Dynamic Quantizer Synthesis for Encrypted State-Feedback Control Systems with Partially Homomorphic Encryption

This study proposes a systematic design procedure for a dynamic quantizer in an encrypted state-feedback control system. By presenting two types of quantizers with different biases (additive and multiplicative), the authors reveal an essential condition that the stability of the control system is inherited and an overflow never occur in a quantization process. The resulting design procedure satisfies this condition and determines the type of quantizer with an appropriate parameter. Furthermore, this study experimentally validates the effectiveness of the proposed design procedure using a practical encrypted state-feedback control system with an inverted pendulum robot (LEGO MINDSTORMS EV3). This study establishes a quantizer synthesis for encrypted control systems using an multiplicative homomorphic encryption scheme.