The first section of this book is devoted to optimal control, and to closely
related areas, such as Hamilton-Jacobi equation theory and singular perturbations.
The section begins with a survey by Andy Teel on receding horizon
optimal control, which is an optimization paradigm for stabilizing nonlinear
systems. This is followed with a survey by Richard Vinter on feedback
strategies in differential games based on the Isaacs equation. Other papers in
this section include a survey of new results for systems of Hamilton-Jacobi
equations by Daniel Ostrov, and new results by Zvi Artstein on limits of singular
perturbations. Also included are new necessary optimality conditions
for delay differential inclusions by Boris Mordukhovich and Lianwen Wang,
a new value function approach to turnpike theory by Pierre Cartigny and
Alain Rapaport, and new results by Gaemus Collins and William McEneaney
on min-plus methods for the Hamilton-Jacobi equations associated with H4
problems. Finally, Boris Mordukhovich and Ilya Shvartsman discuss issues related
to optimization and feedback control of constrained parabolic systems.
The next section of this book is devoted to stabilization, and to related
issues such as Lyapunov function theory. The section begins with two surveys
co-authored by Eduardo Sontag, the first with David Angeli on monotone
systems and their applications in systems biology, and the second with
Michael Malisoff on the input-to-state stabilization of asymptotically controllable
systems with respect to actuator errors under small observation noise.