A dynamic high-gain design for prescribed-time regulation of nonlinear systems

• Published in: Automatica (Oxford) Vol. 115; p. 108860
• Main Authors: Krishnamurthy, Prashanth, Khorrami, Farshad, Krstic, Miroslav
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.05.2020
• Subjects: Finite-time stabilization; High-gain control; Nonlinear systems; Prescribed-time stabilization; Uncertain systems; Uncertain systems; Nonlinear systems; Prescribed-time stabilization; High-gain control; Finite-time stabilization
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2020.108860

“Prescribed-time” stabilization addresses the problem of regulating the state to the origin in a fixed (prescribed) time irrespective of the initial state. While prior results on prescribed-time stabilization considered specific classes of systems such as a chain of integrators with uncertainties matched with the control input (i.e., normal form), we address here a general class of nonlinear systems in a generalized strict-feedback-like structure with state-dependent nonlinear uncertainties throughout the system dynamics. The proposed control design is based on our dynamic high gain scaling technique along with a novel temporal transformation and form of the scaling dynamics with temporal forcing terms. We show that the proposed control design achieves prescribed-time stabilization for the considered general class of uncertain nonlinear systems.