Design of LQR Controller with Infinite Horizon for Delayed Discrete Systems based on Predictive Control and Reduction Method

In this paper, the linear quadratic regulator controller is designed for a specific class of discrete time-delay systems. The controller, which can satisfy the constraints and compensate for the destructive effects while satisfying the constraints, has attracted much attention. The presence of time-varying delays at local control inputs, which can destabilize the system and disrupt the process, has also been investigated. A satellite orbit system is considered thatcorrects the position by a predictive control method based on the constrained model. The aim is to design the linear quadratic regulator controller based on the predictive controller by the reduction method so that the closed-loop system is asymptotically stable for all acceptable uncertainties and time delays and minimizes the effect of external disturbances. This requires a high speed and accurate controller to be able to meet the desired control objectives asmuch as possible. Also, by the theory of stability proof theory with Lyapunov krasovskii function and in the form of linear matrix inequalities, conditions independent of the delay for establishing exponential convergence are obtained. Finally, the effectiveness of the results obtained from the proposed control scheme is demonstrated by a numerical example of the position of the satellite in order to keep it in orbit and reduce fuel consumption

Keywords:

LQR controller , Time-varying time delay , Lyapunov Krasovskii Function , Reduction method , Predictive controller.