  Classical adaptive control proves total-system stability for control of
linear plants, but only for plants meeting very restrictive assumptions.
Approximate Dynamic Programming (ADP) has the potential, in principle, to
ensure stability without such tight restrictions. It also offers nonlinear and
neural extensions for optimal control, with empirically supported links to what
is seen in the brain. However, the relevant ADP methods in use today -- TD,
HDP, DHP, GDHP -- and the Galerkin-based versions of these all have serious
limitations when used here as parallel distributed real-time learning systems;
either they do not possess quadratic unconditional stability (to be defined) or
they lead to incorrect results in the stochastic case. (ADAC or Q-learning
designs do not help.) After explaining these conclusions, this paper describes
new ADP designs which overcome these limitations. It also addresses the
Generalized Moving Target problem, a common family of static optimization
problems, and describes a way to stabilize large-scale economic equilibrium
models, such as the old long-term energy model of DOE.
