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This paper aims to study the attitude control problem with mutating orbital rate and actuator fading.

To avoid malicious physical attacks and hide itself, the spacecraft may irregularly switch its orbit altitude within a specific range, which will bring about variations in orbital rate, thereby causing mutations in the attitude dynamics model. The actuator faults will also cause changes in system dynamics. Both factors affect the control performance. First, this paper determines the potential switching orbits. Then under different conditions, design controllers that can accommodate actuator faults according to the statistical law of actuator fading.

This paper, to the best of the authors’ knowledge, for the first time, introduces the Markovian jump framework to model the possible unexpected mutating of orbital rate and actuator fading of spacecraft and then designs a novel control policy to solve the attitude control problem.

This paper also provides the algorithm design processes in detail. A comparative numerical simulation is given to verify the effectiveness of the proposed algorithm.

This is an early solution for spacecraft attitude control with dynamics model mutations.

The purpose of the study is to investigate strategies for enhancing pollution oversight by local governments while reducing government-enterprise collusion (GEC) levels. Additionally, the factors influencing pollution control efforts at incineration plants are explored. Potential approaches to improving them and for effectively reducing waste incineration pollution are suggested.

The authors examined the most effective methods for mitigating incineration-related pollution and preventing collusion and developed a differential game model involving interactions between local governments and incineration plants. The findings of this work have significant policy implications for central governments worldwide seeking to regulate waste incineration practices.

The results indicate that, first, elevating environmental assessment standards can incentivize local governments to improve their oversight efforts. Second, collusion between incineration plants and local governments can be deterred by transferring benefits from the plants to the local government, while increased supervision by the central government and the enforcement of penalties for collusion can also mitigate collusion. Third, both central and local governments can bolster their supervisory and penalty mechanisms for instances of excessive pollution, encouraging incineration plants to invest more in pollution control. Finally, when the central government finds it challenging to detect excessive incineration-related pollution, enhancing rewards and penalties at the local government level can be a viable alternative.

This study stands out by considering the dynamic nature of pollutants. A differential game model is constructed which captures the evolving dynamics between local governments and incineration plants, offering insights regarding the prevention of collusion from a dynamic perspective. The findings may provide a valuable reference for governments as they develop and enforce regulations while motivating incineration plants to actively engage in reducing waste-incineration pollution.