A FORWARD ITERATIVE DYNAMIC-PROGRAMMING TECHNIQUE FOR OPTIMAL-CONTROLOF NONLINEAR DYNAMIC-SYSTEMS

The use of iterative dynamic programming (IDP) for optimal control of nonlinear dynamic systems is based on treating the control as a stage- wise operation, gridding the state and control variables, and contract ing the grid size iteratively. In applying the backward IDP to obtain the optimal control, it is required to integrate dynamic system equati ons over the interval [t(i), t(f)] with each allowable control, where t(i) is the beginning time of a stage, and t(f) is the final time. Thi s will result in wasting considerable computation time in those state grids that are inaccessible from the specified initial condition by us ing allowable controls. To overcome such a drawback of the backward ID P, a forward IDP technique is proposed in this paper. Due to its forwa rd operation, the proposed IDP provides substantial savings in computa tion time by eliminating the time integrations for inaccessible state grids and avoiding integrations up to the final time in evaluating the optimal control for each state grid point.