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The paper addresses the problem of controller synthesis for control-affinenonlinear systems to meet reach-avoid-stay specifications. Specifically, thegoal of the research is to obtain a closed-form control law ensuring that thetrajectories of the nonlinear system, reach a target set while avoiding allunsafe regions and adhering to the state-space constraints. To tackle thisproblem, we leverage the concept of the funnel-based control approach. Given anarbitrary unsafe region, we introduce a circumvent function that guarantees thesystem trajectory to steer clear of that region. Subsequently, an adaptivefunnel framework is proposed based on the target, followed by the constructionof a closed-form controller using the established funnel function, enforcingthe reach-avoid-stay specifications. To demonstrate the efficacy of theproposed funnel-based control approach, a series of simulation experiments havebeen carried out.

Funnel-based Control for Reach-Avoid-Stay Specifications