control
methods to non-linear systems.
The classical certainty equivalence principle says that
the measurement feedback can be obtained by applying the state
feedback law to a certain ``worst case'' estimate of the state.
However, all the results to date relied heavily on the assumption
that
the ``worst case'' state is unique.
In this paper we study in detail the special case when there
are precisely two ``worst case'' estimates of the state.
Our analysis gives not only sufficient but also necessary conditions
for the special case of two ``worst case'' estimates of the state.
The key element of our construction is a new ``two-point''
Hamilton-Jacobi-Isaac-Belman equation which deals with two states
at the same time.
The results announced here are part of a longer paper which includes
more details on smoothness assumption and how to avoid them.Key Words:
Dissipative control, nonlinear and linear systems, viscosity solutions, nonlinear robust control, game theory, dynamic programming, state estimation.
