APPLICATION OF ITERATIVE DYNAMIC-PROGRAMMING TO STATE CONSTRAINED OPTIMAL-CONTROL PROBLEMS

By using penalty functions, state constraints can be readily incorporated into the main framework of iterative dynamic programming. The procedure is illustrated and tested with several examples, including a model of a fed-batch fermenter described by four ordinary differential equations in the presence of state constraints imposed by algebraic inequalities. Even when the number of constraints is large, the proposed procedure works well. In the presence of constraints, however, the rate of convergence is slower and the choice of the initial control policy becomes important, as is illustrated by a container crane problem described by seven differential equations.