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This dissertation is concerned with the improved iterative
dynamic programming algorithms for solving optimal control
problems. First, a survey of iterative dynamic programming is
proposed for the optimal control problem. The use of iterative
dynamic programming (IDP) for optimal control of nonlinear
dynamical systems is based on treating the control as a
stagewise operation, gridding the state and control variables
and contracting the grid size iteratively. In applying the
backward IDP to obtain optimal control, it is required at each
time stage to perform time integration of system dynamic
equations for each allowable control starting from each state
grid. This will result in wasting considerable computation time
in such state grids that are not connected to a state grid at
the previous time stage by a control. To overcome such a
drawback of backward IDP, a forward IDP technique is proposed.
Due to its forward operation, the proposed IDP provides
substantial savings in computation time by eliminating the
integrations starting from those state grids that are not
approximately reachable with an allowable control. Since the
conventional iterative dynamic programming (IDP) performs the
stage- wise optimization in a backward manner, starting from the
last time stage, the initial profiles for delayed variables in
all but the first time stages are absent. The lack of initial
profiles leads to poor convergence and inaccurate solution in
obtaining optimal control policy for time-delay systems. It is
demonstrated in this dissertation that the forward IDP technique
can be used along with an interpolated integration scheme to
overcome the curse of lacking initial profiles associated with
the backward IDP in dealing with time-delay systems. The
benifits of fast convergence and accurate solutions of using
forward IDP are presented by several examples. In solving a
high dimensional optimal control problems, two approaches are
employed to enhance the possibility of obtaining the true
optimum while reducing the required computation efforts. One
approach employs Sobol''s quasi-random sequence generator to
generate allowable controls and the other utilizes multi-pass
computations. Numerical examples show that the use of multi-pass
IDP computations with small numbers of state grid points and
allowable control values can indeed enhance the possibility of
obtaining a true optimum. This is particularly true when the
allowable control values are generated by using Sobol''s quasi-
random sequence generator. When the optimal control policy is
relatively smooth, a small number of stages give excellent
results when piecewise continuous control policy is used. To
obtain convergence, a good initial control policy may be
necessary. Such a starting control policy is readily obtained by
low order piecewise continuous control policy. In the last
section of this dissertation, we discuess the problem of optimal
periodic control problems in which the initial state and
periodic time are free parameters, and the periodic operation
condition must satisfied for the state and control variables. To
treate this problems, we extended the iterative dynamic
programming to handle this particular requirements.
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