Stepper motor instead of a steering wheel

If we use a stepper motor in the rear car how can we match the speed of the inner wheel and outer wheel at the turnings, So for that we need have a gear ratio to match the speed of the inner wheel and outer wheel. More over how we will have the control to manage the speed of the motor.

You need to think about the characteristics of stepper motors as well. The torque output you may require could feasibly coincide with the motor's stalling frequency. We've had huge problems with trying to use stepper motors at higher torque levels. We found that when a certain resonant frequency was reached (extremely variable in its occurrance) the motor would stall between poles and would not recover. Don't know if this is particularly relevant in this case, but it's worth considering

Irrespective of withstanding the torque at higher levels , how do we manage to transmit the drive to the wheels at the turnings? If we use the stepper motors then the speed of the motor should be matched with the max speed of the vehicle too.

Rear steering will vary in direction depending upon speed and turn purpose, I.E. lane change, sharp turn or parking. Describing the direction and amount of turn angle, when, and at what speed will require a lot of calculations in it's own right. Making it happen is (to me) straight forward once the previous parameters have been established. Chassis/body clearance can be limiting factors on the overall layout but recent technologies can make it happen. Cost is only relevant if you are trying to do this on an economy car.

Stepper motors used for such an application aren't particularly feasible. To start with, several automotive manufacturers have already done research and produced rear-wheel steering vehicles. The problem with stepper motors is that they don't have the power density required for the application. Rather than go into a detailed explanation of the above, consider the speed and force of a hydraulic cylinder, required speed and force to control rear wheel steering, and compare that to a stepper motor. Now, consider the cost of each system. I don't think much of the idea.

Am I correct when I read that the purpose of this is to make small "corrections" in the alignment of the rear wheels as load and road conditions warrant? Is this to improve performance handling of the vehicle by maintaining a better tire to road surface contact patch?

If the answer is yes, Porsche did a lot of work in that end of the field in the early to mid 1970s (Wiessach). Their ultimate solution was to use flexible bushings that altered the geometry of the rear wheel's suspension under cornering and I think accelerating loads. Porsche used that technology and next generations of it in their 928, 993, and later cars.

The advantage of that system is that it is passive and does not require additional energy tapped from the engine (either mechanical or electrical), it is extremely simple (low cost), and very light weight. You can do a patent search to learn more.

If the answer is no, then I don't have a clue.