  The paper addresses the problem of controller synthesis for control-affine
nonlinear systems to meet reach-avoid-stay specifications. Specifically, the
goal of the research is to obtain a closed-form control law ensuring that the
trajectories of the nonlinear system, reach a target set while avoiding all
unsafe regions and adhering to the state-space constraints. To tackle this
problem, we leverage the concept of the funnel-based control approach. Given an
arbitrary unsafe region, we introduce a circumvent function that guarantees the
system trajectory to steer clear of that region. Subsequently, an adaptive
funnel framework is proposed based on the target, followed by the construction
of a closed-form controller using the established funnel function, enforcing
the reach-avoid-stay specifications. To demonstrate the efficacy of the
proposed funnel-based control approach, a series of simulation experiments have
been carried out.

Systems and Control;Systems and Control;Optimization and Control