Model decomposition based method for solving general dynamic optimization problems

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The simultaneous strategy and control parameterization are the two most widely used direct methods for solving dynamic optimization problems. The control parameterization approach generally results in a comparatively smaller nonlinear program (NLP) but has difficulties in dealing with the path constraints. The advantage of the simultaneous approach lies in its ability to handle path constraints, thus eliminating the need to obtain expensive and possibly infeasible intermediate solutions. The disadvantage is that it requires solution of a potentially very large dimensional NLP. This work presents a decomposition strategy, which combines the advantages of the control parameterization and simultaneous approaches for solving dynamic optimization problems with path constraints. Using the proposed strategy, first the set of state variables x is divided into two sets x 1 and x 2, and the system is partitioned into two corresponding sub-systems. The criterion used to partition the state variables and the system model are that the equations which define the state variables involved in the path constraints should be in the same sub-system. For the resulting sub-systems, one is enforced in the master NLP through collocation method as in simultaneous approach, the other is solved together with the sensitivities in a differential and algebraic equations (DAE) solver. This strategy constitutes a general approach in the sense that for problems with a specific structure the method is equivalent to the control parameterization method, while for other problems with special structures the approach is the same as the simultaneous approach. In general it possesses the advantage of the simultaneous method in handling the path constraints since it is directly enforced in the master NLP as well as the advantage of control parameterization in resulting a small master NLP because only a fraction of the state variables are directly discretized. The method is demonstrated through several numerical examples.