Reinforcement learning-based prescribed-time optimal control for chaotic systems with replay attacks and non-affine actuator faults

For a class of Liu chaotic systems with replay attacks and actuator faults, this paper proposes a prescribed-time optimal control strategy by combining reinforcement learning and backstepping. Firstly, this paper introduces the actor–critic neural network in reinforcement learning to effectively calculate the cost function and handle complex time-varying terms in control design. Secondly, this work models replay attacks as historical signal injections controlled by a Bernoulli random variable, and employs the finite coverage principle and a first-order filter for compensation. Additionally, this paper considers input saturation and non-affine actuator faults involving unknown time-varying input power, gain, and bias, and achieves active compensation through single-parameter adaptive rule and robust compensation term. By designing gain parameters in the controller and adaptive laws to be inversely proportional to a prescribed time, the developed optimal controller ensures that the controlled system achieves stability within the prescribed time. Finally, the feasibility of the presented control strategy is confirmed through a simulation experiment.