For a complete solution, I think you're out of luck.
iOS will definitely * DO NOT allow software killing of an application, not to mention a software launch.
Android really allows you to kill the application. Despite the undocumented ones (which I could find), you can use
navigator.app.exitApp ();
to kill the current application.
However, you still cannot restart it programmatically.
I think it would be best to write the reset code to variables and local storage / DB (if used). Then reload the index page through document.location.href = 'index.html?var=xxx'; where xxx = current timestamp. Placing a timestamp at the end ensures that it pulls out a non-cached version of the page.
* Edit: Added not to my Apple statement about killing an application, as it should be.
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