A solution of the discrete minimum-time control problem

An iterative procedure for the synthesis of discrete minimum-amplitude and minimum-time controls is presented. The algorithm is based on some new relations obtained by extending well-known results on the minimum-energy control problem as given in Refs. 1–3. This approach yields a set of implicit algebraic equations from which the desired optimal control sequence is determined by the iteration procedure referred to above. The algorithm has the advantage that convergence to the optimal solution can be guaranteed. Simplicity of the recursion formulas and insensitivity to numerical errors make the procedure well suited for on-line or off-line computations.This work was done at the Institut für Regelungstechnik, Technische Universität Berlin, West Berlin, Germany. The author is indebted to Professor G. Schneider for many stimulating discussions and criticisms during the course of this research.