Design of adaptive finite-time controllers for nonlinear uncertain systems based on given transient specifications

In this paper, we consider designing adaptive finite-time controllers for a class of SISO strict feedback nonlinear plants with parametric uncertainties based on given specifications. In addition to system stability and for the system output and virtual control errors to converge to zero, the specifications also include requirement on transient response in terms of convergence time and convergence rate. If the bound of the compact set in which unknown parameter lies is incorporated, the designed finite-time controller can ensure convergence within two stages. In the first stage the squared norm of the system states including the virtual control errors converges to a given invariant set faster than a specified linear rate. In the second stage the states converge to the origin with a convergence rate faster than a given exponential speed. If the bound of system initial states is also incorporated into the controller, then the states converge to the origin within the given time at a rate faster than the pre-specified exponential rate.