Consciousness Videos

State Space, Part 3: A Conceptual Approach to Controllability and Observability



MATLAB

This video helps you gain understanding of the concept of controllability and observability. Two important questions that come up in control systems engineering are: Is your system controllable? And is it observable? Assuming you have a good linear model of your system, you can answer both questions using some simple matrix operations and the A, B, and C matrices of your state-space model.

In this video, we’re going to approach the answers from a conceptual and intuitive direction.

References:
– Create, analyze, and use state-space representation for control design with MATLAB and Simulink: http://bit.ly/2HrtZQy
– Steve Brunton — Control Bootcamp: http://bit.ly/2HrWAFm

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24 thoughts on “State Space, Part 3: A Conceptual Approach to Controllability and Observability
  1. 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?

  2. 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.

  3. 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

  4. 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.

  5. 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.

  6. 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!

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