See paper "Minimum settling time control design through direct search methods" (preprint on http://arxiv.org/abs/1109.5966) by the same author.
The settling time of a closed-loop response, depending on controller parameters, is an objective function not only non-smooth but actually discontinuous. Since gradient informations are not available (everywhere), we propose to solve this problem with derivative-free optimization methods (amongst which the direct search methods, not building a model of the objective function, will already prove efficient).
Shorter settling times will be obtained on the four examples tried, compared to two state-of-the-art time response shaping techniques.
One method in particular is put forward for being simple and efficient and will already give excellent results. Other direct search methods, like MADS which has the best theoretical convergence guarantees, can be used instead.
Emile Simon (2020). Minimum settling time control design through direct search optimization methods (https://www.mathworks.com/matlabcentral/fileexchange/33022-minimum-settling-time-control-design-through-direct-search-optimization-methods), MATLAB Central File Exchange. Retrieved .
For more details about restarting Nelder-Mead (e.g. fminsearch) to improve its convergence, see the description and file on http://www.mathworks.com/matlabcentral/fileexchange/33328
Files updated according to the second version of the paper on arxiv (mostly a change of the preliminary objective function).
The preprint of the paper will be available very soon on arxiv.
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