As with a full range, cooktops are 220V, induction or not. The other poster questioned whether or not your patio is covered. While I assume it is, weather exposure should not present issues peculiar to induction. A fully exposed electric cooktop of any variety is probably not advisable. But if it were exposed, you're not cooking in the rain, right? As you probably know, induction heat is created through friction of a pulsating magnetic field. It doesn't care where it is, water can be wiped off, and a bit of moisture does not interfere with the inductive process. If you have a source of electricity near, it could be a quick and easy job for an electrician. If I was doing the same thing at my house, I could just feed the existing indoor 220V for the cooktop a few feet to reach my patio - very simply. Your indoor gas cooktop will need power for ignition, but it's a light load and chances are it could be tapped from another circuit nearby. Wherever the power originates from, count on requiring 40 or 50 amps. Since you said four burner, I'm guessing 40 amps. Most codes will require a GFI. Sometimes that can be accomplished with a GFI breaker in your panel, but a small subpanel with GFI adjacent to the receptacle might be called for.
My advice is contrary to that of jimn01. For the reasons you stated, it makes sense to you. You won't get much for your induction cooktop on the used market, but they are costly to buy new. Perhaps you have the ferrous cookware already. It could be an economical outdoor cooking solution. On the other hand, if you have a larger budget and have fabricate a cooking island to accommodate a cooktop anyhow, and gas is nearby, you might just spring for a gas-powered outdoor cooking method. I'd consider a four burner gas cooktop (or full range) next to a gas grill as part of an outdoor cooking station. Decent stainless steel gas cooktops are easily found new for $700 USD, and if you're into seeking a take-out used unit, the floor's the limit on price. Your gas hookup could be cheaper than the 220V electrical, depending on distances involved. Either way, you can permeate the neighborhood with the tasty odors of Indian cooking from your patio!