# On cost design in applications of optimal control

arXiv: https://arxiv.org/abs/2104.00917 · HTML: https://mlsanity.com/paper/2104.00917/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2021.

## Built on by (most cited first, 2 of 2)

- [Guaranteeing Control Requirements via Reward Shaping in Reinforcement Learning](https://mlsanity.com/paper/2311.10026/) (2023)
- [On Convex Data-Driven Inverse Optimal Control for Nonlinear, Non-stationary and Stochastic Systems](https://mlsanity.com/paper/2306.13928/) (2023)

## Abstract (arXiv)

A new approach to feedback control design based on optimal control is proposed. Instead of expensive computations of the value function for different penalties on the states and inputs, we use a control Lyapunov function that amounts to be a value function of an optimal control problem with suitable cost design and then study combinations of input and state penalty that are compatible with this value function. This drastically simplifies the role of the Hamilton-Jacobi-Bellman equation, since it is no longer a partial differential equation to be solved, but an algebraic relationship between different terms of the cost. The paper illustrates this idea in different examples, including H∞ control and optimal control of coupled oscillators.