce the filtering error Impact on the control system, design a new compensation signal
其中,是补偿信号的初值,m1,2是正的设计参数。in, is the initial value of the compensation signal, and m 1,2 are positive design parameters.
设计如下正定Lyapunov函数为Design the following positive definite Lyapunov function:
对L1求其关于时间的导数,得到:Taking the derivative of L1 with respect to time, we get:
结合杨氏不等式,可以得到如下不等式:Combining Young's inequality, we can get the following inequality:
将式(18)代入到式(17)中去,得到:Substituting formula (18) into formula (17), we get:
第2步:根据状态方程(4)与误差变量(8),计算得到状态误差的时间导数:Step 2: According to the state equation (4) and the error variable (8), calculate the state error The time derivative of :
其中,是复合干扰,复合干扰满足 是正的常数。in, It is a composite interference, composite interference satisfy is a positive constant.
同样的,设计如下形式的复合非线性干扰观测器来得到复合干扰的估计值:Similarly, a composite nonlinear disturbance observer is designed to obtain the composite disturbance Estimated value:
其中,是一个中间变量,m2,d>0是待设计参数。in, is an intermediate variable, and m 2,d >0 is a parameter to be designed.
结合式(8)和式(21),计算得到干扰估计误差的时间导数为:Combining equation (8) and equation (21), the interference estimation error is calculated The time derivative of is:
接着,构造第2个虚拟控制和神经网络自适应更新律为:Next, the second virtual control and neural network adaptive update law are constructed as:
其中m2,1,m2,2和m2,a都是设计参数,是辅助变量,常数 Among them, m 2,1 ,m 2,2 and m 2,a are design parameters. is an auxiliary variable, a constant
与第一步相似,构造一个时间常数为的一阶滤波器如下:Similar to the first step, construct a time constant The first-order filter is as follows:
其中,和分别是该滤波器的输入和输出,和是滤波器输入输出的初值,定义一个变量来补偿滤波误差产生的影响:in, and are the input and output of the filter respectively, and is the initial value of the filter input and output, define a variable To compensate for filtering errors Impact:
其中,是补偿信号的初值,m2,2是正的设计参数。in, is the initial value of the compensation signal, and m 2,2 is a positive design parameter.
构造第2个Lyapunov函数:Construct the second Lyapunov function:
对L2求时间导数并将式(20)-(26)代入可得:Taking the time derivative of L2 and substituting equations (20)-(26) into it, we obtain:
结合Young不等式,可以得到:Combined with Young's inequality, we can get:
除此之外,有In addition, there are
将式(29)和(30)代入(28)中,得到:Substituting equations (29) and (30) into (28), we obtain:
第3步:根据状态方程(4)以及误差变量(8),误差变量的时间导数为:Step 3: According to the state equation (4) and the error variable (8), the error variable The time derivative of is:
其中,是复合干扰,假设满足 是正常数。in, is a composite interference, assuming satisfy is a normal number.
设计一个如下形式的非线性干扰观测器:Design a nonlinear disturbance observer of the following form:
其中,m3,d>0是干扰观测器增益,是干扰观测器中的辅助变量。Where m 3,d >0 is the disturbance observer gain, is the auxiliary variable in the disturbance observer.
根据式(8)和(33),计算干扰估计误差时间导数并表示为:According to equations (8) and (33), the time derivative of the interference estimation error is calculated and expressed as:
设计实际的控制器u和神经网络自适应更新律为:The actual controller u and the neural network adaptive update law are designed as:
其中m3,1,m3,2和m3,a都是设计参数,是辅助变量,常数 Among them, m 3,1 ,m 3,2 and m 3,a are design parameters. is an auxiliary variable, a constant
构造如下初值为的补偿信号:The initial value is constructed as follows The compensation signal:
其中,m3,2是正的设计参数。where m 3,2 is a positive design parameter.
设计第3个正定的Lyapunov函数为:Design the third positive definite Lyapunov function as:
计算L3关于时间的导数并且将式(32)-(37)代入,可得:Calculate the derivative of L3 with respect to time and substitute equations (32)-(37) to obtain:
结合Young不等式,可得下面的一组不等式Combining Young's inequality, we can get the following set of inequalities
除此之外,还有In addition, there are
将不等式(39)、(40)代入式(38),可得:Substituting inequalities (39) and (40) into equation (38), we can obtain:
(4)对本文所设计的控制策略进行稳定性和性能分析,验证本发明所提出的控制策略能够保证船舶智能机动系统内包含航向角、偏航率、舵令等所有参数的有限时间稳定,保证船舶航向角与规定航向角的误差在预定时间内缩小到预定范围里,确保系统状态量在约束条件内。(4) The stability and performance of the control strategy designed in this paper are analyzed to verify that the control strategy proposed in this invention can ensure the finite time stability of all parameters in the ship's intelligent maneuvering system, including the heading angle, yaw rate, steering command, etc., and ensure that the error between the ship's heading angle and the specified heading angle is reduced to a predetermined range within a predetermined time, ensuring that the system state quantity is within the constraints.
证明:prove:
整合闭环系统的Lyapunov函数为如下形式:The Lyapunov function of the integrated closed-loop system is as follows:
对L求关于时间的导数并且整合计算,可得:Taking the time derivative of L and integrating the calculations, we get:
其中,设计参数需满足mr,1,mr,a-mr,d,mr,d-2,m1,d-1,mr,2都大于0。Among them, the design parameters must satisfy that m r,1 ,m r,a -m r,d ,m r,d -2,m 1,d -1,m r,2 are all greater than 0.
定义:definition:
因此,式(44)可以转化为:Therefore, formula (44) can be transformed into:
根据以下不等式According to the following inequality
将式(47)代入到式(46)中,得到:Substituting formula (47) into formula (46), we obtain:
其中, in,
易得:Easy to get:
计算式(49),可以得到对所有的t≥td时,成立,其中,是一个常数且满足得到的收敛时间td用下式表示:By calculating formula (49), we can obtain that for all t≥td , Established, among which, is a constant and satisfies The obtained convergence time td is expressed as follows:
根据李亚普诺夫函数的设计,都是有限时间稳定的,有限的时间为td,由于和是有界的,结合坐标变换,和也是有限时间收敛的;根据滤波器和补偿信号的设计可以得到:对于所有的t≥td,和都是有界的;由于Δu有界的,根据辅助系统的设计可知,对于所有的t≥td,也是有界的;由于所以,是有限时间收敛的,其中,r=1,2,3。考虑到可以得到状态是有限时间收敛的,进而,考虑到虚拟控制是一个关于的函数,所以也是有限时间收敛的,结合坐标变换得到状态是有限时间收敛的,因而,相似的方法可以证明其他闭环系统信号u都是有限时间收敛的,即:包含航向角、偏航率、舵令等所有参数都是有限时间稳定的,由于本发明控制策略嵌入了复合非线性干扰观测器和辅助系统,所以其具有抗干扰和抗饱和的性能。According to the design of Lyapunov function, are all stable for a finite time, the finite time being t d , due to and is bounded, combined with coordinate transformation, and It also converges in finite time; according to the design of the filter and compensation signal, it can be obtained that for all t≥t d , and are all bounded; since Δu is bounded, according to the design of the auxiliary system, for all t≥t d , is also bounded; so, is convergent in finite time, where r = 1, 2, 3. Considering You can get the status is finite time convergent, and then, considering the virtual control is a So It also converges in finite time, combined with the coordinate transformation Get Status It converges in finite time, so similar methods can prove that other closed-loop system signals u all converge in finite time, that is, all parameters including heading angle, yaw rate, steering command, etc. are finite time stable. Since the control strategy of the present invention embeds a composite nonlinear disturbance observer and an auxiliary system, it has anti-interference and anti-saturation performance.
根据本文的设计,补偿误差满足r=1,2,3,因此,从上述有限时间收敛分析中可以得到 分别是的界,所以,状态维持在约束条件下,即对于状态 r=2,3,分别是的界,这样,状态同样不违反状态约束。根据和跟踪误差会在规定时间T1,s内收敛到一定的范围内,结合本发明所设计的补偿信号的形式,在适当的参数调整下,可以是任意常数,所以,跟踪误差满足预定时间预定性能,即:船舶航向角与规定航向角的误差在预定时间内缩小到预定范围里,航向角、偏航率等状态参数维持在约束条件内。至此,通过上面的分析,本文的控制目标都能实现。According to the design of this paper, the compensation error satisfy r=1,2,3, so from the above finite time convergence analysis we can get They are So, the state Maintaining the constraints, that is For status r=2,3, They are The boundary, so that the state The state constraint is also not violated. and Tracking Error It will converge to a certain range within the specified time T 1,s In combination with the compensation signal designed by the present invention In the form of, with appropriate parameter adjustment, It can be any constant, so the tracking error meets the predetermined performance within the predetermined time, that is, the error between the ship's heading angle and the specified heading angle is reduced to the predetermined range within the predetermined time, and the state parameters such as the heading angle and yaw rate are maintained within the constraints. So far, through the above analysis, the control objectives of this paper can be achieved.
本发明针对具有外部干扰和输入饱和效应的船舶智能机动系统设计一种有限时间预定性能的约束控制策略,使用复合非线性干扰观测器技术来解决船舶智能机动模型中高度不确定性函数在递推中的影响,结合有限时间性能函数和障碍李雅普诺夫函数设计出时变障碍李亚普诺夫函数既能保证本系统的航向角与参考航向角之间的误差在预定时间内收敛到预定范围内,又能确保系统的航向角、偏航率等状态参数自始至终满足约束条件,辅助系统的引入克服了输入饱和对系统的影响,有限时间控制技术的设计保证了闭环系统内所有变量都是有限时间稳定的,以上分析证明本发明控制策略的控制目标都能够实现,这些控制目标极大程度上提升了船舶智能机动的精度和平衡性。The present invention designs a constraint control strategy with finite-time predetermined performance for a ship intelligent maneuvering system with external interference and input saturation effects, uses a composite nonlinear interference observer technology to solve the influence of highly uncertain functions in the ship intelligent maneuvering model in the recursion, and designs a time-varying obstacle Lyapunov function by combining the finite-time performance function and the obstacle Lyapunov function. This strategy can not only ensure that the error between the heading angle of the system and the reference heading angle converges to a predetermined range within a predetermined time, but also ensure that the system's heading angle, yaw rate and other state parameters meet the constraint conditions from beginning to end. The introduction of the auxiliary system overcomes the influence of input saturation on the system. The design of the finite-time control technology ensures that all variables in the closed-loop system are finite-time stable. The above analysis proves that the control objectives of the control strategy of the present invention can be achieved, and these control objectives greatly improve the accuracy and balance of the ship's intelligent maneuverability.
上述实施方式只为说明本发明的技术构思及特点,其目的在于让熟悉此项技术的人能够了解本发明的内容并据以实施,并不能以此限制本发明的保护范围。凡根据本发明精神实质所做的等效变换或修饰,都应涵盖在本发明的保护范围之内。The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with the technology to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent transformation or modification made according to the spirit of the present invention should be included in the protection scope of the present invention.
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