The Value Function of Singularly Perturbed Control Systems

By Z. Artstein, V. Gaitsgory. 2000

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Some homogenization results for non-coercive Hamilton–Jacobi equations (2006, methodology): “We refer the reader to Alvarez and Bardi [2, 3, 4], Arisawa [7, 8], Arisawa and Lions [9] and Artstein and Gaitsgory [10], Bardi [11] for results in this direction.”
A uniform Tauberian theorem in optimal control (2010, unknown): “Systems with large, but ﬁxed horizons were considered and, in particular, the class of "ergodic" systems (that is, those in which any starting point in the state space Ω is controllable to any point in Ω ) has been thoroughly studied [2, 3, 5, 6, 8, 11, 26].”
Singular Perturbations of Nonlinear Degenerate Parabolic PDEs: a General Convergence Result (2003, background): “More recent results for first-order equations with various boundary conditions are in [11, 9, 8, 2], and our paper [2] makes a systematic use of this approach for controlled degenerate diffusions in the periodic case.”