This paper presents an adaptive neural network acting like a proportional-integral-derivative (PID) controller that uses an intelligent meta-heuristic technique to improve the drug infusion rate (propofol) as a manipulated variable in closed-loop control of anesthesia systems using the Bispectral Index (BIS) as the primary controlled variable. The effect of propofol on the human body is modelled using the pharmacokinetic (PK) and pharmacodynamics (PD) models. A physiological dataset of patients, including gender, weight, height, age, and the like, determines the parameters of the PK/PD mathematical model. The proposed controller seeks to provide the optimal propofol control action, which is in charge of swiftly, precisely, and accurately maintaining a triad of hypnosis, analgesia, and neuromuscular blockade by infusing several drugs that are specific to each state. To train this neural network like a PID controller with the radial basis function (RBF) in a neuron, the meta-heuristic method is employed. The first technique is particle swarm optimization (PSO), which has been widely used in both data estimation and training because of its quick computing speed, while the second technique is the chaotic PSO algorithm, and the third technique is the modified CPSO algorithm (MCPSO). The fundamental proposed procedures of the MCPSO algorithm use the chaos method, including the coefficients of acceleration, and remove the two random parameters from the velocity update equation to generate more randomness in the search space to quickly solve the local minima problem. The PSO, CPSO, and MCPSO meta-heuristic algorithms use the mean square error (MSE) performance index to find and optimize the optimal or the nearly ideal gain parameters of the nonlinear neural network to function like a PID controller. The simulation results show that the proposed controller for different physiological dataset patients is characterized by its efficacy and resilience in terms of controlling the depth of the hypnosis state and the infusion rate of the anesthetic drug during surgery in order to avoid under-or over-dosing of the drug for the patient through the desired value of BIS (50) with minimizing the steady-state error, which is equal to zero without any oscillation. Moreover, the comparison results showed that the proposed RBF-NN-PID controller enhanced the time in one minute to reach the depth of anesthesia at the moderate hypnotic state when compared to the fractional-order adaptive highgain controller, in which the time to reach the depth of anesthesia is two minutes. In contrast, the adaptive neuro-fuzzy controller reached the depth of anesthesia in three minutes. Therefore, the time was improved by 50% and 67%, respectively. In particular, the surgery BIS index was kept at the BIS desired 50 at the moderate hypnotic state without any error and with no oscillation at steady-state.