Application of the Subdivision Strategy in Global Optimal Tracking Control with Adjoining Cell Mapping

The cell mapping method, as its superiority with global optimality, has been used to deal with global optimal control problems for multi–input–multi–output systems through a subdivision strategy. However, the subdivision strategy may cause definite discretization errors of the optimal control solutions. In addition, when the cell mapping method is used for global optimal tracking control, the generated tracking phase difference phenomenon cannot be neglected. This paper improves the subdivision strategy for adjoining cell mapping method by extending the covering region of coarse cells for subdivision operation. And an optimal-sliding mode combined control strategy is proposed to handle optimal tracking control problems for multi–input–multi–output systems. Two examples show that the improved subdivision strategy can guarantee the optimality better and the proposed combined control strategy can make a controlled system catch up a target trajectory with the optimal cost function and keep high precision tracking after that.