CN112327627B - Nonlinear switching system self-adaptive sliding mode control method based on composite learning - Google Patents

Nonlinear switching system self-adaptive sliding mode control method based on composite learning Download PDF

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CN112327627B
CN112327627B CN202011274007.4A CN202011274007A CN112327627B CN 112327627 B CN112327627 B CN 112327627B CN 202011274007 A CN202011274007 A CN 202011274007A CN 112327627 B CN112327627 B CN 112327627B
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许斌
程怡新
马波
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Northwestern Polytechnical University
AVIC Chengdu Aircraft Design and Research Institute
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Abstract

本发明涉及一种基于复合学习的非线性切换系统自适应滑模控制方法，用于解决现有非线性切换系统控制方法实用性差的技术问题。考虑非线性切换系统存在外界干扰和输入非线性，得到切换系统输入死区模型；使用神经网络和切换扰动观测器分别对系统未知非线性函数和复合干扰进行估计，基于平行估计模型构造表征学习性能好坏的预测误差，通过预测误差对神经网络权重更新律和扰动观测器进行调节；基于动态逆技术框架和复合学习策略设计自适应滑模切换控制器；利用预测误差构建滑模时变增益函数，减小了滑模切换抖振的幅度，提升了滑模控制的性能；本发明结合非线性切换系统控制特点，通过设计基于复合学习的自适应滑模控制器有效提升了控制性能。

Figure 202011274007

The invention relates to an adaptive sliding mode control method for a nonlinear switching system based on compound learning, which is used to solve the technical problem of poor practicability of the existing nonlinear switching system control method. Considering the existence of external disturbance and input nonlinearity in the nonlinear switched system, the input dead zone model of the switched system is obtained; the neural network and the switched disturbance observer are used to estimate the unknown nonlinear function and compound disturbance of the system respectively, and the representation learning performance is constructed based on the parallel estimation model. The prediction error is good or bad, and the weight update law of the neural network and the disturbance observer are adjusted by the prediction error; the adaptive sliding mode switching controller is designed based on the dynamic inverse technology framework and compound learning strategy; the sliding mode time-varying gain function is constructed by using the prediction error , reducing the amplitude of the sliding mode switching chattering and improving the performance of the sliding mode control; the invention combines the control characteristics of the nonlinear switching system, and effectively improves the control performance by designing an adaptive sliding mode controller based on compound learning.

Figure 202011274007

Description

基于复合学习的非线性切换系统自适应滑模控制方法Adaptive sliding mode control method for nonlinear switching systems based on compound learning

技术领域technical field

本发明涉及一种非线性切换系统控制方法，特别是涉及一种基于复合学习的非线性切换系统自适应滑模控制方法，属于飞行控制领域。The invention relates to a control method of a nonlinear switching system, in particular to an adaptive sliding mode control method of a nonlinear switching system based on compound learning, which belongs to the field of flight control.

背景技术Background technique

在实际工程中，许多控制对象如变体飞行器、变频电机以及机器人等都可以用非线性切换系统来描述，因此非线性切换系统控制技术引起了广泛关注，在汽车、电力、化工等许多行业都得到了研究与应用。In practical engineering, many control objects such as variant aircraft, variable frequency motors, and robots can be described by nonlinear switching systems. Therefore, the control technology of nonlinear switching systems has attracted extensive attention. researched and applied.

非线性切换系统自身具有较强的不确定性，同时易受到外部干扰和输入死区的影响，现有的控制方法多采用神经网络或模糊逻辑等智能系统逼近不确定性，采用扰动观测器估计外部干扰。这些控制方法只考虑了智能系统的逼近作用，忽视了智能学习策略的本质，没有对不确定性学习性能进行有效评价，且智能逼近系统和扰动观测器之间没有信息交互，鲁棒性性较差，不利于工程实现。因此研究面向学习性能提升的先进控制方法对于非线性切换系统控制研究意义重大且有着迫切需求。The nonlinear switching system itself has strong uncertainty, and is easily affected by external disturbance and input dead zone. The existing control methods mostly use intelligent systems such as neural network or fuzzy logic to approximate the uncertainty, and use disturbance observer to estimate the uncertainty. external interference. These control methods only consider the approximation effect of the intelligent system, ignore the essence of the intelligent learning strategy, do not effectively evaluate the uncertainty learning performance, and there is no information interaction between the intelligent approximation system and the disturbance observer, and the robustness is relatively low. Poor, not conducive to the realization of the project. Therefore, the study of advanced control methods for learning performance improvement is of great significance and urgent need for nonlinear switching system control research.

发明内容SUMMARY OF THE INVENTION

要解决的技术问题technical problem to be solved

为了克服现有非线性切换系统控制方法实用性差的不足，本发明提供一种基于复合学习的非线性切换系统自适应滑模控制方法。该方法考虑非线性切换系统存在不确定性、外界干扰和输入非线性，通过模型转换获取输入死区模型。同时采用神经网络和扰动观测器分别对非线性函数和复合干扰进行估计，通过构造预测误差对学习效果进行评价，进而调节神经网络权重自适应更新律和切换扰动观测器。基于动态逆技术框架和复合学习策略设计了自适应滑模切换控制器，时变的滑模增益函数提升了控制器鲁棒性，便于工程实现。In order to overcome the shortcomings of poor practicability of the existing nonlinear switching system control methods, the present invention provides an adaptive sliding mode control method for nonlinear switching systems based on compound learning. The method considers the existence of uncertainty, external disturbance and input nonlinearity in the nonlinear switching system, and obtains the input dead zone model through model conversion. At the same time, the neural network and the disturbance observer are used to estimate the nonlinear function and the compound disturbance respectively, and the learning effect is evaluated by constructing the prediction error, and then the adaptive update law of the neural network weight and the switching disturbance observer are adjusted. An adaptive sliding mode switching controller is designed based on the dynamic inverse technology framework and compound learning strategy. The time-varying sliding mode gain function improves the robustness of the controller and facilitates engineering implementation.

技术方案Technical solutions

一种基于复合学习的非线性切换系统自适应滑模控制方法，其特征在于以下步骤：A composite learning-based adaptive sliding mode control method for nonlinear switching systems, characterized by the following steps:

步骤1：考虑一类单输入单输出非线性能控标准型切换系统Step 1: Consider a class of single-input single-output nonlinear controllable standard switching systems

Figure BDA0002778558790000021
Figure BDA0002778558790000021

其中，

Figure BDA0002778558790000022
是系统状态向量；uσ(t)∈R是系统输入，y∈R是系统输出；函数σ(t):[0,∞)→M＝{1,2,…,m}是切换信号，且σ(t)＝k时表示第k个子系统是激活的；
Figure BDA0002778558790000023
是关于
Figure BDA0002778558790000024
的未知平滑函数，
Figure BDA0002778558790000025
是关于
Figure BDA0002778558790000026
的未知非零平滑函数；dσ(t)(t)是外部未知干扰；in,
Figure BDA0002778558790000022
is the system state vector; u σ(t) ∈ R is the system input, y∈R is the system output; the function σ(t):[0,∞)→M={1,2,…,m} is the switching signal, And when σ(t)=k, it means that the kth subsystem is activated;
Figure BDA0002778558790000023
its about
Figure BDA0002778558790000024
The unknown smoothing function of ,
Figure BDA0002778558790000025
its about
Figure BDA0002778558790000026
The unknown non-zero smooth function of ; d σ(t) (t) is the external unknown disturbance;

步骤2：将系统输入非线性描述为Step 2: Describe the system input nonlinearity as

Figure BDA0002778558790000027
Figure BDA0002778558790000027

其中，uv,k∈R是带死区的输入，

Figure BDA0002778558790000028
br,k和bl,k是未知的正常数；where u v,k ∈ R is the input with dead zone,
Figure BDA0002778558790000028
b r,k and b l,k are unknown positive constants;

可将(2)进一步描述为(2) can be further described as

Figure BDA0002778558790000029
Figure BDA0002778558790000029

其中in

Figure BDA00027785587900000210
Figure BDA00027785587900000210

信号uk存在如下关系The signal u k has the following relationship

Figure BDA00027785587900000211
Figure BDA00027785587900000211

其中

Figure BDA00027785587900000212
是uv,k的上界值；in
Figure BDA00027785587900000212
is the upper bound value of u v,k ;

则系统(1)可进一步写为Then system (1) can be further written as

Figure BDA0002778558790000031
Figure BDA0002778558790000031

其中，

Figure BDA0002778558790000032
in,
Figure BDA0002778558790000032

步骤3：针对未知函数

Figure BDA0002778558790000033
和
Figure BDA0002778558790000034
用神经网络来逼近Step 3: For unknown functions
Figure BDA0002778558790000033
and
Figure BDA0002778558790000034
Approximate with a neural network

Figure BDA0002778558790000035
Figure BDA0002778558790000035

Figure BDA0002778558790000036
Figure BDA0002778558790000036

其中，

Figure BDA0002778558790000037
和
Figure BDA0002778558790000038
是神经网络最优权重向量，
Figure BDA0002778558790000039
和
Figure BDA00027785587900000310
是神经网络基函数向量，εf,k和εG,k是神经网络残差且存在
Figure BDA00027785587900000311
和
Figure BDA00027785587900000312
和
Figure BDA00027785587900000313
是正常数；in,
Figure BDA0002778558790000037
and
Figure BDA0002778558790000038
is the optimal weight vector of the neural network,
Figure BDA0002778558790000039
and
Figure BDA00027785587900000310
is the neural network basis function vector, ε f,k and ε G,k are the neural network residuals and exist
Figure BDA00027785587900000311
and
Figure BDA00027785587900000312
and
Figure BDA00027785587900000313
is a normal number;

则

Figure BDA00027785587900000314
和
Figure BDA00027785587900000315
的估计值可写为but
Figure BDA00027785587900000314
and
Figure BDA00027785587900000315
The estimated value of can be written as

Figure BDA00027785587900000316
Figure BDA00027785587900000316

Figure BDA00027785587900000317
Figure BDA00027785587900000317

其中，

Figure BDA00027785587900000318
和
Figure BDA00027785587900000319
是神经网络最优权重向量估计值；in,
Figure BDA00027785587900000318
and
Figure BDA00027785587900000319
is the estimated value of the optimal weight vector of the neural network;

定义Δuk＝uv,k-uc,k，则xn的导数可写为Define Δu k =u v,k -u c,k , then the derivative of x n can be written as

Figure BDA00027785587900000320
Figure BDA00027785587900000320

其中，

Figure BDA00027785587900000321
Figure BDA00027785587900000322
in,
Figure BDA00027785587900000321
Figure BDA00027785587900000322

步骤4：针对非线性切换系统(1)，基于复合学习策略设计自适应滑模控制器；Step 4: Design an adaptive sliding mode controller based on a composite learning strategy for the nonlinear switching system (1);

定义输出跟踪误差

Figure BDA00027785587900000323
其中e＝x1-yd，yd是控制参考指令；Define Output Tracking Error
Figure BDA00027785587900000323
Where e=x 1 -y d , y d is the control reference command;

设计滑模面为The sliding surface is designed as

s＝[ΛT 1]E (11)s=[Λ T 1]E (11)

其中，Λ＝[τn-1,(n-1)τn-2,…,(n-1)τ]T，τ>0；Among them, Λ=[τ n-1 ,(n-1)τ n-2 ,...,(n-1)τ] T , τ>0;

滑模面s的导数为The derivative of the sliding surface s is

Figure BDA0002778558790000041
Figure BDA0002778558790000041

其中，

Figure BDA0002778558790000042
in,
Figure BDA0002778558790000042

设计控制器为Design the controller as

Figure BDA0002778558790000043
Figure BDA0002778558790000043

其中in

Figure BDA0002778558790000044
Figure BDA0002778558790000044

Figure BDA0002778558790000045
Figure BDA0002778558790000045

Figure BDA0002778558790000046
Figure BDA0002778558790000046

其中，

Figure BDA0002778558790000047
是Dk(t)的估计值，βk是正的设计参数，mk是滑模增益函数；in,
Figure BDA0002778558790000047
is the estimated value of D k (t), β k is a positive design parameter, and m k is the sliding mode gain function;

构造预测误差znNN为The prediction error z nNN is constructed as

Figure BDA0002778558790000048
Figure BDA0002778558790000048

其中，

Figure BDA0002778558790000049
可由如下的平行估计模型得到in,
Figure BDA0002778558790000049
It can be obtained by the following parallel estimation model

Figure BDA00027785587900000410
Figure BDA00027785587900000410

其中，

Figure BDA00027785587900000411
λn,k是正的设计参数；in,
Figure BDA00027785587900000411
λ n,k is a positive design parameter;

设计滑模增益函数为The sliding mode gain function is designed as

mk＝-γz,kλkznNN (19)m k = -γ z,k λ k z nNN (19)

其中，γz,k是正的设计参数；where γz,k is a positive design parameter;

设计神经网络权重更新律为The weight update law of the designed neural network is

Figure BDA0002778558790000051
Figure BDA0002778558790000051

Figure BDA0002778558790000052
Figure BDA0002778558790000052

其中，γf,k，γG,k，δf,k和δG,k是正的设计参数；where γ f,k , γ G,k , δ f,k and δ G,k are positive design parameters;

设计切换扰动观测器为The switching disturbance observer is designed as

Figure BDA0002778558790000053
Figure BDA0002778558790000053

其中，ξn是中间变量，Lk是正的设计参数；where ξ n is an intermediate variable and L k is a positive design parameter;

步骤4：根据步骤3中(13)得到的控制量uc,k，返回到系统模型(1)，对系统输出y进行跟踪控制。Step 4: According to the control variable uc ,k obtained in (13) in step 3, return to the system model (1), and perform tracking control on the system output y.

有益效果beneficial effect

本发明提出的一种基于复合学习的非线性切换系统自适应滑模控制方法。该方法考虑非线性切换系统存在不确定性、外界干扰和输入非线性，通过模型转换获取输入死区模型。同时采用神经网络和扰动观测器分别对非线性函数和复合干扰进行估计，通过构造预测误差对学习效果进行评价，进而调节神经网络权重自适应更新律和切换扰动观测器。基于动态逆技术框架和复合学习策略设计了自适应滑模切换控制器，时变的滑模增益函数提升了控制器鲁棒性，便于工程实现。有益效果如下：The invention proposes an adaptive sliding mode control method for nonlinear switching systems based on compound learning. The method considers the existence of uncertainty, external disturbance and input nonlinearity in the nonlinear switching system, and obtains the input dead zone model through model conversion. At the same time, the neural network and the disturbance observer are used to estimate the nonlinear function and the compound disturbance respectively, and the learning effect is evaluated by constructing the prediction error, and then the adaptive update law of the neural network weight and the switching disturbance observer are adjusted. An adaptive sliding mode switching controller is designed based on the dynamic inverse technology framework and compound learning strategy. The time-varying sliding mode gain function improves the robustness of the controller and facilitates engineering implementation. The beneficial effects are as follows:

(1)基于平行估计模型构造了预测误差，基于该误差设计神经网络权重更新律，提高不确定性学习精度，便于工程应用；(1) The prediction error is constructed based on the parallel estimation model, and the weight update law of the neural network is designed based on the error to improve the uncertainty learning accuracy and facilitate engineering applications;

(2)设计非线性切换扰动观测器，对外界时变干扰和输入未知死区带来的不利影响进行了有效的估计补偿；(2) The nonlinear switching disturbance observer is designed to effectively estimate and compensate the adverse effects of external time-varying disturbances and input unknown dead zone;

(3)基于预测误差，采用一种改进的时变增益滑模进行控制器设计，减小了控制切换时的抖振；(3) Based on the prediction error, an improved time-varying gain sliding mode is used to design the controller, which reduces the chattering during control switching;

(4)将滑模面信号引入到神经网络和扰动观测器设计中，通过两者的交互协同实现对未知非线性函数和外界时变干扰的有效估计。(4) The sliding mode surface signal is introduced into the design of the neural network and the disturbance observer, and the effective estimation of the unknown nonlinear function and the external time-varying disturbance is realized through the interaction and synergy of the two.

附图说明Description of drawings

图1为本发明实施流程图。FIG. 1 is a flow chart of the implementation of the present invention.

具体实施方式Detailed ways

现结合实施例、附图对本发明作进一步描述：The present invention will now be further described in conjunction with the embodiments and accompanying drawings:

参照图1，本发明基于复合学习的非线性切换系统自适应滑模控制方法具体步骤如下：1, the specific steps of the adaptive sliding mode control method of the nonlinear switching system based on compound learning of the present invention are as follows:

步骤1：考虑变体飞行器机翼摇滚模型Step 1: Consider the variant aircraft wing rock model

Figure BDA0002778558790000061
Figure BDA0002778558790000061

其中，φ、

Figure BDA0002778558790000062
和
Figure BDA0002778558790000063
分别是滚转角、滚转角速率和滚转角加速度，u是控制输入；Among them, φ,
Figure BDA0002778558790000062
and
Figure BDA0002778558790000063
are the roll angle, roll angular rate and roll angular acceleration, respectively, and u is the control input;

模型中各种系数定义为The various coefficients in the model are defined as

Figure BDA0002778558790000064
Figure BDA0002778558790000064

其中，a1到a5是和攻角相关的变量，c1和c2是由后掠角决定的常数；Among them, a 1 to a 5 are variables related to the angle of attack, and c 1 and c 2 are constants determined by the sweep angle;

定义状态量x(t)＝[x1,x2]T∈R2，其中x1＝φ，

Figure BDA0002778558790000065
以后掠角作为切换信号，可将变体飞行器机翼摇滚模型转化为2阶单输入单输出非线性切换系统Define the state quantity x(t)=[x 1 ,x 2 ] T ∈ R 2 , where x 1 =φ,
Figure BDA0002778558790000065
Using the sweep angle as the switching signal, the wing rock model of the variant aircraft can be transformed into a second-order single-input single-output nonlinear switching system

Figure BDA0002778558790000066
Figure BDA0002778558790000066

其中，

Figure BDA0002778558790000067
是系统状态向量；uσ(t)∈R是系统输入，y∈R是系统输出；函数σ(t)∈{1,2}是切换信号；
Figure BDA0002778558790000068
是未知非线性函数；d1(t)＝0.1cos(t2)，d2(t)＝0.1sin(t)是引入的外部干扰；in,
Figure BDA0002778558790000067
is the system state vector; u σ(t) ∈ R is the system input, y ∈ R is the system output; the function σ(t) ∈ {1,2} is the switching signal;
Figure BDA0002778558790000068
is the unknown nonlinear function; d 1 (t)=0.1cos(t 2 ), d 2 (t)=0.1 sin(t) is the external disturbance introduced;

步骤2：将系统输入非线性描述为Step 2: Describe the system input nonlinearity as

Figure BDA0002778558790000071
Figure BDA0002778558790000071

其中，uv,k∈R是带死区的输入，

Figure BDA0002778558790000072
bl,1＝0.5，br,1＝0.1，
Figure BDA0002778558790000073
bl,2＝0.8，br,2＝0.3；where u v,k ∈ R is the input with dead zone,
Figure BDA0002778558790000072
b l,1 = 0.5, b r,1 = 0.1,
Figure BDA0002778558790000073
b l,2 = 0.8, b r,2 = 0.3;

可将(2)进一步描述为(2) can be further described as

Figure BDA0002778558790000074
Figure BDA0002778558790000074

其中in

Figure BDA0002778558790000075
Figure BDA0002778558790000075

信号uk存在如下关系The signal u k has the following relationship

Figure BDA0002778558790000076
Figure BDA0002778558790000076

其中

Figure BDA0002778558790000077
是uv,k的上界值；in
Figure BDA0002778558790000077
is the upper bound value of u v,k ;

则系统(1)可进一步写为Then system (1) can be further written as

Figure BDA0002778558790000078
Figure BDA0002778558790000078

步骤3：针对未知函数

Figure BDA0002778558790000079
用神经网络来逼近Step 3: For unknown functions
Figure BDA0002778558790000079
Approximate with a neural network

Figure BDA00027785587900000710
Figure BDA00027785587900000710

其中，

Figure BDA00027785587900000711
是神经网络最优权重向量，
Figure BDA00027785587900000712
是神经网络基函数向量，εf,k是神经网络残差且存在
Figure BDA00027785587900000713
是正常数；in,
Figure BDA00027785587900000711
is the optimal weight vector of the neural network,
Figure BDA00027785587900000712
is the neural network basis function vector, ε f,k is the neural network residual and exists
Figure BDA00027785587900000713
is a normal number;

则

Figure BDA00027785587900000714
的估计值可写为but
Figure BDA00027785587900000714
The estimated value of can be written as

Figure BDA00027785587900000715
Figure BDA00027785587900000715

其中，

Figure BDA0002778558790000081
和
Figure BDA0002778558790000082
是神经网络最优权重向量估计值；in,
Figure BDA0002778558790000081
and
Figure BDA0002778558790000082
is the estimated value of the optimal weight vector of the neural network;

定义Δuk＝uv,k-uc,k，则x2的导数可写为Define Δu k =u v,k -u c,k , then the derivative of x 2 can be written as

Figure BDA0002778558790000083
Figure BDA0002778558790000083

其中，

Figure BDA0002778558790000084
步骤4：针对非线性切换系统(1)，基于复合学习策略设计自适应滑模控制器；in,
Figure BDA0002778558790000084
Step 4: Design an adaptive sliding mode controller based on a composite learning strategy for the nonlinear switching system (1);

定义输出跟踪误差

Figure BDA0002778558790000085
其中e＝x1-yd，yd是控制参考指令；Define Output Tracking Error
Figure BDA0002778558790000085
Where e=x 1 -y d , y d is the control reference command;

设计滑模面为The sliding surface is designed as

s＝[ΛT 1]E (10)s=[Λ T 1]E (10)

其中，Λ＝τ，τ>0；Among them, Λ=τ, τ>0;

滑模面s的导数为The derivative of the sliding surface s is

Figure BDA0002778558790000086
Figure BDA0002778558790000086

其中，

Figure BDA0002778558790000087
in,
Figure BDA0002778558790000087

设计控制器为Design the controller as

Figure BDA0002778558790000088
Figure BDA0002778558790000088

其中in

Figure BDA0002778558790000089
Figure BDA0002778558790000089

Figure BDA00027785587900000810
Figure BDA00027785587900000810

Figure BDA00027785587900000811
Figure BDA00027785587900000811

其中，

Figure BDA00027785587900000812
是Dk(t)的估计值，βk是正的设计参数，mk是滑模增益函数；in,
Figure BDA00027785587900000812
is the estimated value of D k (t), β k is a positive design parameter, and m k is the sliding mode gain function;

构造预测误差z2NN为Constructing the prediction error z 2NN as

Figure BDA0002778558790000091
Figure BDA0002778558790000091

其中，

Figure BDA0002778558790000092
可由如下的平行估计模型得到in,
Figure BDA0002778558790000092
It can be obtained by the following parallel estimation model

Figure BDA0002778558790000093
Figure BDA0002778558790000093

其中，

Figure BDA0002778558790000094
λk是正的设计参数；in,
Figure BDA0002778558790000094
λk is a positive design parameter;

设计滑模增益函数为The sliding mode gain function is designed as

mk＝-γz,kλkz2NN (18)m k = -γ z,k λ k z 2NN (18)

其中，γz,k是正的设计参数；where γz,k is a positive design parameter;

设计神经网络权重更新律为The weight update law of the designed neural network is

Figure BDA0002778558790000095
Figure BDA0002778558790000095

其中，γf,k和δf,k是正的设计参数；where γ f,k and δ f,k are positive design parameters;

设计切换扰动观测器为The switching disturbance observer is designed as

Figure BDA0002778558790000096
Figure BDA0002778558790000096

其中，ξ2是中间变量，Lk是正的设计参数；where ξ 2 is an intermediate variable, and L k is a positive design parameter;

步骤4：根据步骤3中(12)得到的控制量uc,k，返回到变体飞行器机翼摇滚模型(1)，对滚转角φ进行跟踪控制。Step 4: According to the control amount uc ,k obtained in (12) in step 3, return to the rock model (1) of the variant aircraft wing, and perform tracking control on the roll angle φ.

本发明未详细说明部分属于领域技术人员公知常识。The parts of the present invention that are not described in detail belong to the common knowledge of those skilled in the art.

Claims (1)

1.一种基于复合学习的非线性切换系统自适应滑模控制方法，其特征在于步骤如下：1. a nonlinear switching system adaptive sliding mode control method based on compound learning is characterized in that the steps are as follows: 步骤1：考虑一类单输入单输出非线性能控标准型切换系统Step 1: Consider a class of single-input single-output nonlinear controllable standard switching systems
Figure FDA0003531039510000011
Figure FDA0003531039510000011
 其中，
Figure FDA0003531039510000012
是系统状态向量；uσ(t)∈R是系统输入，y∈R是系统输出；函数σ(t):[0,∞)→M＝{1,2,...,m}是切换信号，且σ(t)＝k时表示第k个子系统是激活的；
Figure FDA0003531039510000013
是关于
Figure FDA0003531039510000014
的未知平滑函数，
Figure FDA0003531039510000015
是关于
Figure FDA0003531039510000016
的未知非零平滑函数；dσ(t)(t)是外部未知干扰；in,
Figure FDA0003531039510000012
is the system state vector; u σ(t) ∈ R is the system input, y∈R is the system output; the function σ(t):[0,∞)→M={1,2,...,m} is the switching signal, and when σ(t)=k, it means that the kth subsystem is active;
Figure FDA0003531039510000013
its about
Figure FDA0003531039510000014
The unknown smoothing function of ,
Figure FDA0003531039510000015
its about
Figure FDA0003531039510000016
The unknown non-zero smooth function of ; d σ(t) (t) is the external unknown disturbance; 步骤2：将系统输入非线性描述为Step 2: Describe the system input nonlinearity as
Figure FDA0003531039510000017
Figure FDA0003531039510000017
 其中，uv,k∈R是带死区的输入，
Figure FDA0003531039510000018
br,k和bl,k是未知的正常数；where u v,k ∈ R is the input with dead zone,
Figure FDA0003531039510000018
b r,k and b l,k are unknown positive constants; 可将(2)进一步描述为(2) can be further described as
Figure FDA00035310395100000112
Figure FDA00035310395100000112
 其中in
Figure FDA0003531039510000019
Figure FDA0003531039510000019
 信号uk存在如下关系The signal u k has the following relationship
Figure FDA00035310395100000110
Figure FDA00035310395100000110
 其中
Figure FDA00035310395100000111
是uv,k的上界值；in
Figure FDA00035310395100000111
is the upper bound value of u v,k ; 则系统(1)可进一步写为Then system (1) can be further written as
Figure FDA0003531039510000021
Figure FDA0003531039510000021
 其中，
Figure FDA0003531039510000022
in,
Figure FDA0003531039510000022
 步骤3：针对未知函数
Figure FDA00035310395100000222
和
Figure FDA0003531039510000023
用神经网络来逼近Step 3: For unknown functions
Figure FDA00035310395100000222
and
Figure FDA0003531039510000023
Approximate with a neural network
Figure FDA0003531039510000024
Figure FDA0003531039510000024
Figure FDA0003531039510000025
Figure FDA0003531039510000025
 其中，
Figure FDA0003531039510000026
和
Figure FDA0003531039510000027
是神经网络最优权重向量，
Figure FDA00035310395100000223
和
Figure FDA0003531039510000028
是神经网络基函数向量，εf,k和εG,k是神经网络残差且存在
Figure FDA0003531039510000029
和
Figure FDA00035310395100000210
和
Figure FDA00035310395100000211
是正常数；in,
Figure FDA0003531039510000026
and
Figure FDA0003531039510000027
is the optimal weight vector of the neural network,
Figure FDA00035310395100000223
and
Figure FDA0003531039510000028
is the neural network basis function vector, ε f,k and ε G,k are the neural network residuals and exist
Figure FDA0003531039510000029
and
Figure FDA00035310395100000210
and
Figure FDA00035310395100000211
is a normal number; 则
Figure FDA00035310395100000212
和
Figure FDA00035310395100000213
的估计值可写为but
Figure FDA00035310395100000212
and
Figure FDA00035310395100000213
The estimated value of can be written as
Figure FDA00035310395100000214
Figure FDA00035310395100000214
Figure FDA00035310395100000215
Figure FDA00035310395100000215
 其中，
Figure FDA00035310395100000216
和
Figure FDA00035310395100000217
是神经网络最优权重向量估计值；in,
Figure FDA00035310395100000216
and
Figure FDA00035310395100000217
is the estimated value of the optimal weight vector of the neural network; 定义Δuk＝uv,k-uc,k，则xn的导数可写为Define Δu k =u v,k -u c,k , then the derivative of x n can be written as
Figure FDA00035310395100000218
Figure FDA00035310395100000218
 其中，
Figure FDA00035310395100000219
Figure FDA00035310395100000220
in,
Figure FDA00035310395100000219
Figure FDA00035310395100000220
 步骤4：针对非线性切换系统(1)，基于复合学习策略设计自适应滑模控制器；Step 4: Design an adaptive sliding mode controller based on a composite learning strategy for the nonlinear switching system (1); 定义输出跟踪误差
Figure FDA00035310395100000221
其中e＝x1-yd，yd是控制参考指令；Define Output Tracking Error
Figure FDA00035310395100000221
Where e=x 1 -y d , y d is the control reference command; 设计滑模面为The sliding surface is designed as s＝[ΛT 1]E (11)s=[Λ T 1]E (11) 其中，Λ＝[τn-1,(n-1)τn-2,...,(n-1)τ]T，τ＞0；Among them, Λ=[τ n-1 ,(n-1)τ n-2 ,...,(n-1)τ] T , τ>0; 滑模面s的导数为The derivative of the sliding surface s is
Figure FDA0003531039510000031
Figure FDA0003531039510000031
 其中，
Figure FDA0003531039510000032
in,
Figure FDA0003531039510000032
 设计控制器为Design the controller as
Figure FDA0003531039510000033
Figure FDA0003531039510000033
 其中in
Figure FDA0003531039510000034
Figure FDA0003531039510000034
Figure FDA0003531039510000035
Figure FDA0003531039510000035
Figure FDA0003531039510000036
Figure FDA0003531039510000036
 其中，
Figure FDA0003531039510000037
是Dk(t)的估计值，βk是正的设计参数，mk是滑模增益函数；in,
Figure FDA0003531039510000037
is the estimated value of D k (t), β k is a positive design parameter, and m k is the sliding mode gain function; 构造预测误差znNN为The prediction error z nNN is constructed as
Figure FDA0003531039510000038
Figure FDA0003531039510000038
 其中，
Figure FDA0003531039510000039
可由如下的平行估计模型得到in,
Figure FDA0003531039510000039
It can be obtained by the following parallel estimation model
Figure FDA00035310395100000310
Figure FDA00035310395100000310
 其中，
Figure FDA00035310395100000311
λk是正的设计参数；in,
Figure FDA00035310395100000311
λk is a positive design parameter; 设计滑模增益函数为The sliding mode gain function is designed as mk＝-γz,kλkznNN (19)m k = -γ z,k λ k z nNN (19) 其中，γz,k是正的设计参数；where γz,k is a positive design parameter; 设计神经网络权重更新律为The weight update law of the designed neural network is
Figure FDA0003531039510000041
Figure FDA0003531039510000041
Figure FDA0003531039510000042
Figure FDA0003531039510000042
 其中，γf,k，γG,k，δf,k和δG,k是正的设计参数；where γ f,k , γ G,k , δ f,k and δ G,k are positive design parameters; 设计切换扰动观测器为The switching disturbance observer is designed as
Figure FDA0003531039510000043
Figure FDA0003531039510000043
 其中，ξn是中间变量，Lk是正的设计参数；where ξ n is an intermediate variable and L k is a positive design parameter; 步骤4：根据步骤3中(13)得到的控制量uc,k，返回到系统模型(1)，对系统输出y进行跟踪控制。Step 4: According to the control variable uc ,k obtained in (13) in step 3, return to the system model (1), and perform tracking control on the system output y.
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