‫Welcome back.
‫So now you know how to go from your non-linear state based equations to your LPI form, and once you
‫have your Lopevi, A, B, C and D matrices, then you discreetness them exactly as it was done in the
‫previous course.
‫This with a equals the identity matrix plus continues a times sample time interval.
‫This could be equals continuous B times sample time interval and then discrete C equals continuous C
‫and discrete the equals continuous D.
‫And then what happens next has the exact same procedure, like in the previous course you have your
‫discrete equations in this form.
‫And so this is a screenshot from the autonomous vehicle course.
‫And just like in the previous course, this matrix, the D equals zero.
‫So this entire term here, it will become zero.
‫Also, from now on, we will call our A, B, C, D and matrices simply A, B, C and D, simply because
‫it's annoying to write the D all the time.
‫But when I say A, B, C and D, then now you know that they are discrete matrices, not continuous
‫matrices unless I specify otherwise.
‫Unlike in the previous course though.
‫Now your state vector is this one here with these six variables and your control input is now a vector,
‫not a scalar.
‫In the previous course, your control input was Delta K, right?
‫So that was your control input here, your steering wheel angle at K.
‫However, now you have three control inputs that the NPC needs to find you to subquery use three subquery
‫and U for some K and transposed in the autonomous vehicle case.
‫You had four states, you had Y that then BPCI beside that and then the inertial Y and then out of those
‫four states you had two outputs and of course one control input.
‫Therefore the A matrix, there was a four by four matrix.
‫It looked like this four by four, then your B matrix was four by one because you have four states and
‫then one control input.
‫Then the C matrix was two by four because you have two outputs in four states.
‫And then finally your matrix was a two by one zero matrix.
‫All right.
‫Because you have two outputs and one control input.
‫But since there is no contribution from that controller input, then this the matrix is a zero matrix.
‫But now in the other case, you have six states and six time derivatives of your states and three control
‫inputs and also three outputs.
‫So these ones here, they will be your outputs as well.
‫So now you're a matrix will be a six by six matrix because you have six states and then six time derivatives
‫of your states.
‫Then your B matrix is a six by three matrix because you have six time derivatives of your states and
‫three control inputs.
‫Then your C matrix is three by six because you have three outputs and six states.
‫And finally your matrix is a three by three zero matrix because you have three outputs and three control
‫inputs, but you have no contribution from your control inputs.