Neuroadaptive control achieving zero-error tracking and designated performance : A novel vanishing damping approach

In this work, we present a novel control approach for uncertain nonlinear systems that is capable of steering the tracking errors towards a desired residual region within pre-specified time, and thereafter further regulating the errors asymptotically to zero. This is achieved by using prescribed time-varying function (PtvF) based transformation, together with neural adaptive law featuring a vanishing damping term. The role of the PtvF transformation is to drive the system errors (from any initial condition) into the desirable bounded region within user-assignable time (rather than infinite time as in existing prescribed performance control (PPC) methods). Whereas, the role of the neural adaptive law with a damping term that vanishes within prescribed time, combined with the “softsign” mechanism in the control, is to further asymptotically regulate the errors to zero, rather than to some stipulated or unknown ultimately uniformly bounded region (which again differs from most existing PPC methods). By using Lyapunov function incorporated with the lower bounds of control gains, a rigorous analysis of the closed-loop system's stability is established. The results are further verified and validated through simulations.