Fast Computation of Tight Funnels for Piecewise Polynomial Systems

Funnels are widely used in safety-critical applications such as robust motion planning as conservative bounds for possible state deviations due to disturbances. However, the problem of finding a tight funnel has been a challenging topic due to the complexity of the Hamilton-Jacobi partial differential equation that appears when solving the problem. In this letter, we consider the funnel-finding problem for piecewise polynomial systems, with which we can approximate a considerably wider range of real-world dynamic systems, compared to global polynomial approximations. We propose techniques that reduce the computational burden of the problem and improve the tightness of the obtained funnel. Through experimental results using three different example systems, we confirm that the proposed method yields a tighter funnel in a shorter time, compared to competing polynomial-based funnel-computing methods.