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

Kunal Garg, Ehsan Arabi, Dimitra Panagou

Published 2019-06-24Version 1

In this paper, we present a control framework for a general class of control-affine nonlinear systems under spatiotemporal and input constraints. First, we present a new result on fixed-time stability, i.e., convergence within a fixed time independently of the initial conditions, in terms of a Lyapunov function. We show robustness of the proposed conditions in terms of fixed-time stability guarantees in the presence of a class of additive disturbances. Then, we consider the problem of designing control inputs for a general class of nonlinear, control-affine systems to achieve forward invariance of a safe set, as well as convergence to a goal set within a prescribed (i.e., user-defined) time. We show that the aforementioned problem based on spatiotemporal specifications can be translated into a temporal logic formula. Then, we present a quadratic program (QP) based formulation to compute the control input efficiently. We show that the proposed QP is feasible, and discuss the cases when the solution of the QP solves the considered problem of control design. In contrast to prior work, we do not make any additional assumptions on existence of a Lyapunov or a Barrier function for the feasibility of the QP. We present two case studies to corroborate our proposed methods. In the first example, the adaptive cruise control problem is considered, where a following vehicle needs to obtain a desired goal speed while maintaining a safe distance from the lead vehicle. For the second example, we consider the problem of robot motion planning for a two-agent system, where the objective of the robots is to visit a given sequence of sets in a prescribed time sequence while remaining in a given safe set and maintaining safe distance from each other.