http://iet.metastore.ingenta.com
1887

Optimal control of linear systems with delays in state and control via Walsh functions

Optimal control of linear systems with delays in state and control via Walsh functions

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

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

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 D (Control Theory and Applications) — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

The paper presents a parameter-embedding approach to the optimal control of linear time-delay systems, and develops a simple computational algorithm via Walsh functions. The algorithm employs the concept of Walsh operational matrices for delay and advance. These operational matrices provide us with a means of numerically integrating differential equations with delayed and advanced arguments; a major task in the process of computing optimal controls for time-delay systems. An attractive feature of the present method is its ultimate simplicity and the resulting piecewise constant controls are convenient in practical implementation.

References

    1. 1)
      • G.L. Kharatishvili . The maximum principle in the theory of optimal processes with time lags. Dokl. Akad. Nauk SSSR , 1
    2. 2)
      • N.N. Krasovskii . Analytic construction of an optimal regulator in a system with time lags. Prickl Mat. & Mekh. (USSR) , 1
    3. 3)
      • Krasovskii, N.N.: `Optimal processes in systems with time lags', Proc. 2nd IFAC Conf., 1963, Switzerland.
    4. 4)
      • D.H. Eller , J.K. Aggarwal , H.T. Banks . Optimal control of time delay systems. IEEE Trans. , 678 - 687
    5. 5)
      • J.K. Aggarwal . Computation of optimal control for time delay systems. IEEE Trans. , 683 - 685
    6. 6)
      • H.C. Chan , W.R. Perkins . Optimization of time delay systems using parameter imbedding. Automatica , 257 - 261
    7. 7)
      • S.A. Gracovetsky , M. Vidyasagar . A simple iterative method for sub-optimal control of linear time delay systems with quadratic cost. Int. J. Control , 997 - 1002
    8. 8)
      • M. Jamshidi , M. Malek-Zavarei . Suboptimal design of linear control systems with time delay. Proc. IEE , 12 , 1743 - 1746
    9. 9)
      • Sannuti, P.: `Near-optimal design of time delay systems by singular perturbation method', Proc. Joint Automatic Computer Conference, 1970, Atlanta, USA, p. 489–496.
    10. 10)
      • P. Sannuti , P.V. Kokotovic . Near optimum design of linear systems by a singular perturbation method. IEEE Trans. , 15 - 22
    11. 11)
      • M.A. Soliman , W.H. Ray . Optimal control for linear quadratic systems having time delays. Int. J. Control , 609 - 627
    12. 12)
      • M.A. Soliman , W.H. Ray . Optimal control of multivariable systems with pure time delays. Automatica , 681 - 689
    13. 13)
      • W.H. Ray , M.A. Soliman . The optimal control processes containing pure time delays—I. Necessary conditions for an optimum. Chem. Eng. Sci. , 1911 - 1925
    14. 14)
      • W.H. Ray . The optimal control processes modelled by transfer functions containing pure time delays. Chem. Eng. Sci. , 209 - 216
    15. 15)
      • J.J. Budelis , A.E. Bryson . Some optimal control results for differential difference systems. IEEE Trans. , 237 - 241
    16. 16)
      • H.N. Koivo , E.B. Lee . Controller synthesis for linear systems with retarded state and control variables and quadratic cost. Automatica , 203 - 208
    17. 17)
      • D.W. Ross . Controller design for time lag systems via a quadratic criterion. IEEE Trans. , 664 - 672
    18. 18)
      • Y. Alekal , P. Brunovsky , D.H. Chung , E.B. Lee . The quadratic problem for system with time delays. IEEE Trans. , 673 - 687
    19. 19)
      • J.K. Aggarwal . Feedback control of linear systems with distributed delay. Automatica , 9 , 367 - 379
    20. 20)
      • K. Inoue , H. Akashi , K. Ogino , Y. Sawaragi . Sensitivity approaches to optimization of linear systems with time delay. IEEE Trans. , 671 - 679
    21. 21)
      • C.F. Chen , C.H. Hsiao . Design of piecewise constant gains for optimal control via Walsh functions. IEEE Trans. , 596 - 603
    22. 22)
      • C.F. Chen , C.H. Hsiao . Walsh series analysis in optimal control. Int. J. Control , 881 - 897
    23. 23)
      • P. Sannuti . Analysis and synthesis of dynamic systems via blockpulse functions. Proc. IEE , 6 , 569 - 571
    24. 24)
      • G.P. Rao , T. Srinivasan . Analysis and synthesis of dynamic systems containing time delays via block-pulse functions. Proc. IEE, IEE , 9 , 1064 - 1068
    25. 25)
      • G.P. Rao , L. Sivakumar . System identification via Walsh functions. Proc. IEE , 1160 - 1161
    26. 26)
      • K.R. Palanisamy , G.P. Rao . Minimum energy control of time-delay systems via Walsh functions. Optimal control appl. & methods , 213 - 226
    27. 27)
      • Rao, G.P., Palanisamy, K.R.: `A new operational matrix for delay via Walsh functions and some aspects of its algebra and applications', Proc. National Systems Conference, 1978, 1, p. 60–61.
    28. 28)
      • Rao, G.P., Palanisamy, K.R.: `Optimal control of time delay systems via Walsh functions', Accepted for presentation at 9th IFIP Conf. on optimization, 4–8 September 1979, Warsaw, Poland.
    29. 29)
      • G.P. Rao , K.R. Palanisamy , T. Srinivasan . Extension of computation beyond the limit of initial normal interval in Walsh series analysis of dynamical systems. IEEE Trans. , 317 - 319
    30. 30)
      • L.S. Shieh , C.K. Yeung , B.C. McInnis . Solution of state space equations via block pulse functions. Int. J. Control , 383 - 392
    31. 31)
      • V.M. Popov . Pointwise degeneracy of linear time invariant delay differential equations. J. Differ. Equations , 541 - 561
    32. 32)
      • A.W. Olbrot . On degeneracy and related problems for linear constant time-lag systems. Ric. Autom. , 203 - 220
    33. 33)
      • A.W. Oldbrot . Algebraic criteria of controllability to zero function for linear constant time lag systems. Control & Cybern. , 59 - 77
    34. 34)
      • A.W. Olbrot . Observability tests for constant time lag systems. Control & Cybern. , 71 - 84
    35. 35)
      • A.C. Tsoi , M. Gregien . (1978) Recent advances in the algebraic system theory of delay differential equations, Recent theoretical advances in control theory.
    36. 36)
      • A.C. Tsoi . An explicit solution to a class of delay-differential equations. Int. J. Control , 39 - 48
    37. 37)
      • A.C. Tsoi . An explicit solution to a class of delay-differential equations. Int. J. Control , 787 - 799
    38. 38)
      • A.C. Tsoi . An explicit solution to a class of functional differential equations. Int. J. Control , 869 - 875
    39. 39)
      • A.K. Choudhury . A contribution to the controllability of time lag systems. Int. J. Control , 365 - 373
    40. 40)
      • H.T. Banks , J.A. Burns . Hereditary control problems: Numerical methods based on averaging approximations. SIAM J. Control & Optimiz. , 169 - 208
    41. 41)
      • H.T. Banks , J.A. Burns , H.A. Antosiewicz . (1975) , An abstract frame work for approximate solutions to optimal control problems governed by hereditary systems.
    42. 42)
      • Banks, H.T., Burns, J.A., Clitt, E.M., Thrift, P.R.: `Numerical solutions of hereditary control problems via approximation technique', 75-6, LCDS Technical Report, 1975.
    43. 43)
      • H.T. Banks , G.A. Kent . Control of functional differential equations of retarded and neutral type to target sets in function space. SIAM J. Control & Optimiz. , 567 - 593
    44. 44)
      • H.T. Banks , A. Manitius . Application of abstract variational theory to hereditary systems—A survey. IEEE Trans , 524 - 533
    45. 45)
      • H.T. Banks , A. Manitius . Projection series for retarded functional differential equations with applications to optimal control problems. J. Differ. Equations , 296 - 332
    46. 46)
      • H.T. Banks . Approximation of non-linear functional differential equation control systems. J. Optimiz. Theory & Appl. , 383 - 408
    47. 47)
      • Manitius, A.: `Optimal control of time lag systems with quadratic performance indexes', Proc. Fourth IFAC Congress, 1969, Warsaw.
    48. 48)
      • Manitius, A.: `Sufficient conditions for function space controllability and feedback stabilizability of linear retarded systems', Proc. IEEE Conf. on Decision and Control, 1976.
    49. 49)
      • M.C. Delfour . The linear quadratic optimal control problem for hereditary differential systems: Theory and numerical solution. Appl. Math. & Optimiz. , 101 - 162
    50. 50)
      • M.C. Delfour , B.J. Kirby . (1974) Linear hereditary systems and their control, Optimal control and its applications.
    51. 51)
      • Delfour, M.C.: `Numerical solution of the optimal control problem for linear hereditary differential systems with a linear quadratic cost function and approximation of Riccati differential equation', CRM. Report 408, 1974.
    52. 52)
      • Delfour, M.C.: `Numerical solution of the operational Riccati differential equation in the optimal control theory of linear hereditary differential systems with a linear-quadratic cost function', Proc. IEEE Conference on Decision and Control, 1974, Arizona, USA, p. 784–790.
    53. 53)
      • M.C. Delfour , S.K. Mitter . Hereditary differential systems with constant delays. I. General case. J. Differ. Equations , 213 - 235
    54. 54)
      • M.C. Delfour , S.K. Mitter . Hereditary differential equations with constant delays. II. A class of affine systems and the adjoint problem. J. Differ. Equations , 18 - 28
    55. 55)
      • Burkhardt, H.: `Ein Beitrag zur Lösung optimaler Steuerungs und Regelungsprobleme mit Hilfe der Walsh-Transformation', June 1974, Dr.-Ing. Thesis, University Karlsruhe.
    56. 56)
      • G.P. Rao . (1983) , Piecewise constant orthogonal functions and their application to systems and control.
http://iet.metastore.ingenta.com/content/journals/10.1049/ip-d.1983.0051
Loading

Related content

content/journals/10.1049/ip-d.1983.0051
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address