Adaptive Neural Output Feedback Trajectory Tracking Control for USVs Under False-data-injection Attacks
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摘要: 本文主要研究网络环境下无人水面船舶 (Unmanned surface vessels, USVs) 遭受虚假数据注入式 (False-data-injection, FDI) 攻击的跟踪控制问题. 其中, 内部和外部不确定以及输入饱和约束等实际因素均考虑在设计中. 在控制设计过程中, 为避免将船舶速度的攻击信号引入闭环系统, 采用分类重构思想, 构造一种新的神经网络 (Neural network, NN) 状态观测器, 同时重构船舶速度和攻击信号. 进一步, 在backstepping 设计框架下, 利用重构的攻击信号补偿USVs 运动学通道因虚假数据注入式攻击引起的非匹配不确定项. 在动力学设计通道中, 利用自适应神经技术和单参数学习法, 重构由内部和外部不确定组成的复合不确定部分, 进而提出自适应神经输出反馈控制方案. 理论分析表明, 即便在FDI 攻击、内外不确定以及执行器饱和约束的情况下, 所提控制方案仍能迫使USVs 跟踪给定的参考轨迹. 同时, 仿真和比较结果证实了所提控制方案的有效性和优越性.Abstract: This paper investigates the tracking control issue of unmanned surface vessels (USVs) under the attack of false-data-injection (FDI) in the network environment, and these actual factors such as internal and external uncertainties and input saturation constraints are also considered in the design. In the control design, to avoid FDI attack signals from the velocity channel being introduced into the closed-loop system, the idea of classification reconstruction is developed. Based on this idea, a novel neural network (NN) state observer is constructed to reconstruct vessels velocity and FDI attack signals. Furthermore, under the backstepping design framework, utilizing the reconstructed attack signals to compensate the mismatched uncertainties in USVs kinematic channel, which is caused by false-data-injection attacks. In the dynamic design channel, adaptive neural technology and single parameter learning method are used to reconstruct the lumped uncertain parts, which consist of internal and external uncertainties, and then the adaptive neural output feedback control scheme is proposed. The theoretical analysis shows that the proposed control scheme can make USVs track a given reference trajectory, even in the presence of FDI attacks, internal and external uncertainties, and actuator saturation constraints. At the same time, the simulation and comparison results illustrate the effectiveness and superiority of the proposed control scheme.
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图 3 轨迹误差${{\boldsymbol{S}}}_1$对比图
Fig. 3 Comparison chart of trajectory errors ${{\boldsymbol{S}}}_1$
图 4 控制输入${\boldsymbol {\tau}}$对比图
Fig. 4 Comparison chart of control inputs${\boldsymbol {\tau}}$
图 5 参数估计值$\hat{{\boldsymbol{\vartheta}}}$
Fig. 5 Parameter estimation values$\hat{{\boldsymbol{\vartheta}}}$
图 6 速度估计误差$\tilde{{{\boldsymbol{v}}}}$对比
Fig. 6 Comparison of velocity estimation errors$\tilde{{{\boldsymbol{v}}}}$
图 7 位置估计误差$\tilde{{\boldsymbol{\eta}}}$对比
Fig. 7 Comparison of position estimation errors$\tilde{{\boldsymbol{\eta}}}$
图 8 有无${\boldsymbol{\sigma}}$时${{\boldsymbol{S}}}_1$对比
Fig. 8 Comparison of${{\boldsymbol{S}}}_1$with or without${\boldsymbol{\sigma}}$
图 9 有无${\boldsymbol{\sigma}}$时$\hat{{{\boldsymbol{v}}}}$对比
Fig. 9 Comparison of$\hat{{{\boldsymbol{v}}}}$with or without${\boldsymbol{\sigma}}$
表 1 设计参数及初始值
Table 1 Design parameters and initial values
指标 项式 数值 观测器 $ k $ 12 $ k_1 $ 0.1 $ k_2 $ 210 $ k_w $ 0.1 $ k_o $ 6 ${\boldsymbol{\Lambda}}_o$ 10$ \times $diag{8, 8, 2} 控制律 $ {\boldsymbol {c}}_1 $ diag{1.3, 1.4, 5.0} $ {\boldsymbol {c}}_2 $ 5$ \times $diag{9, 8, 10} $\omega_f$ 30 $ {\boldsymbol{\Lambda}}_c $ diag{5, 5, 5} $ {\boldsymbol {k}}_c $ 0.1$ \times $diag{1, 1, 1} $ {\boldsymbol{\varsigma}} $ diag{0.01, 0.01, 0.01} 环境扰动 $ {\boldsymbol{\wp}} $ diag{−2, −2, −2} $ {\boldsymbol{\Upsilon}} $ 2 × [1.5, 1.5, 1.0]T 输入饱和限制 $ {\boldsymbol{\kappa}} $ [0.9, 0.9, 0.9]T $ {\boldsymbol{\tau}}_{m} $ [10, 10, 5]T $Q_0$ 0.3 $ {\boldsymbol {k}}_Q $ diag{3, 2, 1} $ {\boldsymbol {k}}_{w_\tau} $ diag{10, 10, 10} 初始值 $ {\boldsymbol{\eta}}(0) $ [−1.0, −1.0, 0.1]T $ \hat{{\boldsymbol{\eta}}}(0) $ [−1.0, −1.0, 0.1]T $ {\boldsymbol {v}}(0) $ [0, 0, 0]T $ {\boldsymbol {S}}(0) $ [0.02, 0.02, 0.01]T $ \hat{\boldsymbol W}_o(0) $ [0.1, 0.1, 0.2]T $ \hat{\boldsymbol W}_c(0) $ [0.1, 0.1, 0.2]T 
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表 2 不同攻击下的控制性能对比
Table 2 Comparison of control performance under different attacks
指标 项式 未攻击 1 倍攻击 4 倍攻击 8 倍攻击 $\int_{0}^{t}\frac{\tau_i(t_f)}{t_f\;+\;0.001}{\rm d}t_f$ $ \tau_1 $ 1.524 1.522 1.535 1.605 $ \tau_2 $ 1.245 1.270 1.428 1.742 $ \tau_3 $ 0.476 0.477 0.484 0.495 $ \int_{0}^{t}|S_{1,i}|{\rm d}t_f $ $ S_{1,1} $ 3.334 3.263 3.097 2.986 $ S_{1,2} $ 3.333 3.302 3.235 3.191 $ S_{1,3} $ 0.412 0.412 0.413 0.412 $\int_{0}^{t}| \tilde{v}_i|{\rm d}t_f$ $ \tilde{v}_1 $ 0.072 0.758 3.052 6.108 $ \tilde{v}_2 $ 0.074 0.632 2.519 5.065 $ \tilde{v}_3 $ 0.008 0.018 0.093 0.193
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