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Minimax solutions of the dual Hamilton-Jacobi equation

Nowakowski A.

Journal of Applied Analysis

2003

Vol. 9, nr 1

75-102

In the paper the existence and continuous dependence of a kind of minimax solution to the dual Hamilton-Jacobi equations is proved. The main difficulties which appear here are a special type of the boundary conditions and the transversality conditions which that solution must satisfy. That type of problems come from optimal control and game theory.

Theconjugate points sufficient conditions for an optimal control

Szymanowska A.

Control and Cybernetics

1998

Vol. 27, no 3

353-362

The paper concerns an application of the idea of field theory and the concept of "concourse of flights" to the sufficient optimality conditions for the optimal control problems stated in terms of focal and conjugate points. The concept of concourse of flights was begun by Young (1969), and later extended by Nowakowski (1988). In the paper the definition of a focal and conjugate point of a field of extremals is given. Using these concepts, we prove that the existence of a field of extremals without conjugate points implies the existence of concourse of flights and consequently we obtain the second order sufficient conditions for the generalized problem of Bolza. Another approach to the concept of focal and conjugate points is given by Zeidan (1983, 1984).