Finite-time control of perturbed dynamical systems based on a generalized time transformation approach

A Framework for Prescribed-Time Control Design via Time-Scale Transformation

“…Therefore, according to (16), one may find ξ µ ∈ H(t µ ) as a necessary and sufficient condition, that is inequality (20).…”

“…The controllers obtained through this approach have also demonstrated disturbance suppressing behavior against non-vanishing and parametric uncertainties [14], [15]. A similar approach has been used in the literature, called the generalized time transformation method [16], which essentially incorporates the same idea. PTCs for systems with matched uncertainty and uncertain input gain have been studied in [17], [18].…”

Predictor-Feedback Prescribed-Time Stabilization of LTI Systems With Input Delay

“…Indeed, one can reformulate the problem, through a suitable time-scaling transformation (see e.g. [40]), to then build on control designs such us homogeneity and sliding mode feedbacks. Other approaches include switched linear feedback with state-dependent switching laws when approaching the terminal time or the use of state-dependent cut-off functions inspired by what is done in the context of 1D reaction-diffusion PDEs [12].…”

“…The need to meet some performance, time constraints and precision has highly motivated the stabilization and estimation in finitetime/fixed-time. More recently, prescribed-time concepts have arisen to achieve a more demanding type of convergence: the time of convergence can be prescribed in the design independently of initial conditions [37], [20], [26], [40], [42]. This type of convergence has emerged for tactical and strategic missile guidance problems but it is not limited to them.…”

Prescribed-time predictor control of LTI systems with distributed input delay

“…Finite-time convergence refers to a terminal time which depends on the system's initial conditions, whereas the terminal time for fixed-time convergence is independent on the system's initial conditions insofar as the terminal time is lower bounded by a bounded function of the initial conditions. More recently, the prescribed-time convergence concept has arisen to deal with a more demanding type of convergence, which allows the terminal time to be prescribed independently of initial conditions and parameters [27], [17], [19], [29], [16], [31]. This type of convergence has emerged for tactical and strategic missile guidance problems but many numerous other applications (e.g.…”