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The problem considered in this paper is the minimum-time problem of nonlinear discrete systems with state and control constrained. In the first half of this paper, the algorithm is given, which solves the minimum-time problem by solving the sequence of the fixed endpoint optimal control problem by the penalty function method. The convergence proof of the algorithm is given. In the latter half of this paper, another algorithm is given, which minimizes the penalty functions which appear in the above fixed endpoint optimal control problems and necessarily contain Heaviside's step functions. This algorithm is especially interesting in the case where the system and the constraints are linear. An illustrative example is given.

Numerical Solution of the Minimum-Time Problem of Nonlinear Discrete Systems