Asynchronous repetitive control of switched systems via periodic event-based dynamic output feedback

2019 ◽  
Vol 37 (2) ◽  
pp. 644-673
Author(s):  
Guoqi Ma ◽  
Xinghua Liu ◽  
Prabhakar R Pagilla ◽  
Shuzhi Sam Ge
Keyword(s):  
Output Feedback ◽  
Switched Systems ◽  
Closed Loop ◽  
Repetitive Control ◽  
Mode Switching ◽  
Dynamic Output Feedback ◽  
Time Varying ◽  
Design Framework ◽  
Dynamic Output ◽  
Event Based

Abstract This paper develops an asynchronous mode-dependent repetitive control strategy with periodic event-based dynamic output feedback for periodic trajectory tracking of continuous-time switched systems subject to time-varying switching delays between system modes and controllers and limited communication capacity in the feedback channel. By employing the input delay approach, the overall system is modelled as an augmented closed-loop switched system with both constant and time-varying state delays. A co-design framework is proposed for simultaneously designing the controller, event-triggering mechanism and mode switching signal. Under the co-design framework, using piecewise Lyapunov functional, free-weighting matrices and average dwell time technique, sufficient conditions are derived for ensuring the augmented closed-loop system to be exponentially stable with a prescribed $H_{\infty }$ attenuation level $\gamma $ for an exogenous disturbance input. The performance of the proposed controller design scheme is verified via numerical simulation results on a switched RLC series circuit system.

Tracking of Periodic Trajectories for Switched Systems Under Time-Varying Asynchronous Switching

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Guoqi Ma ◽  
Xinghua Liu ◽  
Prabhakar R. Pagilla ◽  
Shuzhi Sam Ge
Keyword(s):  
Output Feedback ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Dynamic Output Feedback ◽  
Time Varying ◽  
Decomposition Approach ◽  
Dynamic Output ◽  
2D Model ◽  
Repetitive Controller

In this technical brief, we provide an asynchronous modified repetitive controller design to address the periodic trajectory tracking problem for switched systems with time-varying switching delays between plant modes and controllers. In the feedback channel, a dynamic output feedback mechanism is adopted. By utilizing the lifting technique, the dynamic output feedback-based switched repetitive control system is transformed into a continuous-discrete two-dimensional (2D) model to differentiate the control and learning actions involved in the repetitive controller. For the transformed 2D model, by constructing a piecewise Lyapunov functional and utilizing a matrix decomposition approach, sufficient conditions in terms of linear matrix inequalities (LMIs) and the average dwell time are developed to guarantee closed-loop exponential stability. The performance of the proposed approach is illustrated via a switched RLC series circuit example and numerical simulations are provided.

Design of a Periodic Event-Based Repetitive Controller With Dynamic Output Feedback for Linear Systems

2018 ◽  
Author(s):  
Guoqi Ma ◽  
Prabhakar R. Pagilla
Keyword(s):  
Linear Systems ◽  
Output Feedback ◽  
Closed Loop ◽  
Dynamic Output Feedback ◽  
Output Feedback Controller ◽  
Dynamic Output ◽  
Event Triggering ◽  
Dynamic Output Feedback Controller ◽  
Event Based ◽  
Repetitive Controller

In this paper a periodic event-based repetitive controller with dynamic output feedback is designed for linear systems with exogenous disturbances. The periodic event mechanism is designed such that within any two event triggering instants, the dynamic output feedback controller is open which substantially reduces the control and communication burden when the output does not change significantly. First, by employing the input delay approach, the overall system consisting of the physical plant, the repetitive controller, and the dynamic output feedback controller with periodic event-triggering mechanism is modeled as a closed-loop time-varying delay system. Then, sufficient conditions in terms of linear matrix inequalities are derived to ensure that the closed-loop system is asymptotically stable with a prescribed H∞ attenuation performance level. The controller gains are synthesized by using a matrix decomposition technique. A numerical example is provided to evaluate the proposed design approach.

Finite-time dynamic output feedback stabilization of linear time-varying systems by a piecewise constant method

2018 ◽  
Vol 40 (14) ◽  
pp. 4078-4088
Author(s):  
Chao Liang ◽  
Chenxiao Cai ◽  
Jing Xu
Keyword(s):  
Output Feedback ◽  
Finite Time ◽  
Linear Time ◽  
Dynamic Output Feedback ◽  
Time Varying ◽  
Piecewise Constant ◽  
Output Feedback Controller ◽  
Dynamic Output ◽  
Time Varying Systems ◽  
Dynamic Output Feedback Controller

The paper mainly deals with the problem of finite-time stabilization of linear time-varying systems. A dynamic output feedback controller is designed, which is able to stabilize the linear time-varying systems in finite time. By virtue of extended piecewise constant method, novel criteria for the existence of a dynamic output feedback controller is established in terms of linear matrix inequalities. Compared with the existing method, the proposed method is more efficient from a computational point of view. A simulation is given to illustrate the effectiveness of the obtained result.

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