Turnpike in Lipschitz—nonlinear optimal control
Abstract
We present a new proof of the turnpike property for nonlinear optimal control problems, when the running target is a steady control-state pair of the underlying system. Our strategy combines the construction of quasi-turnpike controls via controllability, and a bootstrap argument, and does not rely on analyzing the optimality system or linearization techniques. This in turn allows us to address several optimal control problems for finite-dimensional, control-affine systems with globally Lipschitz (possibly nonsmooth) nonlinearities, without any smallness conditions on the initial data or the running target. These results are motivated by applications in machine learning through deep residual neural networks, which may be fit within our setting. We show that our methodology is applicable to controlled PDEs as well, such as the semilinear wave and heat equation with a globally Lipschitz nonlinearity, once again without any smallness assumptions.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Feb 17, 2022
- Source ID
- 10.1088/1361-6544/ac4e61
Entities
People
- Borjan Geshkovski
- Carlos Esteve-yagüe
- Darío Pighin
- Enrique Zuazua
Organizations
- Air Force Office of Scientific Research
- Alexander von Humboldt Foundation
- European Commission
- German Research Foundation
- Ministry of Economy, Industry and Competitiveness