Question

What is optimal variation ?

Answer 1

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$\implies$ᴀ ɴᴇᴡ ᴍᴇᴛʜᴏᴅ ғᴏʀ ᴛʜᴇ ᴏᴘᴛɪᴍᴀʟ sᴏʟᴜᴛɪᴏɴs ɪs ᴘʀᴏᴘᴏsᴇᴅ. ʙʏ ɪɴᴛʀᴏᴅᴜᴄɪɴɢ ᴀ ᴠɪʀᴛᴜᴀʟ ᴅɪᴍᴇɴsɪᴏɴ, ᴛʜᴇ ᴠᴀʀɪᴀᴛɪᴏɴ ᴛɪᴍᴇ, ᴀ ᴅʏɴᴀᴍɪᴄ sʏsᴛᴇᴍ ᴛʜᴀᴛ ᴅᴇsᴄʀɪʙᴇs ᴛʜᴇ ᴠᴀʀɪᴀᴛɪᴏɴ ᴍᴏᴛɪᴏɴ ɪs ᴅᴇᴅᴜᴄᴇᴅ ғʀᴏᴍ ᴛʜᴇ ᴏᴘᴛɪᴍᴀʟ ᴄᴏɴᴛʀᴏʟ ᴘʀᴏʙʟᴇᴍ (ᴏᴄᴘ), ᴀɴᴅ ᴛʜᴇ ᴏᴘᴛɪᴍᴀʟ sᴏʟᴜᴛɪᴏɴ ɪs ɪᴛs ᴇǫᴜɪʟɪʙʀɪᴜᴍ ᴘᴏɪɴᴛ.

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Answer 2

Answer:

Hello here's your answer:

Explanation:

A new method for the optimal solutions is proposed. Originating from the continuous-time dynamics stability theory in the control field, the optimal solution is anticipated to be obtained in an asymptotically evolving way. By introducing a virtual dimension, the variation time, a dynamic system that describes the variation motion is deduced from the Optimal Control Problem (OCP), and the optimal solution is its equilibrium point. Through this method, the intractable OCP is transformed to the Initial-value Problem (IVP) and it may be solved with mature Ordinary Differential Equation (ODE) numerical integration methods. Especially, the deduced dynamic system is globally stable, so any initial value will evolve to the extremal solution ultimately.

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