# Efficient Implementation of Rate Constraints for Nonlinear Optimal Control

## TL;DR

This paper introduces a novel on-mesh method for implementing rate constraints in nonlinear optimal control, improving solution properties and computational efficiency over traditional approaches.

## Contribution

The paper presents a general on-mesh implementation technique for rate constraints applicable to all collocation methods, enhancing solution quality and computational speed.

## Key findings

- Achieves over 30% computational speedup.
- Prevents singular control arcs with the new method.
- Applicable to all collocation methods.

## Abstract

We propose a general approach to directly implement rate constraints on the discretization mesh for all collocation methods, for both state and input variables. Unlike conventional approaches that may lead to singular control arcs, the solution of this on-mesh implementation has better properties. Moreover, computational speedups of more than 30% can be achieved by exploiting the properties of the resulting linear constraint equations.