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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.
On the existence of positive solutions of semilinear elliptic equations
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Linear and quasilinear parabolic problems
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Exact controllability of semilinear plate equations
Zhang, X · 2001
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Exact controllability of the semi-linear wave equation
Zhang, X., and Zuazua, E · 2004
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An introduction to semilinear elliptic equations
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Exact controllability for multidimensional semilinear hyperbolic equations
Fu, X., Yong, J., and Zhang, X · 2007
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Controllability and observability of partial differential equations: some results and open problems
Zuazua, E · 2007
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Observation and control for operator semigroups
Tucsnak, M., and Weiss, G · 2009
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Large time control and turnpike properties for wave equations
Zuazua, E · 2011
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Long time versus steady state optimal control
Porretta, A., and Zuazua, E · 2013
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A note on the semiglobal controllability of the semilinear wave equation
Joly, R., and Laurent, C · 2014
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Hölder equivalence of the value function for control-affine systems
Prandi, D · 2014
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Complexity of control-affine motion planning
Jean, F., and Prandi, D · 2015
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Deep learning
LeCun, Y., Bengio, Y., and Hinton, G · 2015
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The turnpike property in finite-dimensional nonlinear optimal control
Trélat, E., and Zuazua, E · 2015
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Optimal Neumann control for the 1d wave equation: Finite horizon, infinite horizon, boundary tracking terms and the turnpike property
Gugat, M., Trélat, E., and Zuazua, E · 2016
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Deep residual learning for image recognition
He, K., Zhang, X., Ren, S., and Sun, J · 2016
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Remarks on long time versus steady state optimal control
Porretta, A., and Zuazua, E · 2016
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Multiplicative controllability for semilinear reaction–diffusion equations with finitely many changes of sign
Cannarsa, P., Floridia, G., and Khapalov, A. Y · 2017
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A proposal on machine learning via dynamical systems
Null-controllability of perturbed porous medium gas flow
Geshkovski, B · 2020
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Efficient MPC for parabolic PDEs with goal oriented error estimation
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Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations
Grüne, L., Schaller, M., and Schiela, A · 2020
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Neural ordinary differential equations
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Controllability under positivity constraints of semilinear heat equations
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Steady-state and periodic exponential turnpike property for optimal control problems in Hilbert spaces
Trélat, E., Zhang, C., and Zuazua, E · 2018
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Turnpike property for two-dimensional Navier–Stokes equations
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The turnpike with lack of observability
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Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs
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The turnpike property in semilinear control
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