An Analytical Approach to Min-Time Control of Discrete-Time Linear Systems with Constrained Input

Employing discrete-time techniques, the min-time control of continuous-time dynamical systems is mainly studied through an analytical framework. To this aim, the exact discrete-time model of the linear time-invariant systems is specified through a zero-order hold. The optimal solution could be directly determined from some necessary conditions. However, the structure of the optimum control sequences is derived by utilizing the well-known Pontryagin principle. Employing the state transition matrix, the states of the control system are computed at the switching times. The switching times of the control signal would be found from a set of nonlinear algebraic equations. Accordingly, the transformation of the system’s states, from a known initial point to a specific value, would be accomplished in the minimum possible time. Applying the proposed scheme, the exact (integer) values of the switching times and the final time are numerically determined from the solution of an algebraic equation. Several discrete-time and continuous-time examples are discussed and simulated to show the feasibility and effectiveness of the suggested procedure in the dynamical systems. The simulation results confirm the method’s advantages over the existing ones.