Seminar Details
2008-09-16 (14.00) : "Computational Approaches to H∞ problems and Differential Games"
At Euler building
Organized by Mathematical Engineering
Speaker :
Brian ANDERSON (Australian National University)
Abstract :
Linear H∞ problems require the solution of Riccati equations with an indefinite quadratic term, which can be computationally challenging. For H2 Riccati equations, numerical problems can often be overcome using the Kleinman iteration, involving a sequence of Lyapunov equations. While this is not directly possible for Riccati equations with an indefinite quadratic term, an iteration involving a sequence of H2 equations is possible which allows a double iteration involving Lyapunov equations.
These ideas are given a game theory interpretation, which then suggests an extension of the results that will also be exposed; the extension indicates how a Hamilton-Jacobi-Bellman-Isaacs equation for a class of nonlinear game theory problems can be solved by iterating of Hamilton-Jacobi-Bellman equations, each of which in turn can be solved by iteration using linear partial differential equations.