I have a third-order nonlinear parametric model and I want to know which is the best method (shooting, collocation, dynamic programming, etc.) to solve a time-optimal (minimum-time) problem with fixed initial and final states.
I would like to perform a Monte-Carlo analysis varying the values of the parameters. Thus, given that I cannot define by hand an initial guess for any value of the parameters, I am particularly interested in the method that best handles poor initial solutions.
Any advice about how to obtain initial guesses would be also appreciated.
Nonlinear systems whose right-hand sides are divided by the state and control and are linear in control are considered. An iterative method is proposed for solving time-optimal control problems for such systems. The method is based on constructing finite sequences of adjacent simplexes with their vertices lying on the boundaries of reachability sets. For a controllable system, it is proved that the minimizing sequence converges to an ɛ-optimal solution in a finite number of iterations
Dear Edgar Ramirez-Laboreo,
I think R. Bellman's Optimality Principle (Dynamic Programming, DP) is well-suited for solving of minimum-time optimization problems. With DP you can graphically illustrate the individual steps of the optimization process - i.e. the possible combinations (actual state, next step) - in two-dimensional space (x, y). This is very helpful in solving various tasks. Various optimization problems can be graphically illustrated when using DP.
In my chapter (written in 1972) you will find various simple examples of using DP. The text is in Polish, but the procedures for using DP are very clear from the graphics.
https://www.researchgate.net/publication/312033832_Dynamic_Programming
Best regards and much success
Anatol Badach
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