Discrete Time LQR Option #359

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1. murrayrm commented on Jan 2, 2020

   

   murrayrm

   on Jan 2, 2020

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   Rather than overload the lqr function, it might make more sense to implement a second function dlqr for the discrete time case. This would match the approach taken by MATLAB.

   Another approach would be to create a function linear_quadratic_regulator that takes a system as its input and then solves the quadratic regulator problem based on whether the system is continuous or discrete.

   Finally, we may also want to implement dlqe and/or linear quadratic estimator at the same time, following PR #351.
2. adam2392 commented on Jan 2, 2020

   

   adam2392

   on Jan 2, 2020

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   Okay, awesome I can try to implement a dlqr function, and should this just also be using https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.solve_discrete_are.html for the solver instead of SLICOT?

   I saw that there was interest in moving away from SLICOT in #27 ?
3. murrayrm commented on Jan 2, 2020

   

   murrayrm

   on Jan 2, 2020

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   I would use the scipy function, though a full implementation could use a method keyword with method=slycot (or slicot?) calling the slycot function and method=scipy (default) calling the scipy version. See issue #255 for a discussion on method.
4. robertobucher commented on Jan 2, 2020

   

   robertobucher

   on Jan 2, 2020 via email

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   Hi Adam I have a temporary solution for both dlqr and lqe functions that I'm using in my practical systems in my Lab at SUPSI since a couple of years. Both are implemented in the package supsictrl.ctrl_repl under supsictrl/src/ctrl_repl.py on my github page for the pysimCoder project. Best regards Roberto

   …

   On 1/2/20 6:49 PM, Adam Li wrote: Okay, awesome I can try to implement a |dlqr| function, and should this just also be using: https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.solve_discrete_are.html for the solver instead of SLICOT? I saw that there was interest in moving away from SLICOT in #27 <#27> ? — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#359?email_source=notifications&email_token=AB7WD7SMTNNUWDIQP3EDFV3Q3YSIZA5CNFSM4KCDWKIKYY3PNVWWK3TUL52HS4DFVREXG43VMVBW63LNMVXHJKTDN5WW2ZLOORPWSZGOEH65YIA#issuecomment-570285088>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AB7WD7UB4JR6LWAUW5C63ETQ3YSIZANCNFSM4KCDWKIA>.
5. murrayrm

   added

   enhancement

   on Dec 26, 2020
6. lucasbellinaso commented on Jan 13, 2021

   

   lucasbellinaso

   on Jan 13, 2021

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   I have solution that I am using in my classes to calculate simple discrete-time LQR:

   def dlqr_calculate(G, H, Q, R, returnPE=False):
     '''
     Discrete-time Linear Quadratic Regulator calculation.
     State-feedback control  u[k] = -K*x[k]
   
     How to apply the function:    
         K = dlqr_calculate(G,H,Q,R)
         K, P, E = dlqr_calculate(G,H,Q,R, return_solution_eigs=True)
   
     Inputs:
       G, H, Q, R  -> all numpy arrays  (simple float number not allowed)
       returnPE: define as True to return Ricatti solution and final eigenvalues
   
     Returns:
       K: state feedback gain
       P: Ricatti equation solution
       E: eigenvalues of (G-HK)  (closed loop z-domain poles)
     '''
     from scipy.linalg import solve_discrete_are, inv, eig
     P = solve_discrete_are(G, H, Q, R)  #Solução Ricatti
     K = inv(H.T@P@H + R)@H.T@P@G    #K = (B^T P B + R)^-1 B^T P A 
   
     if returnPE == False:   return K
   
     from numpy.linalg import eigvals
     eigs = np.array([eigvals(G-H@K)]).T
     return K, P, eigs
   
7. murrayrm

   added this to the 0.9.x milestone on Jan 18, 2021
8. sawyerbfuller commented on Jan 22, 2021

   

   sawyerbfuller

   on Jan 22, 2021

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   Thank you lucas! Feel free to submit a pull request! (https://github.com/python-control/python-control/wiki/How-to-contribute-with-a-pull-request)
9. sawyerbfuller

   linked a pull request that will close this issueDLQR and DLQE #670on Nov 9, 2021
10. murrayrm

    closed this as completedin #670on Dec 31, 2021