Fixed-time Control under Spatiotemporal and Input Constraints: A Quadratic Program Based Approach

Kunal Garg, Ehsan Arabi, Dimitra Panagou

In this paper, we present a control synthesis framework for a general class of nonlinear, control-affine systems under spatiotemporal and input constraints. We consider the problem of finding a control input that confines the closed-loop system trajectories in a safe set 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 corresponding control input. We use slack variables to guarantee feasibility of the proposed QP, and safety of the resulting closed-loop trajectories, under the assumption that the safe set can be rendered forward invariant. Furthermore, when strict complementary slackness holds, we show that the solution of the QP is a continuous function of the system states. 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.

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