How to drive and control capacitive load?
The load in question, from OP's clarification, appears to behave electrically almost like Electroluminiscent Sheet, or an EL panel, popular in LCD backlights and hobby / decorative applications:


Another popular form is EL Wire, with a similar principle of operation.



EL Sheet is easily driven using an "EL Inverter", either a special-purpose IC such as:


SuperTex HV853 High Voltage, Low Noise, Inductorless EL Lamp Driver
OnSemi MC33441 Electroluminescent Lamp Driver IC


... or using a flyback or step-up transformer based inverter design, as described in these articles:


MakeZine's open source EL guide
Making your own 3v Inverter from TalkingElectronics


The schematics in the above articles will give you an idea of the design elements involved, even if you don't want to lift a design outright.

Finally, you can also buy fairly inexpensive EL drivers / EL invertors, such as this $14.95 12 Volt wall-wart driven EL inverter from SparkFun:


EL Panel inverters are also available on eBay and other sites, often at much lower prices than the above. However, do make sure you understand how much capacitance the driver in question is designed for - and thus how much of the Electrochromatic Sheet can be driven by it. Larger pieces typically have higher capacitance hence more powerful / expensive inverters are needed.