Arbitrary-Order Antiderivatives of Canonical Piecewise-Linear Functions

Canonical Piecewise-Linear (CPWL) functions can approximate any continuous single-valued scalar function with arbitrary accuracy through a global and explicit representation. This letter presents a general closed-form expression for computing p-th order antiderivatives of CPWL functions. The proposed analytical formulation is directly parameterized by the CPWL coefficients and avoids recursive integration schemes and symbolic manipulation. Numerical results demonstrate that the proposed method enables efficient and accurate evaluation of p-th order antiderivatives while maintaining low computational cost and memory footprint.