Hybrid optimization scheme for time-optimal control

This paper applies multiple methods of solving general optimization problems to a time-optimal control problem. By applying both constrained optimization and linear programming techniques to a particular problem, the benefits and drawbacks of each method can be easily described. While some of the results will be relative to the problem of interest, this paper describes some guidelines for solving general optimization problems. Linear programming techniques are efficient for finding good initial guesses into a constrained optimization routine. This hybrid approach can often improve efficiency in solving systems where it is difficult to find a good initial guess. Solutions of the time-optimal control problem for a standard two-mass spring-damper system show some interesting properties that illustrate the difficulty of applying constrained optimization exclusively. These solutions also show how the number of optimal switches changes as system parameters change. For those unwilling to apply linear programming to their own problems, the solutions of the time-optimal control problem given here can provide better insight in developing good initial guesses