Hey everyone, thanks for watching this video! If you have any questions or comments that you'd like me to see, please leave them under this comment so that I get notified and can respond. Cheers!
Hi brian I'm from ethiopia. Your videos are exceptional. I'm truly satisfied. I thank you. My question is that can you do such videos on linear quadratic regulator (LQR)?
I would say Katkim show and Christopher Lum(especially for aerospace) are can be added to the list..! Its just amazing that anyone can learn anything over the internet!
Controllability is dual to Observability Poles (eigenvalues) are dual to Zeroes The Initial value theorem IVT is dual to the Final value theorem FVT Stability is dual to instability Robustness is dual to performance Complex numbers are dual to real numbers In physics equivalence, similarity is also known as duality, so we have the the following duals (Jewels):- Energy is equivalent or dual to mass -- Einstein Gravitation is dual to acceleration --- Einstein Potential energy is dual to kinetic energy Space is dual to time -- Einstein Certainty is dual to uncertainty, the Heisenberg certainty/uncertainty principle Energy is literally duality. Energy is transported by the electromagnetic field in the form of photons or wave/particles, quantum duality. Energy is inherently dual. In physics everything is made out of energy hence duality. If energy is conserved and energy is duality then duality must be conserved! The conservation of duality is the fifth law of thermodynamics. Negative curvature is dual to positive curvature (Riemann, Gauss) Hyperbolic geometry is dual to elliptic, spherical geometry A white hole (big bang, divergence) is dual to an infinite mass black hole (convergence) In mathematics: Integration is dual to differentiation Duality creates reality, all observers are inherently dual if they are made out of energy Genes are dual to memes Everything (all things) is/are dual to nothing.
@@ashkabrawn Dark energy is dual to dark matter! Thesis is dual to anti-thesis -- the generalized or time independent Hegelian dialectic. Hegel's cat: Alive (thesis, being) is dual to not alive (anti-thesis, non being) -- Schrodinger's cat. Immanuel Kant: Synthetic a priori knowledge, all knowledge is dual. Philosophy, physics, mathematics, control theory all lead to duality! "Philosophy is dead" -- Stephen Hawking. It looks like Mr Hawking got this one wrong! No philosophy = no duality.
@@ashkabrawn The future is dual to the past. Many worlds (possibilities) or the multiverse would be the future and the one world or universe (reality) is the past. The present or the 'now' is therefore the duality or the biverse. The future meets or intersects the past in the present via duality! Noumenal (before measurement, a priori) is dual to phenomenal (after measurement, a posteriori). Deduction (rational) is dual to induction (empirical) -- Immanuel Kant. Positive is dual to negative. Duality converts possible worlds into the real world or probability = 1. Time is dual:- My absolute time is your relative time and your absolute time is my relative time. Absolute time (Galileo) is dual to relative time (Einstein).
Hey! I have watched your lectures on your UA-cam channel and it is good to see you here again on this MATLAB channel. Great explanation...nice work...Sir 😊
Your definition of controllability is actually reachability, in continuous systems they are equivalent but for discrete systems they are not. To be reachable the system must be able to go from your initial state to any other state, to be controllable the system must be able to go from any initial state to zero. In discrete systems it is easy to see that a A = [0 0; 0 0] would be controllable (gets to zero from any point in one sampling without depending on B), but it would only be reachable if B = [1 0; 0 1] (individually control each state). Great video nonetheless.
To my understanding. D matrix is the direct feed through term, the input will change your measurement (y) directly, not through the system evolution (Ax). And this type of system is rare (never see and cannot think of one). Note that if D is non-zero, the transfer function will not be strictly proper. Another reason maybe, because the maths is the same with or without D being zero, college courses usually design to be easy to understand and illustrate the key concept.
Just something came up in my mind. If you are discretizating a continuous time system, it is likely that the resulting discrete system (Ad,Bd, Cd,Dd) Dd is non-zero. I think there is a paper talks about discretization will introduce something call "sampling zeros". Even the continuous model is strictly proper, the discretized system will not be.
Could you please tell me why will C-matrix be zero when states are not measurable. Also what could be the output y in the examples of train and car? What role do output y and C-matrix play in observability, conceptually?
When we judge people from outside based on their color or financial status, we are observing only a handful of states, and thus we end up fooling ourselves
Correction to my earlier mistake:- A white hole (big bang, divergence) is dual to an infinite mass black hole (convergence) Dark energy is literally hyperbolic geometry or negative curvature Positive is dual to the negative.
![Degrees of Controllability and Gramians [Control Bootcamp]](http://i.ytimg.com/vi/ZNHx62HbKNA/mqdefault.jpg)
Hey everyone, thanks for watching this video! If you have any questions or comments that you'd like me to see, please leave them under this comment so that I get notified and can respond. Cheers!
Make video on the how to interpret sensor data.
exactly what i asked! thank you brian :D
Hi brian
I'm from ethiopia. Your videos are exceptional. I'm truly satisfied. I thank you. My question is that can you do such videos on linear quadratic regulator (LQR)?
@@benallia8262 Glad to hear it!
@@gosayeweldemaryam2415 I'm finishing up a video on LQR right now! Should post next week.
You and Steve Brunton are 2 gems of control systems.!
Indeed! ;)
I couldn't agree more!
As true as it gets.
i just realize both of them are from Seattle
I would say Katkim show and Christopher Lum(especially for aerospace) are can be added to the list..!
Its just amazing that anyone can learn anything over the internet!
Such a practical example (the beam) at the end makes things so much more logic (unobservable modes) than I learned in class
This deserves 100K+ views. Good job, Brian. Stay productive!
That car driving example hits hard ... Brian shows that perfect examples could exists!
Thanks!
Really nice job Brian, you're right to be proud of this one...excellent explanation with well-chosen examples. Thank you for this!
God bless you Brian, finally could understand the intuition behind all that math!
Omg... I just came here after watching Steve's series !! Thanks for the pointers
This is a fantastic explaination of the topic and gave me a better and clearer view of controllability and observability. Thanks a lot!
Thank you Brian
Simple explanation with powerful examples
Controllability is dual to Observability
Poles (eigenvalues) are dual to Zeroes
The Initial value theorem IVT is dual to the Final value theorem FVT
Stability is dual to instability
Robustness is dual to performance
Complex numbers are dual to real numbers
In physics equivalence, similarity is also known as duality, so we have the the following duals (Jewels):-
Energy is equivalent or dual to mass -- Einstein
Gravitation is dual to acceleration --- Einstein
Potential energy is dual to kinetic energy
Space is dual to time -- Einstein
Certainty is dual to uncertainty, the Heisenberg certainty/uncertainty principle
Energy is literally duality. Energy is transported by the electromagnetic field in the form of photons or wave/particles, quantum duality. Energy is inherently dual. In physics everything is made out of energy hence duality.
If energy is conserved and energy is duality then duality must be conserved! The conservation of duality is the fifth law of thermodynamics.
Negative curvature is dual to positive curvature (Riemann, Gauss)
Hyperbolic geometry is dual to elliptic, spherical geometry
A white hole (big bang, divergence) is dual to an infinite mass black hole (convergence)
In mathematics: Integration is dual to differentiation
Duality creates reality, all observers are inherently dual if they are made out of energy
Genes are dual to memes
Everything (all things) is/are dual to nothing.
Did you just cover Heisenberg in more ways than he himself pictured.. 😉😅
@@ashkabrawn Dark energy is dual to dark matter!
Thesis is dual to anti-thesis -- the generalized or time independent Hegelian dialectic.
Hegel's cat: Alive (thesis, being) is dual to not alive (anti-thesis, non being) -- Schrodinger's cat.
Immanuel Kant: Synthetic a priori knowledge, all knowledge is dual.
Philosophy, physics, mathematics, control theory all lead to duality!
"Philosophy is dead" -- Stephen Hawking.
It looks like Mr Hawking got this one wrong! No philosophy = no duality.
@@hyperduality2838 what is the duality for universe, biverse and multiverse ?
@@ashkabrawn The future is dual to the past. Many worlds (possibilities) or the multiverse would be the future and the one world or universe (reality) is the past. The present or the 'now' is therefore the duality or the biverse.
The future meets or intersects the past in the present via duality!
Noumenal (before measurement, a priori) is dual to phenomenal (after measurement, a posteriori).
Deduction (rational) is dual to induction (empirical) -- Immanuel Kant.
Positive is dual to negative.
Duality converts possible worlds into the real world or probability = 1.
Time is dual:- My absolute time is your relative time and your absolute time is my relative time.
Absolute time (Galileo) is dual to relative time (Einstein).
so ying and yang
Probably the most useful video I happen to come across
why this video does not have million likes?
Another Brian Douglas Hood Classic👌
This definitely helps the intuition. Good video!
Hey! I have watched your lectures on your UA-cam channel and it is good to see you here again on this MATLAB channel.
Great explanation...nice work...Sir 😊
Man you are awesome.
Thank you very much.
Nice to find Brian here!
Your videos are art, thanks dude!
Your definition of controllability is actually reachability, in continuous systems they are equivalent but for discrete systems they are not. To be reachable the system must be able to go from your initial state to any other state, to be controllable the system must be able to go from any initial state to zero. In discrete systems it is easy to see that a A = [0 0; 0 0] would be controllable (gets to zero from any point in one sampling without depending on B), but it would only be reachable if B = [1 0; 0 1] (individually control each state). Great video nonetheless.
Great explanation! Thank you so much!
Excellent video. Thank you.
Hello Brian, can you please make a lecture about stabilizability and detectability? those are very confusing terms. Thank you
Great video!
Hi Brian , awesome work!
May I know which software you use for this illustrations?
Thanks
Thank you for this video!
Love your videos! Can you please explain why is the D matrix usually regarded as zero in college courses?
To my understanding. D matrix is the direct feed through term, the input will change your measurement (y) directly, not through the system evolution (Ax). And this type of system is rare (never see and cannot think of one). Note that if D is non-zero, the transfer function will not be strictly proper. Another reason maybe, because the maths is the same with or without D being zero, college courses usually design to be easy to understand and illustrate the key concept.
Just something came up in my mind. If you are discretizating a continuous time system, it is likely that the resulting discrete system (Ad,Bd, Cd,Dd) Dd is non-zero. I think there is a paper talks about discretization will introduce something call "sampling zeros". Even the continuous model is strictly proper, the discretized system will not be.
Hi Brian
Many Thanks for your great videos , do you have notes/slides that can be shared in pdf format ?
Would have been nice of some demonstrations in matlab/simulink, just like part 2
Using reconstructed velocity, by position diferentiation, and these same positions as output can bring more information to estimate other states?
Could you please tell me why will C-matrix be zero when states are not measurable. Also what could be the output y in the examples of train and car? What role do output y and C-matrix play in observability, conceptually?
Hey! good Job Sir,
Hello All.... Is there any specialized Power system course using SIMULINK
Thank you for sharing :)
Это просто превосходно!
Amazing stuff
When we judge people from outside based on their color or financial status, we are observing only a handful of states, and thus we end up fooling ourselves
wow!
Correction to my earlier mistake:-
A white hole (big bang, divergence) is dual to an infinite mass black hole (convergence)
Dark energy is literally hyperbolic geometry or negative curvature
Positive is dual to the negative.
Bnhihhhh
Fantastic video !