Control and filtering problems are intrinsically optimization problems. Either one seeks to control a dynamical systems so as to minimize (or maximize) a given
performance criterion, or in filtering and related problems, one seeks to find the
best estimate, of the state at time t of a dynamical system perturbed by a
stochastic noise process, on the basis of information collected up to time /. So,
at least in theory, one could rely on optimization techniques, in particular
nonlinear (and linear) programming algorithms to compute their solutions. In
practice, however, there are significant hurdles to overcome. Although control
and, in particular, filtering-type problems are highly structured optimization
problems, their intrinsic size makes it impractical to rely on standard nonlinear
programming procedures. In addition, because of its nature the problem might
demand a solution in "feedback" form by which we mean that the control to be
used at time t or the state-estimate at time t can be viewed (actually computed)
as a "simple" adjustment to the control or state-estimate at time t-At.