Modularized design for cooperative control of cyber-physical systems with disturbances and general cooperative targets

https://doi.org/10.1016/j.jfranklin.2020.08.006Get rights and content

Abstract

In this work, cyber-physical systems (CPSs) are described by networked heterogeneous linear systems and a modularized cooperative control architecture is developed for CPSs with general cooperative targets and external disturbances. The proposed control architecture is composed of low- and high-level controls. The low-level control is to make input-output pairs of the resulting closed-loop systems become passivity-short and the high-level distributed control is to achieve cooperative targets. Different from the current state-of-the-art, a) the presented controls can be modularized, and under the controls, each follower can track the reference trajectory generated by linear dynamical systems while rejecting external disturbances; b) with the aid of regulator equations, the constraint on the resulting closed-loop system matrices containing some specific poles can be removed by the new low-level control. The effectiveness of the proposed method is verified by a numerical example.

Introduction

Cyber-physical systems (CPSs) are comprehensive technical systems supporting the deep integration of sensing, computation, communication, and control with physical plants [1]. Driven by advanced computing, communication and network devices, CPSs can greatly improve work efficiency and competitiveness of networked industrial control systems [2]. Recent developments of communication, computing and control technologies have further spurred a broad interest in the CPS topic, including studies for attack strategies [3,4], secure controls under denial-of-service attacks [5,6] and deception attacks [7,8], security protection based on anomaly detections [9], finite-time H controls [10], [11], reliable controls under faults [12], [13], filtering schemes under time-delays [14], [15] and low-complexity architectures of the CPS model identification [16], etc. In particular, design problems for cooperative controls of networked cooperative systems have attracted intensive studies [17]. The cooperative controls deal with networked physical systems and network-enabled distributed controls. Until recently, there are many interesting results [18], [19], [20], [21], including secure/reliable controls [17], [22], [23], consensus [24], [25], [26], formation [27], [28], [29], and cooperative output regulation [30], etc.

Besides, in practical applications, it is usually necessary to decompose the present “controller-oriented structure” into functional modules with a “task-oriented structure” [31] since the modularized design not only provides the flexibility for systems that need to be reconfigured such as manufacturing and robotic systems [32], [33], but also unravels the complexity of analyzing and designing CPSs [34]. Then, cooperative controls of networked heterogeneous systems are required to realize modularization. For example, the work in [35] studied and designed the actuator fault detection module, nominal control module and auxiliary control module so as to achieve the cooperative stability under faults. In addition, it is worth noting that in [34], by using the shortage of passivity (PS) as an analysis and design tool, a nice modularized design methodology was developed for cooperative controls of networked systems. By the modularized design scheme, the low-level control can be individually designed for each of heterogeneous systems while their high-level control can also be synthesized separately. As a result, low- and high-level controls separately designed but carried out together can guarantee the cooperative stability of heterogeneous systems. Due to its task-oriented and less complex controller design, the modularized cooperative control design methodology can be very well applied into robots, smart grids, smart buildings, unmanned aerial vehicles (UAVs), especially, for the case in the presence of attacks, faults, uncertainties, etc. For instance of consensus control designs of power systems under communication attacks in [17], by using the modularized design method in [34], the high-level control was studied and designed in terms of fictitious pure integrator systems, so that the cooperative stability under attacks was guaranteed by the designed control. Based on the above-mentioned, modularized design problems for cooperative controls with guaranteed non-trivial consensus of networked heterogeneous systems have been fully solved. Nevertheless, modularized design issues for networked heterogeneous linear systems with external disturbances and more general cooperative targets (e.g., the tracking reference signal is ri=Div with v˙=Sv, defined in (1) and (3) below) remain open. Such works contribute to smart grids and UAV formations to achieve more cooperative control targets.

Motivated by the above discussions, the main purpose of this paper is to address modularized design problems for cooperative controls of networked heterogeneous linear systems with general cooperative targets and external disturbances. The contributions of this paper are two-fold. 1) Contrary to the existing results (e.g., [34]), a more general and realistic case is considered: a) the considered reference signal is ri=Div with v˙=Sv and b) each follower is subjected to the external disturbance. For the situation, the PS as the analysis tool, a systematic and modularized design scheme for low- and high-level controls of heterogeneous physical systems is developed, so that under the proposed controls, every follower tracks the desired trajectory while restraining the external disturbance. 2) With the aid of regulator equations, the constraint in [34] on the resulting closed-loop system matrices containing some specific poles can be removed by the new low-level control.

Section snippets

Problem formulation

The cooperative system under consideration is composed of an exosystem and l heterogeneous physical linear systems. The dynamics of the cooperative system is described by the following formv˙(t)=Sv(t),x˙i(t)=Aixi(t)+Biui(t)+Eiv(t),ei(t)=Cixi(t)ri(t),ri(t)=Div(t),i=1,,lwhere xiRni, uiRmi, eiRmi, and riRmi i=1,,l, denote the state, control input, tracking error and the reference signal of the ith system, respectively. vRq is the state of exosystem (1), and it can be described as a

Main results

In this section, PS as an analysis tool, a modularized design methodology for low- and high-level controls of heterogeneous systems is developed such that the cooperative stability is achieved.

An illustrative example

We consider an example about the cooperative control of UAVs (whose model is borrowed from [38]), and the corresponding systems are given in the form of (1) to (3) with l=4 and for i=1,2,3,4,Ai=[0.68030.00020.104900.14630.00624.67269.79421.00500.00060.571701000],Bi=[0.01541.328700]T,Ci=[0001],Ei=[0000000i]T,S=[0110],D1=[1.09870.4243],D2=[2.18980.8598],D3=[3.28101.2953],D4=[4.37221.7309].The communication structure of the cooperative system is plotted in Fig. 1. According to

Conclusion

This paper studied modularized design problems for cooperative control of CPSs with general cooperative targets and external disturbances. With the aid of the PS concept and regulator equations, a modularized design approach for cooperative control of CPSs was proposed. By the presented modularized design scheme, low- and high-level control separately designed but carried out together guaranteed that each follower tracks the desired reference trajectory while rejecting the external disturbance.

Declaration of Competing Interest

There is no conflict of interest in the submission of this manuscript, and manuscript is approved by all authors for publication. I would like to declare on behalf of my co-authors that the work described was original research that has not been published previously. All the authors listed have approved the manuscript that is enclosed.

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant 61873056, Grant 61621004 and Grant 61420106016, the Fundamental Research Funds for the Central Universities in China under Grant N2004001, N2004002, N182608004 and the Research Fund of State Key Laboratory of Synthetical Automation for Process Industries in China under Grant 2013ZCX01.

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