Abstract
Optimal control problem for linear two-dimensional (2-D) discrete systems with mixed constraints is investigated. The problem under consideration is reduced to a linear programming problem in appropriate Hubert space. The main duality relations for this problem is derived such that the optimality conditions for the control problem are specified by using methods of the linear operator theory. Optimality conditions are expressed in terms of solutions for conjugate system.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Attasi S (1973) Systémes lineaires homogénes é deux indices. Rapp. Laboria 31
Bisiacco M (1995) New results in 2-D optimal control theory. Multidimensional Systems and Signal Processing 6:189–222
Bisiacco M, Fornasini E (1990) Optimal control of two-dimensional systems. SIAM J. Control and AppUcation 28:582–601
Bisiacco M, Fornasini E, Marchesini G, Giovani D (1990) Dynamical regulation of 2-D system: A state-space approach. Linear Algebra Applic. 122/123/124:195–218
Bose NK (ed) (1977) Special issue on multidimensional systems. Proc. IEEE 65:3–7
Dymkov MP (1993) The linear-quadratic regulator problem for 2-D systems. Izvestiya Academii nauk Belarusi 1:3–7
Dymkov MP (1993) The maximal deviation problem for two-dimensional differential-difference control system on the plane. Doclady Academii nauk Belarusi 37/1:3–7
Dymkov MP (1994) The optimal control problem for the linear differential-difference 2-D systems with quadratic functional. Doclady Academii nauk Belarusi 38/2:5–8
Fornasini E, Marchesini G (1976) State space realization of two-dimensional filters. IEEE Trans. Autom. Control AC-21:484–491
Gaishun IV (1991) Complete controllability and observability conditions two-dimensional discrete systems. DifferentiaPnye Uravnenya 11:1871–1881
Gaishun IV, Quang VK (1992) Solvability of the some class of the operator equations and controllability of Roesser's systems. Doclady Academii nauk USSR 323:16–19
Gaishun IV (1996) Multidimensional control systems. Nauka i Technica, Minsk, (in Russian)
Givone DD, Roesser RP (1973) Minimization of multidimensional linear iterative circuits. IEEE Trans. Comput. C-22:673–678
Kaczorek T (1985) Two-dimensional linear systems. Springer-Verblag, Berlin
Kaczorek T, Klamka J (1987) Local controllability and minimum energy control of n-D linear systems. Bull. Pol. Acad. Techn. Sci. 35/11–12:679–685
Kaczorek T (1995) Generalized 2-D continuous-discrete linear systems with delays. Appl. Math. and Comput. Sci. 5:439–454
Klamka J (1994) Controllability of 2-D continuous-discrete linear systems. Proc. XVII-SPETO, Poland: 271–276
Klamka J (1994) Minimum energy control for 2-D systems. Systemce Science 9:33–42
Kurek JE (1987) Observability and reconstructability of 2-D linear digital systems. IEEE Trans. Autom. Control. AC-32:170–172
Kurek JE, Zaremba MB (1993) Iterative learning control synthesis on 2-D system theory. IEEE Trans. Autom. Control. AC-38:121–125
Levis FL (1992) A review of 2-D implicit systems. Automatica 28:345–354
Rogers E, Owens DH (1992) Stability analysis for linear repetive processes. Springer-Verlag, Berlin
Roesser RP (1975) A discrete state-space model for linear image processing. IEEE Trans. Autom. Control. AC-20:1–10
Sebek M (1988) Polinomial approach to pole placement in MIMO n-D systems. Proc. 1988, IEEE Internat. Symposium on Circuits and Systems Theory, Helsinki, 1:93–96
Ter-Kricorov AM (1977) Optimal control and Mathematical Economics. Nauka, Moskow, (in Russian)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dymkov, M. Linear optimal control problem for discrete 2-D systems with constraints. Mathematical Methods of Operations Research 47, 117–129 (1998). https://doi.org/10.1007/BF01193840
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01193840