Composite Prescribed‐Time Optimized Backstepping Control of Strict‐Feedback Heterogeneous Multi‐Agent Systems With Output Constraints: A Monotone Tube Boundary and Reinforcement Learning Approach

ABSTRACT This paper proposes a monotone tube‐based optimal and prescribed‐time backstepping consensus control strategy for nonlinear multi‐agent systems in strict‐feedback form. The control laws are derived from a combination of optimal policy obtained through reinforcement learning (RL) and prescribed‐time control techniques. This approach ensures that followers can track the leader within a predefined time frame, irrespective of initial conditions, through online learning. The model accounts for uncertainties and disturbances in all state variables without assuming the boundedness of unknown nonlinear functions. The gradient descent method is utilized to streamline the adaptation laws for updating neural network weights in reinforcement learning, which are modified to guarantee the system's prescribed‐time stability. To address output constraints, a Monotone Tube Boundary (MTB) methodology is employed, ensuring the prescribed performance of the tracking error while maintaining output constraints. Unlike the Prescribed Performance Function (PPF), the MTB approach allows for the pre‐assignment of transient characteristics for tracking error, avoiding excessive overshoot and enhancing adjustability. A solution is proposed to mitigate the complexity explosion caused by the derivative of virtual control laws, treating these derivatives and unknown functions as general nonlinear functions at each step. A neural network and a disturbance observer estimate unknown nonlinear functions and disturbances, ensuring prescribed‐time stability. The neural network inputs are truncated to require only the output of neighboring agents for control, resulting in a simpler control law and reducing energy consumption for data transmission. The method's effectiveness is demonstrated through simulations, showcasing its superiority over existing approaches.