Prescribed‐time regulation of nonlinear uncertain systems with unknown input gain and appended dynamics

The prescribed-time stabilization problem for a general class of uncertain nonlinear systems with unknown input gain and appended dynamics (with unmeasured state) is addressed. Unlike the asymptotic problem, objective requires convergence state vector to origin in finite time interval that can be arbitrarily picked (i.e., “prescribed”) by control system designer irrespective system's initial condition. considered allowed have terms throughout as well (that effectively generate time-varying non-vanishing disturbance signal into nominal system). design based on transformation scale, dynamic high-gain scaling, adaptation temporal forcing terms, composite law includes two components. first component analogous prior scaling-based designs, but time-dependent function place gain, while second has non-smooth form ensure spite disturbances. efficacy proposed illustrated through numerical simulation studies example (a “synthetic” fifth-order “real-world” electromechanical