How can I find the controllability conditions or controllability distribution for discrete time nonlinear state-space system?

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• 
  Erol Kurt · Gazi University

  for any controlibility one needs to have the eigenvalues of the system as a result of linear and ninlinear operators. For this just think of the largest eigenvalud which drives the system. See the Jacobian and related subjects from any chaos ir nonlinear dynamics book.

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  for any controlibility one needs to have the eigenvalues of the system as a result of linear and ninlinear operators. For this just think of the largest eigenvalud which drives the system. See the Jacobian and related subjects from any chaos ir nonlinear dynamics book.

  Mar 28, 2012
• 
  Deleted

  AFAIK, for nonlinear systems, the equivalent to contralibilty is usally called flatness. Hope this is a helpful starting point.

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  AFAIK, for nonlinear systems, the equivalent to contralibilty is usally called flatness. Hope this is a helpful starting point.

  Mar 28, 2012
• 
  Alberto Lorandi Medina · Universidad Veracruzana

  Https://docs.google.com/viewer?a=v&q=cache:vrp0zdcuqkkj:www.ece.rutgers.edu/~gajic/psfiles/chap5.pdf+&hl=en&pid=bl&srcid=adgeeshov03br8ryegn2dsbt3vhhr1q0wfnwjslp6i5jgpkgyaxokv8gtxlvk28ihpa9hgak86b2qirkfvj6qhcirinxm441ixavysao_ptxyv-nuzuqi7nvi_rzgbcjsfamjomqyjz7&sig=ahietbrdqlabf9cdniheluyq8a74jsjewg

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  Https://docs.google.com/viewer?a=v&q=cache:vrp0zdcuqkkj:www.ece.rutgers.edu/~gajic/psfiles/chap5.pdf+&hl=en&pid=bl&srcid=adgeeshov03br8ryegn2dsbt3vhhr1q0wfnwjslp6i5jgpkgyaxokv8gtxlvk28ihpa9hgak86b2qirkfvj6qhcirinxm441ixavysao_ptxyv-nuzuqi7nvi_rzgbcjsfamjomqyjz7&sig=ahietbrdqlabf9cdniheluyq8a74jsjewg

  Mar 28, 2012
• 
  Adolfo Silva · National Institute for Space Research, Brazil

  You can applied the controllability test at each iteration from the system driven derive from Jacobian! I don't know if it useful for you problem!

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  You can applied the controllability test at each iteration from the system driven derive from Jacobian!
  
  I don't know if it useful for you problem!

  Mar 30, 2012
• 
  Deleted

  Here is the right link from Alberto: http://www.ece.rutgers.edu/~gajic/psfiles/chap5.pdf but it does not answer the question, the theory in this pdf is only about linear system...

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  Here is the right link from Alberto:
  http://www.ece.rutgers.edu/~gajic/psfiles/chap5.pdf
  but it does not answer the question, the theory in this pdf is only about linear system...

  Mar 30, 2012
• 
  Alberto Lorandi Medina · Universidad Veracruzana

  Sorry I did not see that need's the nonlinear case

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  Sorry I did not see that need's the nonlinear case

  Mar 30, 2012
• 
  Hebertt Sira-Ramirez · Center for Research and Advanced Studies of the National Polytechnic Institute

  Linearity or affine character in the control inputs doesn't make much sense in discrete time nonlinear systems. This is lost at the second iteration. The concept of vector fields does not directly apply to discrete time nonlinear systems either, much the less the concept of distribution. What you deal with is control parameterized transition maps from instant to instant. However, differentials, or Khaler differentials, and their "linear subspaces" may be used to chacterize a lot of concepts in this field. You may then take their duals and identify these objects as vector fields. The geometry is of a quite different flavor and non-intuitive, though. A good reference is earlier work by M. Fliess and El-Asmi (see also "Reversible linear and nonlinear discrete-time dynamics" in ieee explore. A beautiful paper by J. Grizzle may be found in http://scholar.google.com.mx/scholar_url?hl=es&q=http://citeseerx.ist.psu.edu/viewdoc/download%3Fdoi%3D10.1.1.34.3800%26rep%3Drep1%26type%3Dpdf&sa=X&scisig=AAGBfm3uEBYrXWT4_tJ0L19KwjfOy9-EvA&oi=scholarr&ei=dwF6T7yVF4bq2AX8pbm1Bg&ved=0CBoQgAMoAjAA). Search also under J.F. Pomet et al, Aranda et al. More recently: see papers by C. Moog, Ulle Kotta etc.

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  Linearity or affine character in the control inputs doesn't make much sense in discrete time nonlinear systems. This is lost at the second iteration. The concept of vector fields does not directly apply to discrete time nonlinear systems either, much the less the concept of distribution. What you deal with is control parameterized transition maps from instant to instant. However, differentials, or Khaler differentials, and their "linear subspaces" may be used to chacterize a lot of concepts in this field. You may then take their duals and identify these objects as vector fields. The geometry is of a quite different flavor and non-intuitive, though. A good reference is earlier work by M. Fliess and El-Asmi (see also "Reversible linear and nonlinear discrete-time dynamics" in ieee explore. A beautiful paper by J. Grizzle may be found in http://scholar.google.com.mx/scholar_url?hl=es&q=http://citeseerx.ist.psu.edu/viewdoc/download%3Fdoi%3D10.1.1.34.3800%26rep%3Drep1%26type%3Dpdf&sa=X&scisig=AAGBfm3uEBYrXWT4_tJ0L19KwjfOy9-EvA&oi=scholarr&ei=dwF6T7yVF4bq2AX8pbm1Bg&ved=0CBoQgAMoAjAA). Search also under J.F. Pomet et al, Aranda et al. More recently: see papers by C. Moog, Ulle Kotta etc.

  Apr 2, 2012
• 
  Seshadhri Srinivasan · ABB

  First for discrete time system... it matters how you find the discretized version. If you are using an Euler method with H.o.T. eliminated- it is equivalent to using Zero Order Hold... most of the properties of linear systems are retained and you can use the controllability tests for linear systems to ascertain the stability. If you are discretizing using Trapezoidal or other methods... you need to linearize around different points and then study controllability. Let me know if this helps you.

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  First for discrete time system... it matters how you find the discretized version. If you are using an Euler method with H.o.T. eliminated- it is equivalent to using Zero Order Hold... most of the properties of linear systems are retained and you can use the controllability tests for linear systems to ascertain the stability. If you are discretizing using Trapezoidal or other methods... you need to linearize around different points and then study controllability. Let me know if this helps you.

  Jun 15, 2012