DYNAMIC OPTIMIZATION WITH STATE-VARIABLE PATH CONSTRAINTS

A new method for solving dynamic optimization problems that contain pa th constraints on the state variables is described. We establish the e quivalence between the inequality path-constrained dynamic optimizatio n problem and a hybrid discrete/continuous dynamic optimization proble m that contains switching phenomena. The control parameterization meth od for solving dynamic optimization problems, which transforms the dyn amic optimization problem into a finite-dimensional nonlinear program (NLP), is combined with an algorithm for constrained dynamic simulatio n so that any admissible combination of the control parameters produce s an initial value problem that is feasible with respect to the path c onstraints. We show that the dynamic model, which is in general descri bed by a system of differential-algebraic equations (DAEs), can become high-index during the state-constrained portions of the trajectory. D uring these constrained portions of the trajectory, a subset of the co ntrol variables are allowed to be determined by the solution of the hi gh-index DAE. The algorithm proceeds by detecting activation and deact ivation of the constraints during the solution of the initial value pr oblem, and solving the resulting high-index DAEs and their related sen sitivity systems using the method of dummy derivatives. This method is applicable to a large class of dynamic optimization problems. (C) 199 8 Elsevier Science Ltd. All rights reserved.