Discretized quadratic optimal control for continuous-time two-dimensional systems

In this brief, a discretized quadratic optimal control for continuous-time two-dimensional (2-D) system is newly proposed. It introduces a new state vector (a new virtual control input) to directly convert the original continuous-time 2-D quadratic cost function into a decoupled discretized form. As a result, a new virtual discrete-time 2-D model with the new virtual input is constructed for indirectly finding the desired discretized quadratic optimal regulator for the continuous-time 2-D system. The recently developed dynamic programming in discrete-time 1-D descriptor form is utilized to determine the desired discretized quadratic optimal regulator. This method provides a novel approach for discretized quadratic optimal control of continuous-time 2-D systems. An illustrative example is presented to demonstrate the effectiveness of the proposed procedure.