###### Abstract  
With the rapid growth of distributed energy sources, power grid has become a flexible and complex networked control system. However, it increases the chances of being a denial-of-service attack, which degrades the performance of the power grid, even causing cascading failures. To mitigate negative effects from denial-of-service attack and enhance the reliability of the power grid, we propose a networked control system structure based optimization scheme that is derived from a Stackelberg game model for the frequency regulation of a power grid with distributed energy sources. In the proposed game model, both denial-of-service attacker and control system designer as a defender are considered without using any analytical model. For defenders, we propose a sparse neural network based DES control and system structure design scheme. The neural network is used to approximate the desired control output and reinforce signals for the improvements of short- and long-term performance. It also introduces the sparse regulation of column grouping in the neural network learning process to explore the structure of control system that involves the placement of sensor, distributed energy sources actuator, and communication topology. For denial-of-service attackers, the related attack constraints and attack rewards are established. The solution of game equilibrium is considered as an optimal solution for both denial-of-service attack strategy and control structure. An offline optimization algorithm is proposed to solve the game equilibrium. The effectiveness of proposed scheme is verified by two cases, which illustrate the optimal solutions of both control structure and denial-of-service attack strategy. DoS attack; reinforcement learning; neural network; distributed energy resources; power grid; smart grid +
Footnote †: journal: Applied  
destroy control operations in real time [5]. In particular, blocking real-time control signals can cause the instability of the power grid [6]. A lot of security control approaches, such as stochastic time delay system, triggering strategy, and game theory, have been applied to the prevention of DoS attacks in power grid. **Stochastic time delay system:** In a stochastic time delay system, DoS is modeled as a stochastic process with a delay in the signal. Subject to intermittent DoS attacks, [PERSON] et al. proposed a decentralized solution of adaptive output feedback control for a power grid [7]. A switching-type state estimator is presented to estimate the state of power grid by using discontinuous output measurement. [PERSON] et al. modeled DoS attacks as a Markov process that converted DoS attacks to stochastic noises of NCSs first [8]. Then, a resilient control model was used to process the converted noises. **Triggering strategy:** Event-triggering time-sequence of control signal is adopted to reduce communication costs in the system. The triggering time sequence is able to defend against DoS attacks. [PERSON] et al. proposed a resilient event-triggering based frequency control method for power system control in energy-limited DoS attacks [1]. The proposed event-triggered communication scheme can tolerate a certain degree of data loss in the open communication induced by energy-limited DoS attacks. [PERSON] et al. designed a periodically resilient event-triggering communication scheme to identify DoS attacks initiated by power-constrained pulse-width-modulated jammers [9]. **Game theory:** In game theory based cyber security model, a game model is constructed for both DoS attacker and defender to obtain a Nash equilibrium as an optimal solution. [PERSON] et al. modeled the interactions between the transmission power of sensors and the interference power of DoS attacker by a signal-to-interference-and-noise-ratio (SINR) based network [10]. A modified Nash Q-learning algorithm was proposed to analyze the related interactions as well. [PERSON] et al. analyzed the resilient control issues of NCS under DoS attack via a unified game approach [5]. [PERSON] et al.