Reinforcement learning based privacy-preserving consensus tracking control of nonstrict-feedback discrete-time multi-agent systems

• An improved Liu cryptosystem is proposed to mitigate encryption–decryption mismatches, ensuring reliable plaintext recovery for privacy preservation in MAS communications. • A reinforcement learning actor–critic framework is integrated with backstepping to compensate for unknown dynamics and signal-decryption errors, enhancing adaptive consensus tracking performance. • The proposed RL-based privacy-preserving controller guarantees that consensus tracking errors and all closed-loop signals remain ultimately bounded, as proven via Lyapunov stability theory. • Simulation studies validate the effectiveness of the control strategy for nonstrict-feedback discrete-time multi-agent systems under privacy constraints.