Turnpike in Lipschitz-nonlinear optimal control

Esteve Yagüe C, Geshkovski B, Pighin D, Zuazua Iriondo E (2022)

Publication Language: English

Publication Status: Accepted

Publication Type: Journal article

Future Publication Type: Journal article

Publication year: 2022


Publisher: Nonlinearity

Book Volume: 5

Pages Range: 1652-1701

Journal Issue: 34

DOI: 10.1088/1361-6544/ac4e61

Open Access Link: https://doi.org/10.1088/1361-6544/ac4e61


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 dynamics. Our strategy combines the construction of suboptimal quasi-turnpike trajectories 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 the large-layer regime of residual neural networks, commonly used in deep learning applications. 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.

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Esteve Yagüe, C., Geshkovski, B., Pighin, D., & Zuazua Iriondo, E. (2022). Turnpike in Lipschitz-nonlinear optimal control. Nonlinearity, 5(34), 1652-1701. https://doi.org/10.1088/1361-6544/ac4e61


Esteve Yagüe, Carlos, et al. "Turnpike in Lipschitz-nonlinear optimal control." Nonlinearity 5.34 (2022): 1652-1701.

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