Not so long ago i experimented with control systems that are looking for extremum of functions and, as i believe, users are familiar with them to one degree or another. As sources, i refer to two works:
Extremum Seeking. Model-Free Real-Time Optimization Page 9.
Extremum seeking control with Sliding Mode
These works are good in that they contain simple schemes that you can experiment with. I did this in Mathematica. I drew attention to the fact that these systems are quite slow (the convergence rate can reach 50-500 seconds). And at the same time, a “game with parameters” does not give any result, except for a negative one - the systems cease to be stable. For example, by making the gain or amplitude of the modulating effects large enough.
Are methods, publications or books known where this problem would be addressed?