Constant-Current for a 20W LED
Most LED control circuits just have a series resistor to control the LED current. This is OK if the supply voltage is more or less constant, but it the voltage varies so will the LED current and luminosity. If you want constant luminosity you also want constant current. This means that the series resistance must vary with supply voltage. This is about the simplest circuit for it:  



This is a constant current source dimensioned for 1mA, which is too little for your application, but the principle remains the same. The base-emitter voltage of the transistor is 0.6V, so given that the zener creates a drop of 5.6V between \$V_+\$ and the transistor's base there remains 5V for the resistor. \$\dfrac{5V}{5k\Omega} = 1mA\$.  

If your LED is 20W @ 11V then you need 1.8A of current, so I'll calculate the other components for this value. Replace the zener by 3 x 1N4148, this gives you a 0.6V drop over R1 (three diodes because we'll use a darlington, which has 2 x 0.6V between base and emitter). \$R1 = \dfrac{0.6V}{1.8A} = 0.33\Omega / 1W\$.
The TIP125 darlington transistor has an \$H_{FE}\$ of 1000, R2 should be \$\dfrac{10V}{1.8A / 1000} = 5k\Omega\$.
Since \$V_{CE(SAT)}\$ for the transistor is 2V, and you have an additional voltage drop over R1 of 0.6V, you'll need a 14V power supply to be sure that there's enough left for the LED!
The darlington will dissipate \$2V \times 1.8A = 3.6W\$, so you'll have to mount it on a heat sink.  


  a note on current sources:
  Current sources are the dual of voltage sources, which are more common; we use them all the time in power supplies. This duality means that certain parameters are each other's opposites.
  Whereas a voltage source will try to keep the voltage at its output constant regardless of the load, a current source will keep the output current constant regardless of the load. That means for a current source the output voltage will vary, like for a voltage source the current will be variable.
  An ideal voltage source will have zero output impedance, an ideal current source will have infinite output impedance. And while an ideal voltage source should never be short-circuited because the current will go to infinite, an ideal current source should never be left open, because the voltage which determines the set current will go to infinite.