Zero-Sum Game Based Optimal Secure Control

This chapter is focused on the optimal secure control scheme for CPSs based on the game-theoretical approach. The physical plant is described as a linear time-invariant discrete-time model with Gaussian noises. Assume the controller and the actuator are distributed and connected over communication network. The attacker can hijack the network and modify actuator readings to deteriorate the system performance. The controller (i.e., the defender) and the attacker are described as two players in the zero-sum game. An infinite-horizon quadratic cost index, which the defender wants to minimize yet the attacker intends to maximize, is defined. Combining the dynamic programming and the game theory, the optimal defense policy and the attack scheme are simultaneously derived to achieve a Nash balance. The main contributions of this chapter can be summarized as follows.