# Second-Order Analysis and Numerical Approximation for Bang-Bang Bilinear Control Problems

arXiv: https://arxiv.org/abs/1707.06880 · HTML: https://mlsanity.com/paper/1707.06880/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2017.

## Built on by (most cited first, 1 of 1)

- [Is Bang-Bang Control All You Need? Solving Continuous Control with Bernoulli Policies](https://mlsanity.com/paper/2111.02552/) (2021)

## Abstract (arXiv)

We consider bilinear optimal control problems, whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient second-order conditions for bang-bang controls, which guarantee local quadratic growth of the objective functional in L1. In addition, we prove that for controls that are not bang-bang, no such growth can be expected. Finally, we study the finite-element discretization, and prove error estimates of bang-bang controls in L1-norms.