Geodesic
On the smoothness of solutions of linear-quadratic regulator for degenerate diffusions
Lobachevskii journal of mathematics, Tome 17 (2005), pp. 11-23.

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The paper studies the smoothness of solutions of the degenerate Hamilton–Jacobi–Bellman (HJB) equation associated with a linear-quadratic regulator control problem. We establish the existence of a classical solution of the degenerate HJB equation associated with this problem by the technique of viscosity solutions, and hence derive an optimal control from the optimality conditions in the HJB equation.
Keywords: stochastic differential equation, Hamilton–Jacobi–Bellman equation, linear-quadratic problem, viscosity solutions, applications to control theory. 
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M. A. Baten. On the smoothness of solutions of linear-quadratic regulator for degenerate diffusions. Lobachevskii journal of mathematics, Tome 17 (2005), pp. 11-23. http://geodesic.mathdoc.fr/item/LJM_2005_17_a1/

[1] T. M. Apostol, Mathematical Analysis, Addison-Wesley, 1974 | MR | Zbl

[2] Bardi, M. and Capuzzo-Dolcetta, I., Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhäuser, Boston, 1997 | MR | Zbl

[3] Bensoussan, A., Stochastic Control by Functional Analysis Methods, North-Holland, Amsterdam, 1982 | MR

[4] Crandall, M. G., Ishii, H. and Lions, P. L., “User's guide to viscosity solutions of second order partial differential equations”, Bull. Amer. Math. Soc., 27 (1982), 1–67 | DOI | MR

[5] Da Prato, G., “Direct solution of a Riccati equation arising in stochastic control theory”, Appl. Math. Optim., 11 (1984), 191–208 | DOI | MR | Zbl

[6] Fleming, W. H. and Soner, H. M., Controlled Markov Processes and Viscosity Solutions, Springer-Verlag, New York, 1993 | MR | Zbl

[7] S. Koike and M. Morimoto, “On variational inequalities for leavable bounded-velocity control”, Appl. Math. Optim., 18 (2003), 1–20 | DOI | MR

[8] J. L. Menaldi and M. Robin, “On some cheap control problems for diffusions process”, Trans. Amer. Math. Soc., 278 (1983), 771–802 | DOI | MR

[9] Nisio, M., Stochastic Control Theory, ISI Lecture Notes, 9, MacMillan, 1981 | MR | Zbl