Optimal Control of Nonlinear Systems Using Block Pulse Functions

블럭펄스 함수를 이용한 비선형 시스템의 최적제어

  • Jo, Yeong-Ho (Dept.of Electric Electronics Computer Engineering, Sungkyunkwan University) ;
  • An, Du-Su (Dept.of Electric Electronics Computer Engineering, Sungkyunkwan University)
  • 조영호 (성균관대 전기전자컴퓨터공학부) ;
  • 안두수 (성균관대 전기전자컴퓨터공학부)
  • Published : 2000.03.01

Abstract

In this paper, we presented a new algebraic iterative algorithm for the optimal control of the nonlinear systems. The algorithm is based on tow steps. The first step transforms optimal control problem into a sequence of linear optimal control problem using the quasilinearization method. In the second step, TPB(two point boundary condition problem) is solved by algebraic equations instead of differential equations using BPF(block pulse functions). The proposed algorithm is simple and efficient in computation for the optimal control of nonlinear systems. In computer simulation, the algorithm was verified through the optimal control design of Van del pole system and Volterra Predatory-prey system.

Keywords

References

  1. D. E. Kirk, Optimal Control Theory, Prentice-hall Inc., 1970
  2. M. F. Hassan and M. G. Singh, 'Hierarchical Successive Approximation Algorithms for Non-linear Systems. Part J. Generalisation of the Method of Takahara', Large Scale Systes, VOL. 2, pp. 65-79, 1981
  3. M. F. Hassan and M. G. Singh, 'Hierachical Successive Approximation Algorithms for Non-linear Systems. Part II. Algorithms Based on Costate Coordination ',Large Scale Systems, VOL. 2, pp. 81-95, 1981
  4. Z. H. Jiang and W. Schaufelberger, Block Pulse Functions and Their Applications in Control Systems, Springer-verlag, 1992
  5. K. B. Datta & M. Mohan, Orthogonal Functions in Systems and Control, Word Scientific Publishing Co., 1995
  6. N. S. Hsu and B. Cheng, 'Analysis and Optimal Control of time-varying linear systems Via block-pulse functions', Int. J. Control, Vol. 33, No.6, pp. 1123-1133, 1981
  7. 이한석, 조영호, 이명규, 안두수, '블럭펄스 함수에 의한 비선형계의 2계층 최적제어,' 대한전기학회 논문지, 47권 4호, pp. 494-502, 1998
  8. W. Shienyu, 'Convergence of block pulse series approximation solution for optimal control problem', Int. J. Systems Sci. Vol. 21, No.7, pp. 1355-1368, 1990
  9. A. Deb, G. Sarkar, M. Bhattachariee and S. K. Sen, 'All-integrator Approach to Linear SISO Control System Analysis using Block Pulse Functions (BPF)', J. Franklin Inst., Vol. 334B, No.2, pp. 319-335, 1997 https://doi.org/10.1016/S0016-0032(96)00054-3
  10. J. D. Pearson, 'Approximation methods in optimal control', J. Electron Control, Vol. 13, pp. 435-469, 1962
  11. M. S. Mahmoud, 'Closed-loop multilevel Control of large nonlinear systems via invariant imbedding techniques', Comput. Elect. eng. Vol. 4, pp. 3-23, 1977 https://doi.org/10.1016/0045-7906(77)90003-9