A motorized roller shade configured to connect to a power-over-Ethernet network includes a motor for rotating the shade to roll and unroll shade material to and from a roller tube to raise and lower the shade. A bank of ultra-capacitors positioned in the roller tube provides power to the motor and to logic and control circuitry also positioned within the roller tube. The logic and control circuitry charges the ultra-capacitors though power derived from the power-over-Ethernet network, without any power-over-Ethernet switches in the network to provide additional power, and controls the operation of the motor to achieve a desired target velocity. Synchronized operation of multiple motorized roller shades is achieved though autonomous operation of the shades by their corresponding logic and control circuitry. In exemplary embodiments, a lighting element controlled by the logic and control circuitry allows controlled lighting of the shade.