This study researches the vibration control approach for vehicle active suspension discrete-time systems with actuator time delay under road disturbances. First, the discrete-time models for the quarter vehicle active suspension system with actuator time delay are presented, and road disturbances are considered as the output of an exosystem. By introducing a discrete variable transformation, the discrete-time system with actuator time delay and the quadratic performance index are transformed into equivalent ones without the explicit appearance of time delays. Then, the problem of original vibration control with actuator time delay is transformed into the optimal vibration control for a non-delayed system with respect to the transformed performance index. Based on the maximum principle, the feedforward and feedback optimal vibration control law is obtained from Riccati and Stein equations. The existence and uniqueness of the optimal control law is proved. A reduced-order observer is constructed to solve the physically realizable problem of the feedforward compensator. Finally, the feasibility and effectiveness of the proposed approaches are validated by a numerical example.

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The main cause of coal mine safety accidents is the unsafe behavior of miners who are affected by their emotional state. Therefore, the implementation of effective emotional supervision is important for achieving the sustainable development of coal mining enterprises in China. Assuming rational players, a signaling game between miners (emotion-driven and judgement-driven) and managers is established from the perspective of Affective Events Theory in order to examine the impact of managers’ emotions on coal miners’ behavior; it analyzes the players’ strategy selections as well as the factors influencing the equilibrium states. The results show that the safety risk deposits paid by managers and the costs of emotion-driven miners disguising any negative emotions affect equilibrium. Under the separating equilibrium state, the emotional supervision system faces “the paradox of almost totally safe systems” and will be broken; the emotion-driven miners disguising any negative emotions will be permitted to work in the coal mine, creating a safety risk. Under the pooling equilibrium state, strong economic constraints, such as setting suitable safety risk deposits, may achieve effective emotional supervision of the miners, reducing the safety risk. The results are verified against a case study of the China Pingmei Shenma Group. Therefore, setting a suitable safety risk deposit to improve emotional supervision and creating punitive measures to prevent miners from disguising any negative emotions can reduce the number of coal mine safety accidents in China.

This paper is to develop a simplified optimized tracking control using reinforcement learning (RL) strategy for a class of nonlinear systems. Since the nonlinear control gain function is considered in the system modeling, it is challenging to extend the existing RL‐based optimal methods to the tracking control. The main reasons are that these methods' algorithm are very complex; meanwhile, they also require to meet some strict conditions. Different with these exiting RL‐based optimal methods that derive the actor and critic training laws from the square of Bellman residual error, which is a complex function consisting of multiple nonlinear terms, the proposed optimized scheme derives the two RL training laws from negative gradient of a simple positive function, so that the algorithm can be significantly simplified. Moreover, the actor and critic in RL are constructed by employing neural network (NN) to approximate the solution of Hamilton–Jacobi–Bellman (HJB) equation. Finally, the feasibility of the proposed method is demonstrated in accordance with both Lyapunov stability theory and simulation example.

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