Posted Dec 1, 1995

A New Type of HJBI Inequality Governing Situations Where Certainty Equivalence Fails

By J. William Helton and Andrei Vityaev

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This paper deals with the generalization of H 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.

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