Model Predictive Control 5 - Prediction with state space models

[@norawit_nangsue]

I've been struggling with these notations. Now, I'm clearly understand them right now. Thank you so much

[@jemert96]

Good video, I'm not a mathematician so I was getting lost in all the formulas. This clears up some confusion for me

[@MrManifolder]

Excellent series in both content and execution! I can't thank you enough! However, there are some minor mistakes in the upper right of slide 5: the state prediction formulae achieved via substituting the recursive state updates. 1. The formula for x(k+2) was not correctly substituted into the formula for x(k+3). Hence, there is an 'A' missing in front of the square brackets, i.e. it should read as follows: x(k+3) = A ( 'A' [ A x(k) + B u(k) ] + B u(k+1) ) + B u(k+2). 2. The formula for x(k+4) has as its left-hand side "x(k+1)". 3. The formula for x(k+4) has carried mistake 1 through its calculation, resulting in another missing 'A' from in front of the inner square brackets. That is, it should read as follows: x(k+4) = A ( A ( 'A' [ A x(k) + B u(k) ] + B u(k+1) ) + B u(k+2) ) + B u(k+3). Other than these small errors, a really instructive and insightful video!

[@johnrossiter2323]

MrManifolder Thanks

[@warnerlosh]

I was going to make exactly this comment (though this one is more complete than the one I was going to type, so bravo)

[@ToddPerkins]

so many questions answered. thank you Professor Rossiter

[@michalkramarczyk1276]

i think you are missing one 'A' starting from third equation on the right (x(k+3)). All the best!

[@siddhyarthkumar1193]

respected sir, where can i find the matlab files you refer to, in the videos????

[@adelsalam9735]

thanks

[@faboxbkn]

Thank you very very much.

[@nirwairbajwa]

The series is excellent. But there is a minor mistake at 7:08 in this video in last line, its x(k+4) instead of x(k+1)

[@zeminfeng4652]

Dear Mr John Could you have any experiment for the state space model that D is not equal to 0, because the model is obtained by system identification of ARX model. how i should handle it when i design MPC? thank you very much.

[@natezimmer4489]

The pipe "|" is a common operator seen probability as "given". For example, P(Y|X). i.e. the probability of Y given X. Seems appropriate in this context as well. Not really confusing, makes information more clear as to whats known.

[@jonaswinter5816]

When splitting the general expression into 'known' and 'unknown' variables, how comes the 'u(k|k)' ends up in the 'unknown part'? Do we not know the inputs of the current state (k)?

[@johnrossiter2323]

The current input is a choice to be made now.

[@anillamichhane2180]

@@johnrossiter2323 That's what I was going to ask but got the answer. Thanks

[@NickMulder]

mistake at the bottom of slide 5 ... :)