I went to see the rehearsal of Brahms's 2nd concert by Seiji Ozawa. It was interesting to observe how Ozawa tried to overcome the ill-posed problem of conducting the full orchestra, consisting of a million different parameters. What he did was first to vocalize what he sensed with fitting language, and then translate it into appropriate action commands. For example, he talked about "consonants" and "vowels", and asked the violinists to be more outgoing with the "vowels". In terms of specific action, he instructed them to press the bow stronger. Thus, he acted as a transformer of sensory perceptions into motor actions. You need to be a keen appreciator of music as well as a general actionist of instruments in order to be a good conductor.
At the end of the day, with all the skills of perception and verbalizing action commands, it is still an ill-posed problem, conducting a full orchestra. Someone close to the orchestra mentioned that at the moment Ozawa appeared at the podium, the sound changed. That means something beyond a simple controlled action is happening. Perhaps being conducted is like expressing one's heart in the presence of a experienced mentor. If you feel that your mentor is understanding and is attentive to what you say, your words become more expressive, more true to heart, profound. Thus, the ill-posed problem is overcome by the spontaneity of the agents involved.
We all live an ill-posed life spontaneously.