Fixed-time control under spatiotemporal and input constraints: A Quadratic Programming based approach

In this paper, we present a control synthesis framework for general class of nonlinear, control-affine systems under spatiotemporal and input constraints. First, study the problem fixed-time convergence in presence The relation between domain attraction stability with respect to constraints required time is established. It shown that increasing authority or can expand stability. Then, consider finding confines closed-loop system trajectories safe set steers them goal within fixed time. To end, Quadratic Program (QP) formulation compute corresponding input. We use slack variables guarantee feasibility proposed QP Furthermore, when strict complementary slackness holds, show solution continuous function states, establish uniqueness solutions forward invariance using Nagumo's theorem. two case studies, an example adaptive cruise instance two-robot motion planning problem, corroborate our methods.