Non-linear?
#1 flows 1 LPM, #2 flows 2 LPM and #3 flows 4 LPM.
#1=1
#2=2
#1+#2=3
#3=4
#1+#3=5
#2+#3=6
#1+#2+#3=7
Looks pretty linear to me... You'll need to get creative with your control system, but ons and offs are more reliable than something infinitely progressive. And who really needs more than 7 stages?
"PWM" stands for "pulse width modulation" or "pulse width modulator"; it's a square wave signal that turns something on and off at a certain frequency. A 25 hertz PWM signal turns something on and off 25 times per second. If it's at 100% duty cycle, then it's always on. If it's at 50% duty cycle, then it spends as much time on as it does off. A good PWM will let you put whatever duty cycle you want onto a valve. Certain valves need different frequencies, and they're really sensitive to it; NOS ProShots work between 20-80% duty cycle at 25 hertz, above that and they tend to not open at all an above it they tend to not close at all. But they're variable within that duty cycle range. ProShots at 25 hertz sound badass.
A solid state relay acts like a regular relay, only it has no moving pieces so it can flip really fast and doesn't wear out nearly as quick. If you're using 25-35 hertz PWM signals, you can use solid state relays to control as many amps as you want for cheap.
When it comes to controlling a motor, you aren't really limited by frequency; usually the higher the frequency the smoother the control. Typically PWM's are used on motors instead of valves, and the frequency can be well into the kilohertz.
There is another way of controlling a valve with a PWM, which is to use it at high frequencies and actually hold the plunger half-way or quarter-way open at any given time, instead of totally opening it and closing it many times a second. OEM's do this all the time for pressure regulators or idle air controllers, and it lets a valve last a long time instead of wearing it out within a few hours, but it requires a feedback loop of some sort to be able to dial the plunger to exactly where it needs to be.
When you end up using high frequencies, amplifying the available amperage becomes a more expensive proposition than using solid state relays. You need to use amplification transistor doodads like what CNC machines and industrial robotics use, which I know little about other than that they're expensive.