Constrained Nonlinear Reach Controllability on 2D Simplices

Abstract. This paper establishes sufficient conditions for achieving reach controllability in a two-dimensional simplex using continuous feedback controllers. A notable feature of these conditions is their ability to handle nonlinear dynamics and a moving control set, while ensuring that any feedback response exits the simplex through the relative interior of its exit facet in a monotonic fashion. These characteristics are particularly valuable for mitigating measurement and implementation errors in practical applications. Additionally, we use this result to obtain the existence of piecewise continuous solutions when the problem’s dynamics are affine in the control variable.