Cards you control are always face up and may exist in one of two places: in your hand to the left of your mech mat or in your active row to the right of your mat. Whenever a card is placed in the active row (when played, gained, or discarded), it is always placed to the right of any existing active cards. You may arrange your hand however you wish, but active cards (i.e., cards in your active row) are always kept in the order they were placed.
Special benefits (Solve, Upgrade, and Meld) allow you to tuck cards under your mech mat; they are no longer in your hand or your active row and thus are not considered “cards you control.”