Currently being marketed as an officially licensed controller designed for younger gamers, today Sony introduced the Hori Mini Wired Gamepad for PS4, which is 40% smaller than the DualShock 4 (DS4) and retails for $29.99 USD (MSRP) / $39.99 CAD (MSRP) this holiday season.
Here's Sony Peripherals Marketing and Licensing Group Manager
Anand Agarwal with the rest of the deets, to quote:
We’re pleased to introduce a new controller from Hori, the officially licensed
Mini Wired Gamepad for PlayStation 4, designed with younger gamers in mind.

This controller is 40% smaller than the DualShock 4 and has a simple form factor with a flat design that makes it easy to fit into smaller hands. Best of all, the controller has a low price of $29.99 USD (MSRP) / $39.99 CAD (MSRP), making it a great purchase for companion play on games like Knack 2.
The Mini Wired Gamepad provides the essential functions to play most PS4 games while still providing a great gaming experience — that includes the right and left sticks, R1/L1/R2/L2 buttons, directional buttons, and action buttons. Certain touch pad inputs can be simulated via the left or right sticks.

The wired controller includes a 10ft cable, making for an easy plug-and-play experience. While this controller does not include some features of DualShock 4, including a touch pad, light bar, stereo headset jack, speaker, vibration, or motion sensing, it comes at a great value and helps open gaming to the whole family.
Find out more about the gamepad
here. The blue Mini Wired Gamepad launches across U.S. and Canada this holiday.