Stability analysis of iterative optimal control algorithms modelled as linear unit memory repetitive processes

Access Full Text

Stability analysis of iterative optimal control algorithms modelled as linear unit memory repetitive processes

For access to this article, please select a purchase option:

Buy article PDF
£12.50
(plus tax if applicable)
Add to cart
Buy Knowledge Pack
10 articles for £75.00
(plus taxes if applicable)
Add to cart

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IEE Proceedings - Control Theory and Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

IEE
Published

The theory of unit memory repetitive processes is used to investigate local convergence and stability properties of algorithms for the solution of discrete optimal control problems. In particular, the properties are addressed of a method for finding the correct solution of an optimal control problem where the model used for optimisation is different from reality. Limit profile and stability concepts of unit memory linear repetitive process theory are employed to demonstrate optimality and to obtain necessary and sufficient conditions for convergence. Two main stability theorems are obtained from different approaches and their equivalence is proved. The theoretical results are verified through simulation and numerical analysis, and it is demonstrated that repetitive process theory provides a useful tool for the analysis of iterative algorithms for the solution of dynamic optimal control problems.

Inspec keywords: control system analysis; discrete systems; iterative methods; convergence; optimal control

Other keywords: linear unit memory repetitive processes; stability analysis; dynamic optimal control problems; iterative optimal control algorithms; discrete optimal control problems

Subjects: Interpolation and function approximation (numerical analysis); Discrete control systems; Optimal control; Control system analysis and synthesis methods

References

    1. 1)
      • P.D. ROBERTS . Numerical investigation of a stability theorem arising from the 2-dimensional analysis of an iterative optimal control algorithm. Multidimens. Syst. Signal Process. , 109 - 127
    2. 2)
      • L.S. Pontryagin , V.G. Boltyanskii , R.V. Gamkrelidze , E.F. Mishchenko . (1963) , The mathematical theory of optimal processes.
    3. 3)
      • D.H. Owens . Asymptotic stability of differential multipass processes. Electron. Lett. , 446 - 447
    4. 4)
      • A.E. BRYSON . Optimal control –1950 to 1985. IEEE Control Syst. Mag. , 3 , 26 - 33
    5. 5)
      • ROBERTS, P.D.: `A MATLAB graphical user interface for investigating the local stability of iterative optimal control algorithms', 455, UKACC International Conference Control'98, September 1998, Swansea, UK, p. 1629–1634.
    6. 6)
      • BANKS, S.P., DINESH, K.: `Approximate optimal control of nonlinear systems', 4th International Conference on Optimization: techniques and applicationsICOTA'98, July 1998, Perth, Australia, p. 767–774.
    7. 7)
      • E.P. HOFER , B. TIBKEN . An iterative method for the finite bilinear quadratic control problem. J. Optim. Theory Appl. , 411 - 427
    8. 8)
      • ROGERS, E., OWENS, D.H.: `The influence of boundary conditions on the stability of repetitive processes modelled as 2D linear systems', 13th IFAC World Congress on Automatic control, July 1996, San Francisco, USA, 6, p. 155–158.
    9. 9)
      • BANKS, S.P., MCCAFFREY, D.: `Approximate optimal controllers for nonlinear parabolic systems', 15th IMACS World Congress on Scientific computation, modelling and applied mathematics, 1997, Berlin, Germany, 5, p. 185–190.
    10. 10)
      • GALKOWSKI, K., ROGERS, E., OWENS, D.H.: `1D discrete state-space model approximations to the dynamics of a class of 2D linear system', 2nd Portuguese Conference on Automatic control, September 1996, Porto, Portugal, p. 419–424.
    11. 11)
      • ROBERTS, P.D.: `Computing the stability of iterative optimal control algorithms through the use of two-dimensional system theory', 427, UKACC International Conference Control'96, September 1996, Exeter, UK, p. 981–986.
    12. 12)
      • ROBERTS, P.D.: `An algorithm for optimal control of nonlinear systems with model-reality differences', 12th IFAC Congress on Automatic control, 1993, Sydney, Australia, 8, p. 407–412.
    13. 13)
      • P. MARCHAND . (1999) , Graphics and GUIs with MATLAB.
    14. 14)
      • Z. AGANOVIC , Z. GAJIC . The successive approximation procedure for finite time optimal control of bilinear systems. IEEE Trans. Autom. Control , 1932 - 1935
    15. 15)
      • M. Athans , P.L. Falb . (1966) , Optimal control.
    16. 16)
      • BECERRA, V.M.: `Development and applications of novel optimal control algorithms', 1994, PhD Thesis, City University, Department of Electrical, Electronic and Information Engineering, London.
    17. 17)
      • E. ROGERS , D.H. OWENS . (1992) Stability analysis for linear repetitive processes, Lecture Notes in Control and Information Sciences.
    18. 18)
      • E. FORNASINI , G. MARCHESINI . Doubly-indexed dynamical systems: state space models and structural properties. Math. Syst. Theory , 1502 - 1517
    19. 19)
      • ROBERTS, P.D., BECERRA, V.M.: `An algorithm for optimal nonlinear batch process control with model-reality differences and unmatched terminal constraints', IFAC International Symposium on Advanced control of chemical processesADCHEM'97, June 1997, Banff, Canada, p. 517–522.
    20. 20)
      • AMANN, N., ROGERS, E., OWENS, D.H.: `Convergence rates for learning control algorithms –a repetitive process theory approach', 13th IFAC World Congress on Automatic control, 1996, San Francisco, USA, 6, p. 445–450.
    21. 21)
      • E.P. ROESSER . A discrete state space model for linear image processing. IEEE Trans. Auto. Control , 1 - 10
    22. 22)
      • V.M. BECERRA , P.D. ROBERTS . Dynamic integrated system optimization and parameter estimation for discrete time optimal control of nonlinear systems. Int. J. Control , 2 , 257 - 281
    23. 23)
      • ROBERTS, P.D.: `Unit memory repetitive processes and iterative optimal control algorithms', IEE International Conference Control'94, IEE Conf. Publ. 389, March 1994, Warwick, UK, p. 460–465.
    24. 24)
      • ROBERTS, P.D.: `Unit memory repetitive process aspects of iterative optimal control algorithms', 33rd Conference on Decision and control, December 1994, Lake Buena Vista, Florida, USA, p. 1394–1399.
    25. 25)
      • A.E. Bryson , Y.C. Ho . (1969) , Applied optimal control.
    26. 26)
      • W.H. SCHMIDT . (1993) , Iterative methods for optimal control processes governed by integral equations.
http://iet.metastore.ingenta.com/content/journals/10.1049/ip-cta_20000391
Loading

Related content

content/journals/10.1049/ip-cta_20000391
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading