Predefined-Time Adaptive Fuzzy Inverse Optimal Control for Uncertain Nonlinear Systems

A novel adaptive fuzzy predefined-time inverse approach is presented in this study, which enhances practical predefined-time stability to predefined-time stability. Unlike the existing optimal predefined-time control approaches, this method realizes the optimal performance without resolving the Hamilton–Jacobi–Bellman (HJB) equation, which simplifies the design and learning process. Firstly, by combining a Sontag-type function and a series of singularity-avoidance functions, an auxiliary controller is devised. Based upon this auxiliary controller, an inverse optimal predefined-time controller is set up. Secondly, based upon the method of two Lyapunov functions, it is demonstrated that the tracking error converges asymptotically to a predetermined interval within a predefined time and the inverse optimal stabilization is attained. Lastly, the availability of this method is testified through an example of the electromechanical system.