云计算支持的网络控制系统安全与弹性控制策略

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网络控制系统弹性控制是当前IT领域中的一个重要课题，尤其是在云计算日益普及的背景下。传统的网络控制系统（NCSs）受限于资源，往往依赖于云端的计算能力来处理复杂的任务。然而，这种依赖性带来了新的挑战，尤其是关于云端的信任度以及控制系统与云端之间网络安全性的保障。《云环境下的网络控制系统安全与韧性设计》这篇论文由Zhiheng Xu和Quanyan Zhu撰写，他们隶属于纽约大学布鲁克林分校的电气与计算机工程系。文章的核心内容聚焦于解决这些问题，提出了一个安全且具有弹性的机制。首先，他们利用定制化的加密算法对控制问题的数据进行加密，确保数据在传输过程中的隐私和安全性。这一步骤至关重要，因为保护了敏感的控制信息免受潜在的恶意攻击，如数据篡改或窃取。其次，论文开发了一种验证方法，用于核实云端计算结果的完整性。这种方法旨在确认云端返回的计算结果是否准确无误，防止错误的信息影响到整个控制系统的正常运行。这是保障CE-NCSs可靠性和准确性的关键环节。此外，为了提高NCSs在连续接收错误云端输入时的韧性，他们设计了一种切换模式机制（SMM）。当系统连续接收到不正确的控制指令时，SMM能够自动转换至备份策略，比如切换到本地处理或者利用其他可信的通信源，确保系统的持续稳定运行，即使在云端服务中断时也能维持基本的控制功能。通过理论分析和实际案例研究，论文作者展示了这个机制如何有效地提升网络控制系统的弹性控制能力。他们强调，这种机制不仅提高了系统的安全性，还提升了系统的鲁棒性，使得云计算支持的网络控制系统能够在面临各种安全威胁时依然能够保持高效运作。网络控制系统的弹性控制是一个结合了云计算、网络安全、加密技术及系统恢复策略的复杂课题，它对于保障工业自动化、智能交通等领域的重要应用具有重要意义。未来的研究将继续探索更高级别的安全措施和更加智能化的故障应对策略，以适应不断发展的网络环境。

graphic mechanisms, we encrypt the quadratic problem as-

sociated with MPC prior to the computations in the cloud,

and propose an efﬁcient method to verify its solutions from

the cloud. We show that no false solutions can succeed in the

veriﬁcation with a non-negligible probability.

b) Secondly, to guarantee stability and enhance resiliency, we

design a switching mechanism SMM using an event-triggered

MPC scheme and H

∞

-optimal control. Under this mecha-

nism, the NCSs switch to a Buffer Mode when control inputs

are unavailable from the cloud for a short duration, or switch

to a Safe Mode when control inputs are unavailable for a long

duration. We demonstrate that the SMM guarantees the sta-

bility of CE-NCSs.

c) Finally, both analytical and experimental results show that

our mechanism can boost efﬁciency for NCSs. The experi-

mental results also corroborate that the SMM can guarantee

stability for CE-NCSs when control inputs are unavailable

for either a short or long period of time.

1.4 Organization

The rest of the paper is organized as follows: Section 2 presents

the problem formulation, three cloud attack models, the design

goals, and the framework of the proposed mechanism. In Section 3,

we develop speciﬁc strategies and techniques to achieve data conﬁ-

dentiality and integrity. In Section 4, we propose a switching mech-

anism to deal with availability issues. Both theoretical analysis and

experiment results are presented in Section 5. Finally, Section 6

concludes this paper.

2. PROBLEM STATEMENTS

Each CE-NCS has two layers: cyber layer and physical layer.

The cyber layer consists of wireless communications and a cloud,

while the physical layer incorporates a plant, actuators, and sensors,

and a controller. The integration of the controller with the cloud

constitutes a cloud-based controller. Fig. 2 illustrates a feedback

architecture of a CE-NCS. The controller of a CE-NCS is struc-

turally different from other general NCSs. Instead of solving an

off-line control problem, the controller of a CE-NCS formulates a

dynamic optimization problem based on the sensor data, and out-

sources the computations of the control decisions to a cloud. After

receiving the solutions from the cloud, the controller sends them to

the actuators of the physical system.

To describe in detail the architecture of a CE-NCS, we ﬁrst intro-

duce the physical layer control problem. In this work, we present a

discrete-time linear system to capture the dynamics of the physical

plant and use Model Predictive Control (MPC) framework to de-

sign optimal control to stabilize the system. The computations of

the MPC control inputs are outsourced to the cloud, which can be

subject to adversarial attacks. To this end, the second part of this

section presents three attack models on the CE-NCS, and outline

the design goals and framework of the proposed mechanism.

2.1 System Dynamics and MPC Algorithm

MPC has been widely used in many domains of industries and

civil applications, such as process control of chemical plants and

oil reﬁneries, energy systems in building, and autonomous vehicles

[1, 31]. MPC is a model-based control strategy that uses a sys-

tem model to predict the future behaviors of the system to establish

appropriate control inputs [28]. To achieve prediction, MPC strat-

egy provides a moving ﬁnite-horizon problem based on the system

model, and control inputs can be computed by solving this prob-

lem at each sampling instant. One advantage of MPC is that it

Figure 2: Architecture of a CE-NCS: The integrated system

consists of a plant, sensors, actuators, and a cloud-based con-

troller. The cloud-based controller is composed of a local con-

troller, a wireless network, and a cloud. The network is de-

ployed to transmit data of computations to the cloud and the

control solutions from the cloud. The controller aims to stabi-

lize the plant and achieve system objectives.

allows the system to operate constraints on control inputs or sys-

tem states [15], while it is difﬁcult for the other control strategies,

e.g., Linear Quadratic Regulator (LQR) and H

∞

-optimal control,

to handle constraints. The second advantage is that MPC enables an

on-line design, which can deal with disturbance in real time, while

LQR and H

∞

-optimal control are off-line designs. In addition,

∞

-optimal control considers the worst-case disturbance, leading

to more conservative and expansive control inputs. A main chal-

lenge of MPC is that the controller needs to solve a optimization

problem at each sampling time, resulting in a higher computational

complexity. This motivates us to introduce a CE-NCS framework

to outsource the computations of the MPC problem to the cloud.

To apply MPC, we use a discrete-time linear system model to

describe the system dynamics of a control system, given by

x(k + 1) = Ax(k) + Bu(k), (1)

where x(k) ∈ R

n×1

is the state vector of the NCS, x(0) = x

∈

n×1

is the given initial state value, u(k) ∈ R

l×1

is the control

input, A ∈ R

n×n

and B ∈ R

n×l

are constant matrices.

At each sampling time k, a ﬁnite-horizon MPC problem P is a

minimization problem, which is given as follows:

P : min

U (k)

J(x(k), U (k))

N−1

τ =0



kˆx(k + τ |k)k

+ ηkˆu(k + τ |k)k



, (2)

subject to

ˆx(k + τ + 1|k) = Aˆx(k + τ |k) + B ˆu(k + τ |k),

ˆx(k|k) = x(k), ˆu(k + τ|k) ∈ U ,

U(k) = [ˆu

(k|k), ˆu

(k + 1|k), . . . , ˆu

(k + N − 1|k)]

where J : R

n×1

× R

lN×1

→ R is the objective function, η is a

tuning parameter for the desired control performance, and U(k) ∈

lN×1

is the solution sequence of the problem P. ˆx(k + τ|k)

denotes an estimate value of x(k + τ), based on the feedback state

x(k). Through out this paper, k · k represents the Euclidean norm.

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