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摘要: 研究了控制信号被恶意篡改的信息物理系统的安全控制问题. 首先, 提出一种改进果蝇优化核极限学习机算法(Kernel extreme learning machine with improved fruit fly optimization algorithm, IFOA-KELM)对攻击信号进行重构. 然后, 将所得重构信号作为系统扰动加以补偿, 进而设计模型预测控制策略, 并给出了使被控系统是输入到状态稳定的条件. 另外, 本文从攻击者角度建立优化模型得到最优攻击策略用以生成足够的受攻击数据, 基于此数据, 来训练改进果蝇优化核极限学习机算法. 最后, 使用弹簧−质量−阻尼系统进行仿真, 验证了改进果蝇优化极限学习机算法和所提安全控制策略的有效性.Abstract: This paper investigates the security control problem of cyber-physical systems whose control signals are maliciously tampered. Firstly, a kernel extreme learning machine with improved fruit fly optimization (IFOA-KELM) algorithm is proposed to reconstruct the attack signal. Secondly, with the reconstructed signal treated as disturbance, a model predictive control strategy is designed to secure the system, and a condition that guarantees the input-to-state stability of the attacked system is given. In addition, to train the proposed algorithm, enough data of the system attacked with an optimal strategy is generated. This strategy is obtained by solving an optimization problem from the attacker＇ s perspective. Finally, a numerical example of the spring-mass-damping system is illustrated to verify the effectiveness of the IFOA-KELM algorithm and the proposed control strategy.
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图 8 IFOA-KELM测试样本绝对误差
Fig. 8 The error between the real attack and the attack learned by IFOA-KELM
图 11 LSSVM测试样本绝对误差
Fig. 11 The error between the real attack and the attack learned by LSSVM
图 9 FOA-KELM测试样本绝对误差
Fig. 9 The error between the real attack and the attack learned by FOA-KELM
图 10 PSO-BP测试样本绝对误差
Fig. 10 The error between the real attack and the attack learned by PSO-BP
图 13 受攻击系统引入MPC前后的状态轨迹
Fig. 13 The state trajectory of the attacked system with MPC and without MPC
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