A Quadratic Program based Control Synthesis under Spatiotemporal Constraints and Non-vanishing Disturbances

In this paper, we study the effect of non-vanishing disturbances on the stability of fixed-time stable (FxTS) systems. We present a new result on FxTS, which allows a positive term in the time derivative of the Lyapunov function with the aim to model bounded, non-vanishing disturbances in system dynamics. We characterize the neighborhood to which the system trajectories converge, as well as the convergence time. Then, we use the new FxTS result and formulate a quadratic program (QP) that yields control inputs which drive the trajectories of a class of nonlinear, control-affine systems to a goal set in the presence of control input constraints and nonvanishing, bounded disturbances in the system dynamics. We consider an overtaking problem on a highway as a case study, and discuss how to both set up the QP and decide when to start the overtake maneuver in the presence of sensing errors.