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

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