Optimal control of final state constrained systems

Abstract

In using penalty functions to handle final state equality constraints, we propose a systematic scheme for adjusting the penalty function factors, so that all the constraints are satisfied within a specified tolerance, and so that the Performance index is minimized. Two typical engineering problems, which are used to test the procedure, show that the proposed method of adjusting the penalty function factors can be used for reasonably complex systems to yield reliable results.A I'aide des fonctions de pbnalite pour traiter les contraintes d'egalite d'etat final, nous proposons une methode systematique dans le but d'ajuster les facteurs de fonction de penalite, de fapon a ce que toutes les contraintes soient satisfaites a I'interieur d'une tolerance specifiee, et de telle sorte que I'indice de performance soit minimise. Deux problemes d'ingenierie typiques, qui sont utilises pour tester la procedure, montrent que la methode proposee pour I'ajustement des facteurs de fonction de penalite peut servir a des systemes raisonablement complexes et donner des resultats fiables.

Two-Step Method for Dynamic Optimization of Inequality State Constrained Systems Using Iterative Dynamic Programming

“…desired state than obtained by Mekarapiruk and Luus31 . The total computation time for the two steps is 1348 secs.…”

Evaluation of Penalty Functions for Optimal Control

“…To reduce the size of th e fluctuations in the cont rol policy, 8 is decreased by a small amount such as 1% after every pass. By using this approach, Mekar apiruk and Luus (1997b) were able to solve a very difficult crane opt imizat ion problem involving six final state const ra ints . That problem was first pr esented by Sakawa and Shindo (1982) and has been considered by several resear chers Dadebo and McAuley (1995) , Goh and Teo (1988) , Teo et al (1991).…”

“…They concluded that absolute deviation from the desired state is a better choice than the square of deviation in the penalty function , and suggested that each penalty function factor be chosen to be approximately the same size as the performance index. Their work was extended by Mekarapiruk and Luus (1997b) to provide a more systematic way of choosing penalty function factors so that the optimum value of the performance index can be obtained, and so that all the state variables are transferred to the desired values within a specified tolerance.…”

Global Optimization with Nonfactorable Constraints

“…The CSTR system with nonlinear dynamics is an example of an optimal control problem with multiple solutions, first studied by Aris and Amundson 30 and subsequently by Lapidus and Luus 31 and Mekarapiruk and Luus. 32 where The nonfactorable function in this system is defined as follows:…”

“…Nonlinear Continuous Stirred Tank Reactor (CSTR) Problem. The CSTR system with nonlinear dynamics is an example of an optimal control problem with multiple solutions, first studied by Aris and Amundson and subsequently by Lapidus and Luus and Mekarapiruk and Luus where The nonfactorable function in this system is defined as follows: where = t f / N , and N is the number of time intervals in the parametrized problem.…”