Hierarchical Optimal Control of Non-linear Systems using Fast Walsh Transform

FWT를 이용한 비선형계의 계층별 최적제어

  • Published : 2000.08.01

Abstract

This paper presents a new algorithm for hierarchical optimal control of nonlinear systems. The proposed method is simple because the solutions are obtained by only exchanging informations of coefficient vector based on interaction prediction principle and FWT(fast Walsh transform) in upper and lower level. Since we solve two point boundary problem with Picard's iterative method and the backward integral operational matrix of Walsh function to obtain the optimal vector of each independent subsystem, the algorithm is simple and its operation is fast without inverse matrix and kronecker product operation. In simulation, the proposed algorithm's usefulness is proved by comparison with the global optimal control methods.

Keywords

References

  1. M. F. Hassan and M. G. Singh, ' Hierarchical Successive Approximation Algor-ithms for Non-linear Systems. Part I. Generalisation of the Method of Takahara', Large Scale Systes, VOL. 2 , pp. 65-79, 1981
  2. M. F. Hassan and M. G. Singh, ' Hierachical Successive Approximation Algori-thms for Non-linear Systems. Part II. Algorithms Based on Costate Coordination ',Large Scale Systems, VOL. 2, pp. 81-95, 1981
  3. 이한석, 조영호, 이명규, 안두수, '블럭펼스 함수에 의한 비선형계 2계층 최적제어', 대한전기학회논문지, 제47권, 제4호, pp. 494-502, 1998
  4. N.J.Smith and A.P.Sage., 'An introduction to hierarchical systems theory', COMP & ELECT. ENG.', VOL. 1, pp. 55-71, 1973 https://doi.org/10.1016/0045-7906(73)90027-X
  5. M. G. Singh and A. Titli, Systems : Decomposition, Optimisation and Control, Pergamon Press, 1978
  6. S. C. Tsay and T. T. Lee, 'Analysis and Optimal Control of Linear Time-varying Systems via General Orthogonal Polynomials', Int. J. System Science, Vol. 18, No. 8, pp. 1579-1594, 1987 https://doi.org/10.1080/00207728708967137
  7. C. F. Chen and C. H. Hsiao. 'Design of Piecewise Constant Gains for Optimal Control via Walsh Function', IEEE Trans. on Automatic Control, Vol. 20, No. 5, pp. 596-602, 1975 https://doi.org/10.1109/TAC.1975.1101057
  8. 이명규, '고속월쉬변환에 의한 선형시변계의 해석 및 최적제어를 위한 새로운 접근방법', 제47권, 제1호, pp. 75-82, 1998
  9. W. K. Pratt, 'Transform Image Coding', Proc. IEEE, Vol. 57, pp. 58-68, 1969
  10. A. Ghandakly and P. Idowu, ' Design of a Model Reference Adaptive Stabilizer for the Exciter and Governor Loops of Power Generators', IEEE Transactions on Power Systems, VOL. 5, NO. 3, pp. 887-893, 1990 https://doi.org/10.1109/59.65918
  11. 안두수, Walsh함수와 시스템 제어, 복두출판사, 2000
  12. Kreysig, Advanced engineering mathmatics, Wiley, 1993