On Nonuniqueness of Solutions of Hamilton–Jacobi–Bellman Equations
- University of Szczecin, Institute of Mathematics (Poland)
An example of a nonunique solution of the Cauchy problem of Hamilton–Jacobi–Bellman (HJB) equation with surprisingly regular Hamiltonian is presented. The Hamiltonian H(t, x, p) is locally Lipschitz continuous with respect to all variables, convex in p and with linear growth with respect to p and x. The HJB equation possesses two distinct lower semicontinuous solutions with the same final conditions; moreover, one of them is the value function of the corresponding Bolza problem. The definition of lower semicontinuous solution was proposed by Frankowska (SIAM J. Control Optim. 31:257–272, 1993) and Barron and Jensen (Commun. Partial Differ. Equ. 15(12):1713–1742, 1990). Using the example an analysis and comparison of assumptions in some uniqueness results in HJB equations is provided.
- OSTI ID:
- 22749969
- Journal Information:
- Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 3 Vol. 77; ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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