A 2D-based approach to guaranteed cost repetitive control for uncertain discrete-time systems

2010 ◽  
Vol 32 (6) ◽  
pp. 720-733 ◽  
Author(s):  
Wentao Chen ◽  
Weidong Zhang
Keyword(s):  
Discrete Time ◽  
Repetitive Control ◽  
Discrete Time Systems ◽  
Guaranteed Cost ◽  
Time Systems

scholarly journals Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems

Algorithms ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 20 ◽  
Author(s):  
Yong-Hong Lan ◽  
Jun-Jun Xia ◽  
Yue-Xiang Shi
Keyword(s):  
Dynamic System ◽  
Control Problem ◽  
Discrete Time ◽  
Repetitive Control ◽  
Original System ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Guaranteed Cost ◽  
Time Systems ◽  
Repetitive Controller

In this paper, a robust guaranteed-cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, a repetitive controller, combined with preview compensator, is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed-cost preview repetitive control problem is transformed into a guaranteed-cost control problem for the augmented dynamic system. For a given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by using a parameter-dependent Lyapunov function method and linear matrix inequality (LMI) techniques. Incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included, to show the effectiveness of the proposed method.

scholarly journals State Feedback Guaranteed Cost Repetitive Control for Uncertain Discrete-Time Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-16
Author(s):  
Wentao Chen ◽  
Yechun Lin ◽  
Qingping Wu
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Cost Control ◽  
Repetitive Control ◽  
Guaranteed Cost Control ◽  
State Feedback Control ◽  
Control Law ◽  
Discrete Time Systems ◽  
Guaranteed Cost ◽  
Time Systems

This paper considers the problem of guaranteed cost repetitive control for uncertain discrete-time systems. The uncertainty in the system is assumed to be norm-bounded and time-varying. The objective is to develop a novel design method so that the closed-loop repetitive control system is quadratically stable and a certain bound of performance index is guaranteed for all admissible uncertainties. The state feedback control technique is used in the paper. While for the case that the states are not measurable, an observer-based control scheme is adopted. Sufficient conditions for the existence of guaranteed cost control law are derived in terms of linear matrix inequality (LMI). The control and observer gains are characterized by the feasible solutions to these LMIs. The optimal guaranteed cost control law is obtained efficiently by solving an optimization problem with LMI constraints using existing convex optimization algorithms. A simulation example is provided to illustrate the validity of the proposed method.

scholarly journals Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems

2018 ◽  
Author(s):  
Yong-Hong Lan ◽  
Xia Jun-Jun
Keyword(s):  
Dynamic System ◽  
Control Problem ◽  
Discrete Time ◽  
Repetitive Control ◽  
Original System ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Guaranteed Cost ◽  
Time Systems ◽  
Repetitive Controller

A robust guaranteed cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, the repetitive controller combined with preview compensator is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed cost preview repetitive control problem is transformed into the guaranteed cost control problem for the augmented dynamic system. For given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by combining parameter-dependent Lyapunov function method with linear matrix inequality (LMI) techniques. By incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included to show the effectiveness of the proposed method.

Optimal Full Information H2 Guaranteed Cost Control of Discrete-Time Systems

2010 ◽  
Author(s):  
Richard Conway ◽  
Roberto Horowitz
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Discrete Time ◽  
Optimization Problem ◽  
Full Information ◽  
Discrete Time Systems ◽  
Dynamic Uncertainty ◽  
Guaranteed Cost ◽  
H2 Performance ◽  
Time Systems

This paper presents, for discrete-time LTI systems with unstructured dynamic uncertainty, a methodology for designing full information controllers which minimize the upper bound on robust H2 performance given in [1]. It is first shown that this optimal control problem can be cast as a semi-definite program. Then, it is shown that this optimization problem can be solved efficiently and accurately using discrete algebraic Riccati equations.

Sign in / Sign up

Export Citation Format

Share Document