Performance-Dependent Privacy Preserving for Switched Multiple Systems Under Active Disturbance Rejection Control

Disturbances and uncertainties affect the performance of control systems and must be addressed. In addition, due to the potential privacy leakage caused by the informatization and networking of control systems, ensuring system privacy has become an important technical challenge. The topic of this paper is active disturbance rejection control (ADRC) with differential privacy preserving for switched multiple systems. By adding privacy noise with Laplace and uniform distribution to the system state, the novel privacy-preserving ADRC (PP-ADRC) framework ensures the required ADRC performance and privacy of system information in a non-ideal network environment. The innovation of this paper is embodied in three aspects: (i) The designed performance-dependent differential privacy preserving mechanism (PD-DPPM) under Laplace noise can adaptively balance system privacy and control performance. (ii) The presented privacy budget lower bound of uniform noise can determine the size of the uniform noise, making the PD-DPPM method more general in the field of privacy preservation. (iii) The newly constructed dual design of switching law and controller for PP-ADRC can ensure boundedness and $H_{\infty } $ performance. Lastly, illustrative examples are provided to explain effectiveness. Note to Practitioners—In practical applications, active disturbance rejection control (ADRC), which consists of extended state observer (ESO), is a practical and effective technique for dealing with nonlinearity and uncertainty. In addition, for multimodal systems, the switched systems consisting of multiple subsystems and control laws can adjust the working mode for achieving better control performance according to changes in real-time system state. Therefore, ADRC is adopted to improve the control performance and efficiency of the switched systems. In the switched ADRC systems, the feedback channel carrying sensitive information about the system state and operation is a key link in closed-loop control. Once it is leaked or stolen, the operation and security of the control system will be destroyed. Therefore, designing a privacy-preserving method for switched ADRC systems to prevent sensitive feedback information from being stolen and ensure the safe and stable operation of the system is of great significance. The designed performance-dependent differential privacy preserving mechanism (PD-DPPM) can achieve privacy and security of feedback information based on real-time system performance, and achieve a balance between privacy and control.