基于自适应模糊神经网络的非线性系统模型预测控制

doi:10.11949/0438-1157.20191531

摘要/Abstract

摘要：

针对非线性动态系统的控制问题，提出了一种基于自适应模糊神经网络(adaptive fuzzy neural network, AFNN)的模型预测控制(model predictive control, MPC)方法。首先，在离线建模阶段，AFNN采用规则自分裂技术产生初始模糊规则，采用改进的自适应LM学习算法优化网络参数；然后，在实时控制过程，AFNN根据系统输出和预测输出之间的误差调整网络参数，从而为MPC提供一个精确的预测模型；进一步，AFNN-MPC利用带有自适应学习率的梯度下降寻优算法求解优化问题，在线获取非线性控制量，并将其作用到动态系统实施控制。此外，给出了AFNN-MPC的收敛性和稳定性证明，以保证其在实际工程中的成功应用。最后，利用数值仿真和双CSTR过程进行实验验证。结果表明，AFNN-MPC能够取得优越的控制性能。

关键词: 非线性系统, 动态建模, 模型预测控制, 过程控制, 模糊神经网络, 自适应学习率

Abstract:

Aiming at the control problem of nonlinear dynamic systems, a model predictive control (MPC) method based on adaptive fuzzy neural network (AFNN) was proposed. First, in the offline modeling phase, a rule automatic splitting technique is used to generate initial fuzzy rules, and an improved adaptive LM learning algorithm is adopted to optimize network parameters. Second, in the real-time control process, the network parameters of the AFNN are adjusted according to the error between the system output and the predicted output, so that providing an accurate prediction model for the MPC. Furthermore, the gradient descent optimization algorithm with adaptive learning rate is used to solve optimization problem and obtain the nonlinear control law online, which is applied to control the dynamic system. In addition, the convergence and stability analysis of the proposed AFNN-MPC are given to ensure its successful application in practical engineering. Finally, numerical simulation and two-CSTR process experiments are used to verify the effectiveness of AFNN-MPC algorithm. The results show that the proposed AFNN-MPC has superior control performance.

Key words: nonlinear systems, dynamic modeling, model predictive control, process control, fuzzy neural network, adaptive learning rate

中图分类号:

TP 273

周红标, 张钰, 柏小颖, 刘保连, 赵环宇. 基于自适应模糊神经网络的非线性系统模型预测控制[J]. 化工学报, 2020, 71(7): 3201-3212.

Hongbiao ZHOU, Yu ZHANG, Xiaoying BAI, Baolian LIU, Huanyu ZHAO. Model predictive control of nonlinear system based on adaptive fuzzy neural network[J]. CIESC Journal, 2020, 71(7): 3201-3212.

图/表 17

图1 MIMO型FNN的拓扑结构

Fig.1 Architecture of MIMO-type FNN

表1 RAS的算法流程

Table 1 Algorithm flow of RAS

Algorithm 1: RAS
Set the cluster number r = 1
Calculate the center of the first cluster v₁;
Calculate the mean variance ${\overset{ˉ}{g}}_{j}$ according to Eq. (10) and Eq.(11);
while ${\overset{ˉ}{g}}_{I}$ >g_thdo
Split the Ith cluster into two new centers;
r = r + 1;
while current iteration times t₁<T₁ & \|J_m(t₁) - J_m(t₁-1)\| > εdo
forj=1:rdo
Find input training samples for cluster v_j ;
Calculate the center of cluster v_j according to Eq. (13);
end
t₁++;
end while
end while
return r clusters;

表1 RAS的算法流程

Table 1 Algorithm flow of RAS

Algorithm 1: RAS
Set the cluster number r = 1
Calculate the center of the first cluster v₁;
Calculate the mean variance ${\overset{ˉ}{g}}_{j}$ according to Eq. (10) and Eq.(11);
while ${\overset{ˉ}{g}}_{I}$ >g_thdo
Split the Ith cluster into two new centers;
r = r + 1;
while current iteration times t₁<T₁ & \|J_m(t₁) - J_m(t₁-1)\| > εdo
forj=1:rdo
Find input training samples for cluster v_j ;
Calculate the center of cluster v_j according to Eq. (13);
end
t₁++;
end while
end while
return r clusters;

表2 AFNN的算法流程

Table 2 Algorithm flow of AFNN

Algorithm 2: AFNN
Set the maximum iteration times T_max;
Obtain r clusters using RAS algorithm;
Create an initial four-layer FNN;
while current iteration times t<T_max do
for p=1:Pdo
Calculate the outputs of FNN y_p(t) by Eq.(8);
Make the error of each sample e_p(t) by Eq. (15);
Make the submatrices ψ_p(t) by Eq. (21);
Make the subvectors ω_p(t) by Eq. (22);
end
Update the adaptive learning rate η(t) by Eq. (18);
Make the quasi-Hessian matrix Ψ(t) by Eq. (19);
Make the gradient vector Ω(t) by Eq. (20);
Update the parameter vector Θ(t) by Eq. (17);
t++;
end while

图2 AFNN-MPC的控制架构

Fig.2 Control architecture of AFNN-MPC

表3 AFNN-MPC算法流程

Table 3 Algorithm flow of AFNN-MPC

Algorithm 3: AFNN-MPC
Generate offline data using GMN signal;
Develop AFNN predictive model offline;
Initialize the parameters of MPC;
fork←1 to ndo
Sample the plant output y(k);
Update the parameters of AFNN by Eq.(24)—Eq.(26);
Calculate the prediction outputs ?(k+h);
while current iteration times t_c<T_cdo
Compute the control increment Δu^k(t_c) by Eq. (39);
Compute the control signal u^k(t_c) by Eq. (31);
t_c++;
end while
Apply u(k+1) to the controlled process;
end

图3 AFNN结构辨识阶段的MMSE曲线

Fig.3 MMSE curve during AFNN structure identification

图4 AFNN参数学习阶段的RMSE曲线

Fig.4 RMSE curve during AFNN parameter training

图5 测试样本的预测结果

Fig.5 Prediction results of testing samples

图6 AFNN-MPC的控制效果

Fig.6 Control performance of AFNN-MPC

图7 控制信号u的变化情况

Fig.7 Change of the control signal u

图8 两级CSTR过程的示意图

Fig.8 Schematic of two-CSTR process

图9 GMN激励信号和CSTR响应信号

Fig.9 GMN excitation signal and CSTR response signal

图10 AFNN的RMSE和建模结果

Fig.10 RMSE and modeling results of AFNN

图11 AFNN-MPC的控制结果

Fig.11 Control results of AFNN-MPC

图12 控制信号Qcw1和Qcw2的变化情况

Fig.12 Changes of control signal Qcw1 and Qcw2

表4 不同算法在To1上的控制结果

Table 4 Control results of different algorithms for To1

Controller	No.	IAE	ISE	Dev^max
PID	-	147.20	110.22	3.05
FLC	49	139.45	102.71	2.78
GPC	-	135.58	107.29	2.80
FNN-MPC	20	130.48	100.43	2.66
WFNN-MPC	20	132.66	101.10	2.68
AFNN-MPC	14	126.00	95.31	2.59

表5 不同算法在To2上的控制结果

Table 5 Control results of different algorithms for To2

Controller	No.	IAE	ISE	Dev^max
PID	-	180.72	170.82	3.28
FLC	49	160.04	158.90	2.99
GPC	-	175.13	156.29	3.01
FNN-MPC	20	156.72	149.64	2.81
WFNN-MPC	20	152.54	151.08	2.82
AFNN-MPC	14	149.66	144.70	2.70

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