WebScheduler has a javascript function to move to a selected date. Here is the snippet to move to a week from the currently selected date:

function MoveSchedulerByCalendar() {
    var sched = ISGetObject("WebScheduler1");
    sched.Calendar.MoveDayBy(7);
    sched.RefreshAll(true);
}
function MoveSchedulerBySelectedDate() {
    var sched = ISGetObject("WebScheduler1");
    
    var currentDate = sched.ViewSettings.SelectedDate;
    currentDate.setDate(currentDate.getDate() + 7);
    sched.RefreshAll(true);
}

The first snippet will be applicable if the Calendar object is loaded, if the Calendar is not loaded you could use the second snippet. 

Regarding the lack of documentation for WebScheduler, I will inform this to our documentation team for consideration. 

Thanks Glenn,

It helps me a lot.

How about the event in server when calendar change? 

Looking to your script, I guess that I can catch event Webscheduler_Load and check if date is changed or not. If there is other easy way to catch calendar change event, pls show me how.

Thanks & Regards,

Huy.