Turnpike in Lipschitz—nonlinear optimal control

Abstract We present a new proof of the turnpike property for nonlinear optimal control problems, when running target is steady control-state pair underlying system. Our strategy combines construction quasi-turnpike controls via controllability, and bootstrap argument, does not rely on analyzing optimality system or linearization techniques. This in turn allows us to address several problems finite-dimensional, control-affine systems with globally Lipschitz (possibly nonsmooth) nonlinearities, without any smallness conditions initial data target. These results are motivated by applications machine learning through deep residual neural networks, which may be fit within our setting. show that methodology applicable controlled PDEs as well, such semilinear wave heat equation nonlinearity, once again assumptions.