This letter considers a wireless network where an access point (AP) broadcasts timely updates to several mobile users. The timeliness of information owned by a user is characterized by the recently proposed age of information. While frequently broadcasting the timely updates and always using the maximum power can minimize the age of information for all users, that wastes valuable communication resources (i.e., time and energy). For addressing the age-energy trade-off, it is critical to develop an efficient scheduling algorithm identifying broadcast times and allocating the power. Moreover, unpredictable users' movement would cause rapidly-varying communication channels; in particular, those channels can be non-stationary or adversarial. Our main contribution is to develop an online scheduling algorithm and a channel-agnostic scheduling algorithm for the mobile network with a provable performance guarantee.