A Constructive PMP-Based Decomposition Method for Two-Input Linear Time-Optimal Control

The proposed approach decomposes in a special way the original two-input linear time-optimal control problem into two single-input linear time-optimal problems whose optimal solutions are subsequently recombined. A lemma and a theorem establish conditions under which the recombined control vector is a candidate for the optimal solution and provide a simple criterion, based on the Pontryagin Maximum Principle, to determine whether the obtained control is truly optimal or only near optimal. The method is illustrated on a modified canonical double integrator system with two independent inputs. The resulting control system preserves the bang-bang structure and switching sequence of the true optimal solution, while providing a transition time that exceeds the optimal value by only 0.55%. The proposed method offers a basis for developing a technique regarding the multi-input linear time-optimal control problems.