October 18, 2000 from 3:30 - 4:30 in K9509, SFU
Rafal Goebel, Simon Fraser University
Convex problems of optimal control, Hamiltonian systems, and monotone operators.
Every convex problem of optimal control gives rise to a saddle function called the Hamiltonian, and an associated Hamiltonian differential inclusion. These notions play a central role in the analysis of the problem --- they appears in optimality conditions and, through the Hamilton-Jacobi PDE, characterize the value function. The latter is of great interest, as it is used to construct the optimal feedback mapping, a preferred notion of solution to a control problem.
After describing the mentioned basic objects, I will discuss the properties of the Hamiltonian system, focusing on the structure guaranteed by the convexity of the underlying problem. The crucial property - preservation of monotone operators by the Hamiltonian flow - will be shown to have far reaching consequences for the value function and the optimal feedback.