Robust control for uncertain networked systems with communication constraints
Introduction
Networked control systems (NCSs) are feedback control systems in which the communication between spatially distributed system components like sensors, actuators and controller occurs through band-limited digital communication networks, the structure of the NCSs can be seen in Fig. 1. The main difference between NCSs and traditional control systems is the insertion of the shared network with limited transmission capacity and non-ideal network conditions, such as network-induced delay, packets dropout, sensors/actuators fault and so on. Generally speaking, the researches on NCSs can be classified into two categories: researches focused on control [2], [5], [6], [8], [9], [16], [21], [23], [29] and researches focused on communication [4], [15], [17], [19], [20], [24]. The main task of the former is to build proper NCSs models and design networked controller to guarantee the quality of performance (QoP) of NCSs, such as robustness, performance and H2 performance. The aim of the latter is to find proper network access scheduling to guarantee the quality of service (QoS) of NCSs.
Most of above mentioned researches assume that there is no restriction in the communication channels of sensor–controller or controller–actuator [4], [6], [15], [21], [23], that is, the communication medium can accommodate all sensors or actuators simultaneously. However, this is not always true in some practical systems [1], [7], [10], [11], [18], [26], [28], such as large-scale systems. In those systems, limitation on the number of sensors and actuators that are granted access to the network simultaneously to transfer measurements of sensors to the controller and control signals computed by the controller to the actuators. In the context of access constraints, (i) a communication sequence method is needed to decide which sensor/actuator has the permission to communicate with the controller/plant; (ii) a controller should be designed to stabilize the system in the presence of limited medium access constraints, random networked delay. In order to solve these problems, a control and communication co-design strategy is proposed in [27] for systems without time delay, wherein a periodic communication sequence is proposed. Later, improved co-design method can be seen in [13], [26], wherein the time delay is considered. However, the periodic communication policies require all the sensors and actuators to be strictly scheduled. Although periodic communication sequences are easy for implementation, they are not suitable for the dynamic, complex network conditions. The reason is that once the sensors/actuators fail, or packet losses during the transmission or large network-induced delay occurs, the designed communication sequences may fail to stabilize the NCSs. More recently, a stochastic access modeling method is proposed in [10], wherein the assignment of the active actuator subset is dependent on an event modeled by a Markov chain and the whole system is modeled as a Markovian jump systems. Among the pioneering papers, the work of [10] is closely related to this study, since stochastic assignment algorithm is proposed in both studies. However, in [10], (a) only access constraint of controller–actuator is considered; (b) the access or not of the communication is governed by a Markov chain, however, some of the elements in transition probability matrix are difficult or costly to be measured [25], which restricts their applications; and (c) robustness of access rates is not considered.
Generally speaking, when considering NCSs with limited communication capacity, most of the references mentioned above focusing on the communication approach except the work of [10], i.e., for a pre-designed controller feedback gain, design a communication sequence to stabilize the system. Different from these works, our investigation focuses on the control technology, the design process is as follows: firstly, a set of stochastic variables satisfying Bernoulli probability distribution are proposed to describe the access status of each sensor and actuator, “1” for access and “0” for not access. The access rates of sensors or actuators are described by the expectation of the corresponding stochastic variables, which is also related with the current working condition of the sensors and actuators. Including these variables in the system, a new NCSs model considering both limited access capacity and random networked delay is proposed. It should be noted that the considered uncertainties include both plant uncertainties and access rate uncertainties. Using Lyapunov functional method, sufficient conditions for the robust mean square stability (RMSS) of the proposed NCSs model are obtained. A corresponding algorithm is proposed to obtain the designed controller feedback gain. Finally, an example is given to illustrate the application and efficiency of the proposed method.
Compared with the existing researches, the main contributions of this paper include:
- (1)
The problem of medium access constraints of sensor–controller and controller–actuator are considered for NCSs, which has not been taken a full consideration in the existing researches.
- (2)
A stochastic access determine method is proposed for the communication scheduling, wherein the access status of each sensor or actuator is governed by a Bernoulli distributed white sequence, and the access rates in the proposed method are easier to be measured than the transition probabilities in [10].
- (3)
A novel co-design strategy of state feedback controller and random access assignment is proposed for NCSs, and a new Lyapunov functional method is proposed for the controller design.
- (4)
In the proposed NCSs model, random network-induced delays are taken into consideration and the uncertainties of the access rates of each sensor or actuator are considered, which has been omitted by most of existing researches.
Section snippets
System description and preliminaries
Consider the discrete-time linear system as follows:where and are, respectively, the state vector, control vector and disturbance input, is the controlled output vector. A, B, C, D and are matrices with compatible dimensions, is parameter uncertainty satisfyingwhere H and E are constant matrices with appropriate dimensions and is unknown time-varying matrix satisfying
Main results
Based on the Lyapunov–Krasovskii functional method, we can obtain the following results. Theorem 1 Systems (7), (8) is RMSS if there exist matrices with appropriate dimensions, such thatwhere
Numerical example
In this section, an illustrative example is proposed to show the effectiveness of the proposed method. Considering medium access constraints of sensor-controller channel and controller-actuator channel, only three out of four sensors can communicate with the controller and only one out of two actuators are granted access to the network to transfer signals simultaneously.
In order to demonstrate the effectiveness of the proposed design method, three cases are considered: in the first case, no
Conclusion
In this paper, we consider the control and communication co-design for networked control systems (NCSs) with medium access limitations, network-induced delay and uncertainties on both system dynamic and access rate of the sensors. The access status of every sensor or actuator is governed by a stochastic variable and a novel communication sequence method is proposed. By using Lyapunov functional method and linear matrix inequality technology, sufficient conditions for the robust mean square
Acknowledgement
This work was supported by the National Natural Science Foundation of China (Grant nos. 61074024 and 61074025 and 61273114 and 61273115) and the Natural Science Foundation of Jangsu Province of China (BK2012847 and BK2012469).
References (30)
- et al.
Stability analysis of networked control systemsa sum of squares approach
Automatica
(2012) - et al.
Stability analysis of stochastic networked control systems
Automatica
(2012) - et al.
Design and implementation of a new fuzzy pid controller for networked control systems
ISA Transactions
(2008) - et al.
A new delay system approach to network-based control
Automatica
(2008) - et al.
Real-time scheduling method for networked discrete control systems
Control Engineering Practice
(2009) - et al.
Sampled-data gain scheduling of continuous LTV plants
Automatica
(2009) Stability robustness analysis of linear systems with delayed perturbations
Journal of the Franklin Institute
(1999)- et al.
Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities
Automatica
(2009) - et al.
Communication and control co-design for networked control systems
Automatica
(2006) - et al.
Optimal linear estimation for networked systems with communication constraints
Automatica
(2011)
Control and communication challenges in networked real-time systems
Proceedings of the IEEE
Scheduling-and-control codesign for a collection of networked control systems with uncertain delays
IEEE Transactions on Control Systems Technology
estimation for uncertain systems with limited communication capacity
IEEE Transactions on Automatic Control
Stabilization of networked control systems with a new delay characterization
IEEE Transactions on Automatic Control
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