Prescribed‐time regulation of nonlinear uncertain systems with unknown input gain and appended dynamics. (21st December 2022)

• Record Type: Journal Article
• Authors: Krishnamurthy, Prashanth; Khorrami, Farshad
• Is Part Of: International journal of robust and nonlinear control. Volume 33:Number 5(2023)
• Page Start: 3004
• Page End: 3026
• Publication Date: 2022-12-21
• Subjects: adaptive control -- high‐gain control -- nonlinear control systems -- prescribed‐time stabilization -- uncertain systems; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.6549
• Languages: English
• ISSNs: 1049-8923

Abstract

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