An Algorithm to Obtain Control Solutions Achieving Minimum-Time State Transfer of a Linear Dynamical System Based on Convexity of the Reachable Set

This paper presents a new numerical method to compute control solutions achieving minimum-time state transfer for a linear dynamical system with bounded control input. The method can be used to generate bang-bang control input solutions in cases that would pose difficulties for methods based on solving directly for input switch-times. For the considered problem, the optimum control input is uniquely determined by the initial value of the co-state vector. The proposed method is based on an iterative computation of the initial co-state vector, as embedded in the geometry of the reachable set. True optimality of the solution is implicit from Pontryagin´s minimum principle, while the convexity property of the reachable set ensures that the solution converges to match the required boundary conditions. Example simulation results involving motion control of flexible structures are given to demonstrate the usefulness of the algorithm in solving practical control problems.