Application of the Preview Control Method to the Optimal Tracking Control Problem for Continuous-Time Systems with Time-Delay

Abstract

This paper considers the application of the preview control method to the optimal tracking control problem for a class of continuous-time systems with state and input delays. First, through a transformation, the system is transformed into a nondelayed one. Then, the tracking problem of the time-delay system is transformed into one of a nondelayed system via processing of the reference signal. We then apply preview control theory to derive an augmented system for the nondelayed system and design a controller with preview function assuming that the reference signal is previewable. Finally, we obtain the optimal control law of the augmented error system and thus obtain that of the original system by letting the preview length of the reference signal go to zero. Numerical simulations are provided to illustrate the effectiveness and validity of our conclusions.

Padé-Approximation-Based Preview Repetitive Control for Continuous-Time Linear Systems

“…subject to the state equation (12), where Q z ∈ R n×n and R ∈ R q×q are both positive definite matrices, Q z � diag Q x Q e Q v , Q x ∈ R n×n , Q e ∈ R m×m , and Mathematical Problems in Engineering erefore, the problem of PRC design based on Padé approximation can be transformed into solving the optimal control input u(t) of system (12) under the performance index (14). To this end, we have to ensure the existence conditions of stabilizability of (A, B) and the detectability of (Q (1/2) z , A).…”

“…Combining LMI-based PC with other control schemes, some new concepts are proposed, such as adaptive PC [7], fault tolerant PC [8], H ∞ PC [9], observer-based PC [10], and distributed PC [11]. However, in continuous-time systems, the methods that can be used to deal with PC issue are relatively limited, and differential operation is widely used instead of differential operation [12][13][14][15][16].…”

Preview repetitive control with equivalent input disturbance for continuous‐time linear systems

“…Taking the identical equation of the derivative of the control input as a part of the augmented systems, the optimal preview controller in finite horizon was deduced in [24,25]. By variable substitution and state prediction, the PC problem for linear continuoustime systems with input delay was investigated in [26] and [27]. In [28], the optimal consensus PC for descriptor multi-agent systems was considered based on LQR.…”

The Application of Predictor Feedback in Designing a Preview Controller for Discrete-Time Systems with Input Delay

“…Robust control and function control strategies were given, respectively, for discrete-time delay systems in [27,28]. More recently, the optimal control problem was studied for systems with both state and input delays based on the method of letting the preview length go to zero [29]. Optimal tracking controllers for the delay systems are obtained.…”