Optimal control for a class of 2-D shift variant systems

This paper suggests a new method of solving optimal control problem for F-MM I (first Fornasini-Marchesini´s model) state space model of discrete two-dimensional (2-D) systems with variable coefficients. This method not only resolves the boundary conditions complexities in the 2-D optimal control problems, but also guarantees reduction of computation compared to the other methods. In order to solve the standard 2-D LQR Problem, It is shown that the 2-D system under a specified quadratic performance index can be cast as a new semi-one-dimensional (semi-1-D) system which is called “L-shaped model”. This model can be applied to other 2-D models as well. Using a theorem and two conclusions in 1-D optimal control theory, an algorithm is introduced to solve optimal control for 2-D systems. Finally, evaluation of the approach is illustrated through a numerical example. Result shows the effectiveness of the proposed procedure.