Robust Control Barrier and Control Lyapunov Functions with Fixed-Time Convergence Guarantees

This paper studies control synthesis for a general class of nonlinear, control-affine dynamical systems under multiple constraints. We enforce forward invariance of static and dynamic safe sets to ensure safety of the system trajectories, and furthermore enforce convergence to a given goal set within a user-defined time in the presence of input constraints. We use robust variants of control barrier functions (CBF) and control Lyapunov functions (CLF) to incorporate a class of additive disturbances in the system dynamics, and sensing errors in the system states. To solve the underlying constrained control problem, we formulate a quadratic program and use the proposed robust CBF-CLF conditions to compute the control input. Finally, we showcase the efficacy of the proposed method on a numerical case study involving multiple underactuated marine vehicles.

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