Concave shaping of prescribed lyapunov decay under input constraints

This letter studies prescribed Lyapunov-decay shaping under bounded-input constraints. For a prescribed Lyapunov window, certified decay is evaluated by the corresponding windowed nominal exponential rate. Within the control Lyapunov function framework, the standard linear comparison law is shown to be structurally limited under input bounds, because increasing the exponential rate necessarily increases the required actuation, especially on high Lyapunov levels. Strictly concave comparison laws are then shown to be well suited to this setting: they reduce high-level decay demand while reallocating decay toward lower levels over sufficiently large Lyapunov windows, rather than uniformly increasing the demand over the whole sublevel set. A sufficient feasibility-preserving concave-shaping condition and an endpoint-based design algorithm are developed. Simulations on an inverted pendulum illustrate the theoretical results and the performance of the resulting CLF-QP controllers.

Content

Subjects

CLF-QP

concave comparison law

Control Lyapunov function

decay shaping

input saturation

DDC Class

629.8: Control and Feedback Control Systems

600: Technology