Dynamic Output Feedback Linear Quadratic Control for CPSs Under Sparse Attacks

In this article, a linear quadratic (LQ) control based on dynamic output feedback (DOF) strategy is proposed for cyber–physical systems (CPSs) under sparse actuator and sensor attacks. The control scheme is divided into three steps. First, the studied system is transformed into a set of hybrid systems based on all possible attack sets. Second, the DOF LQ (dLQ) control scheme is studied for the case of the correct attack set, including analyzing the impact of the similarity transformation on the cost of the dLQ, determining the optimal explicit form of the similarity transformation, and giving the computational expression for the unique observable saddle point of the dLQ. Finally, two online attack detection mechanisms are proposed: 1) adaptive switching mechanism (ASM) and 2) improved ASM (IASM). The difference between the two mechanisms is that IASM detects attacks faster. The hybrid control scheme combining dLQ control method with each of the two mechanisms ensures the asymptotic stability of the closed-loop system. Distinguishing from the classical data-based optimal control method which calculates the system states online from time to time, the hybrid control scheme proposed in this article only needs to solve for the system states during a time period when the control mode is switched, which greatly reduces the computational complexity. The effectiveness and superiority of the proposed method are illustrated by two simulation examples, respectively.