Optimal control of inequality constrained DAE systems

An augmented Lagrangian method for optimal control of continuous time DAE systems

“…Case 2 had the same outcome, all of the tests resulted in the objective value 2.87972. The solution of Case 3 resulted in the objective 2.95321, which agrees with the results reported in [12]. Table I display the time taken to obtain the solution in each approach.…”

“…3) Figure 2 shows the optimal control and the evolution of the states obtained for for Case 3 using the Multiple Shooting Method. The control profile has the same shape than the control profiles depicted in [12], for the same problem. …”

Comments on “Optimal Use of Mixed Catalysts for Two Successive Chemical Reactions”

“…From (12), it follows that (13) implies λ A = λ B k 1 x A /k 2 x B = 0, and hence H = 0, at all the points of the singular segment. However, we have already found the form of H at t = t f and seen that it is maximized by u = 0.…”

“…To verify the derived results, the problem with kinetic constants k 1 = k 3 = 1 and k 2 = 10, which were assumed by Gunn and Thomas [2], and also used in [3][4][5][6][7][8][9][10][11][12][13], is solved numerically under different tolerances using the time-scaling method [13], since it can optimize both the control parameters and the switching times effectively. The time-scaling method was proposed by Teo et al [16].…”

“…tor length equals 12 is 0.476946 according to [1], and, for the case that reactor length equals 1, Bell and Sargent [12] achieved the best literature result of 0.048080. However, using the time-scaling method [13], the authors derived different results from these reported ones with errors larger than their respective optimization tolerances.…”