Optimal control of 2-dimensional systems: a new approach

This paper suggests a new method of solving optimal control problem for General state space model of discrete two-dimensional (2-D) systems which is called 2-DGM. This method resolves the boundary conditions complexities in the 2-D optimal control problems, and 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 specific quadratic performance index can be cast as a new semi-one-dimensional (semi-1-D) system. This semi-one-dimensional system is called “L-shaped model”. The generality of this method makes it usable for other 2-D models as well. Using a theorem and three conclusions in 1-D optimal control theory, an algorithm is introduced to solve optimal control for 2-D systems. Finally, Simulation results are presented to illustrate the effectiveness of our proposed method.