Optimal control for linear systems with time delay in control input based on the duality principle

Abstract

This paper presents the optimal regulator for a linear system with time delay in control input and a quadratic criterion. The optimal regulator equations are obtained using the duality principle, which is applied to the optimal filter for linear systems with time delay in observations. Performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulator available for linear systems without delays. Simulation graphs and comparison tables demonstrating better performance of the obtained optimal regulator are included.

Linear quadratic regulation for discrete-time systems with multiplicative noises and input delays

“…Control of such systems have been an active research area for many decades, see e.g. [4], [16], [13], [18], [17] for the discrete-time case and [1], [12], [15], [14] for the continuous-time case.…”

Robust deconvolution and control of uncertain and time delay systems

“…Optimal control of time-delay systems has been an active research area since the late 1960s, first in the H 2 (LQG) and then in the H ∞ settings, see e.g. [16,85] for the discrete-time case and [7,44,60,61,83] for the continuous-time case. Time delay can appear in state and/or in input/output(I/O) of the system model.…”

“…In addition to those methods, there are some other methods for time-delay systems, e.g. Basin et al [6,7] provided finite time horizon LQR control for systems with time delay in state and input where Hamilton-Jacobi-Bellman (HJB) equation is used.…”

“…Since the introduction of Smith predictor [80], there have been a lot of works on optimal control for systems with I/O delays [7,33,83]. In recent years, multiple time-delay issues have attracted significant research interest.…”