Prescribed-time control under spatiotemporal and input constraints: A QP based approach.

Abstract

In this paper, we present a control synthesis framework for a general class of control-affine nonlinear systems under spatiotemporal and input constraints. We consider the problem of finding a control input that confines the closed-loop system trajectories into a safe set (or equivalently, renders a safe set positively invariant under the closed-loop system dynamics), and steers them to a goal set within a fixed time. To this end, we present a quadratic program (QP) based formulation to compute the control input. We show that the proposed QP is feasible, and that the solution of the QP is a continuous function of the state variables. Under the assumption of forward invariance of the safe set, we use slack variables to guarantee feasibility of the proposed QP, and safety of the resulting closed-loop trajectories. We present two case studies, an example of adaptive cruise control problem and an instance of two-robot motion planning problem, to corroborate our proposed methods.