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OPTIMAL CONTROL FOR TWO‐DIMENSIONAL LINEAR SYSTEMS WITH VARIABLE COEFFICIENTS
Author(s) -
Li Jimshone,
Tsai Jason ShengHong,
Shieh LeangSan
Publication year - 1999
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1111/j.1934-6093.1999.tb00023.x
Subject(s) - variable (mathematics) , control theory (sociology) , mathematics , control variable , control (management) , computer science , mathematical optimization , statistics , mathematical analysis , artificial intelligence
An optimal control method for two‐dimensional (2‐D) linear systems with variable coefficients and free boundary conditions in Roesser's model is proposed in this paper. Based on Roesser's model, an equivalent general 1‐D model of the 2‐D system is presented, and the problem of minimizing a 2‐D linear quadratic (LQ) cost function is solved for the case where complete state information is available. The solution is obtained by using the proposed dynamic programming in 1‐D descriptor form to solve the Riccati equation and then arriving at the optimal control law and minimum cost. The proposed control methodology can be applied to discrete‐time models of systems described by partial differential equations and can also be used in the field of signal processing.