USE OF VARIABLE STAGE-LENGTHS FOR CONSTRAINED OPTIMAL-CONTROL PROBLEMS

The use of variable stage-lengths allows a relatively small number of time stages to be used for establishing: an accurate optimal control p olicy for systems exhibiting sudden switches in the control policy. Su ch problems, where there are also state inequality constraints and whe re the final time is specified, are considered here. To handle the sta te inequality constraints, auxiliary state variables are introduced, a nd to satisfy the specified final time restriction, a quadratic penalt y function with a shift term is used. Both of these restrictions are i ncorporated into a penalty function which is included in the augmented performance index. The approach is illustrated and tested with the op timal control of a tubular reactor, where the maximum temperature is s pecified. It was found that an optimal control policy consisting of on ly 10 stages of variable length gives the same performance index as wa s obtained with 96 stages of equal length. The use of 15 stages gives marginally better results. In each case, the state constraint is satis fied throughout the given time interval, and the computation time by i terative dynamic programming is reasonable.