MULTIPLE VALUED ITERATIVE DYNAMICS MODELS OF NONLINEAR DISCRETE-TIME CONTROL DYNAMICAL SYSTEMS WITH DISTURBANCE

- Journal title : Journal of the Korean Mathematical Society
- Volume 50, Issue 1, 2013, pp.17-39
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2013.50.1.017

Title & Authors

MULTIPLE VALUED ITERATIVE DYNAMICS MODELS OF NONLINEAR DISCRETE-TIME CONTROL DYNAMICAL SYSTEMS WITH DISTURBANCE

Kahng, Byungik;

Kahng, Byungik;

Abstract

The study of nonlinear discrete-time control dynamical systems with disturbance is an important topic in control theory. In this paper, we concentrate our efforts to multiple valued iterative dynamical systems, which model the nonlinear discrete-time control dynamical systems with disturbance. After establishing the validity of such modeling, we study the invariant set theory of the multiple valued iterative dynamical systems, including the controllability/reachablity problems of the maximal invariant sets.

Keywords

nonlinear discrete-time control dynamical system;disturbance;invariance;steady state;controllability/reachability;

Language

English

Cited by

1.

References

1.

R. Agarwal, M. Bohner, D. O'Regan, and A. Peterson, Dynamic equations on time scales: a survey, J. Comput. Appl. Math. 141 (2002), no. 1-2, 1-26.

2.

D. K. Arrowsmith and C. M. Place, An Introduction to Dynamical Systems, Cambridge University Press, 1990.

3.

Z. Arstein and S. Rakovic, Feedback invariance under uncertainty via set-iterates, Automatica 44 (2008), 520-525.

4.

P. Ashwin, X. C. Fu, T. Nishikawa, and K. Zyczkowski, Invariant sets for discontinuous parabolic area-preserving torus maps, Nonlinearity 13 (2000), no. 3, 819-835.

6.

R. Findeisen, L. Imsland, F. Allgower, and B. A. Foss, State and output feedback non- linear model predictive control: An overview, Euro. J. Control 9 (2003), no. 9, 179-195.

7.

X. C. Fu, F. Y. Chen, and X. H. Zhao, Dynamical properties of 2-torus parabolic maps, Nonlinear Dynam. 50 (2007), no. 3, 539-549.

8.

X. C. Fu and J. Duan, On global attractors for a class of nonhyperbolic piecewise affine maps, Phys. D 237 (2008), no. 24, 3369-3376.

9.

B. Kahng, Maximal invariant sets of multiple valued iterative dynamics in disturbed control systems, Int. J. Circuits, Systems and Signal Processing 2 (2008), 113-120.

10.

B. Kahng, Positive invariance of multiple valued iterative dynamical systems in disturbed control models, in Proc. Med. Control Conf. Thessaloniki, Greece, 2009, pp. 663-668.

11.

B. Kahng, The approximate control problems of the maximal invariant sets of non-linear discrete-time disturbed control dynamical systems: an algorithmic approach, in Proc. Int. Conf. on Control and Auto. and Sys. Gyeonggi-do, Korea, 2010, pp. 1513-1518.

12.

B. Kahng, A survey of maximal invariance in multiple valued iterative dynamics models for nonlinear control and automation, preprint, 2012.

13.

B. Kahng and J. Davis, Maximal dimensions of uniform sierpinski fractals, Fractals 18 (2010), no. 4, 451-460.

14.

B. Kahng and M. Mendes, The controllability problems of the maximal invariant sets of discrete time dynamical systems, preprint, 2008.

15.

E. Kerrigan, J. Lygeros, and J. M. Maciejowski, A geometric approach to reachability computations for constrained discrete-time systems, in IFACWorld Congress, Barcelona, Spain, 2002.

16.

E. Kerrigan and J. M. Maciejowski, Invariant sets for constrained nonlinear discrete- time systems with application to feasibility in model predictive control, in Proc. 39th IEEE Conf. on Decision and Control, Sydney, Australia, 2000.

17.

D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, Constrained model predictive control: stability and optimality, Automatica J. IFAC 36 (2000), no. 6, 789- 814.

18.

D. Q. Mayne, M. Seron, and S. V. Rakovic, Robust model predictive control of con- strained linear systems with bounded disturbances, Automatica J. IFAC 41 (2005), no. 2, 219-224.

19.

M. Mendes, Dynamics of Piecewise Isometric Systems with Particular Emphasis to the Goetz Map, Ph. D. Thesis, University of Surrey, 2001.

20.

C. J. Ong and E. G. Gilbert, Constrained linear systems with disturbances: enlargement of their maximal invariant sets by nonlinear feedback, in Proc. Amer. Control Conf. Minneapolis, MN, 2006, pp. 5246-5251.

21.

S. V. Rakovic, E. C. Kerrigan, K. I. Kouramas, and D. Q. Mayne, Invariant approximations of the minimal robustly positively invariant sets, IEEE Trans. Automat. Control 50 (2005), no. 3, 406-410.

22.

S. V. Rakovic, E. C. Kerrigan, D. Q. Mayne, and K. I. Kouramas, Optimized robust control invariance for linear discrete-time systems: Theoretical foundations, Automatica J. IFAC 43 (2007), no. 5, 831-841.

23.

S. V. Rakovic, E. C. Kerrigan, D. Q. Mayne, and J. Lygeros, Reachability analysis of discrete-time systems with disturbances, IEEE Trans. Automat. Control 51 (2006), no. 4, 546-561.

24.

R. Vidal, S. Schaert, O. Shakernia, J. Lygeros, and S. Sastry, Decidable and semi-decidable controller synthesis for classes of discrete time hybrid systems, in Proc. 40th IEEE Conf. on Decision and Control, 2001.