Robust global stabilisability by means of sampled-data control with positive sampling rate

This work proposes a notion of robust reachability of one set from another set under constant control. This notion is used to construct a control strategy, involving sequential set-to-set reachability, which guarantees robust global stabilisation of non-linear sampled data systems with positive sampling rate. Sufficient conditions for robust reachability of one set from another under constant control are also provided. The proposed method is illustrated through a number of examples, including the study of the sampled-data stabilisation problem of the chemostat.     

Global practical tracking of a class of nonlinear systems using linear sampled-data control

This paper considers the problem of global practical tracking via sampled-data control for a class of uncertain nonlinear systems. Under a lower triangular linear growth condition, a sampled-data state feedback controller is first constructed such that the states are globally bounded and the error between the system output and the reference signal will be rendered smaller than a given tolerance. When only the output of the system is measurable, a sampled-data output feedback controller, whose observer and control law are both linear, is constructed to solve the global practical tracking problem.     

Periodic sampling: maximising the sampling period

The process of periodic sampling is investigated for a class of nonlinear systems. The objective is to achieve the longest sampling period that is compatible with a specified error bound. It is shown that there are robust optimal controllers that achieve this objective. It is also shown that the performance of such optimal controllers can be approximated by bang-bang controllers – controllers that are relatively easy to design and implement.     

Stabilisation analysis for switched neutral systems based on sampled-data control

In this paper, the problem of stabilisation analysis for switched neutral systems based on sampled-data control and average dwell time approach is investigated. Delay-dependent stabilisation results are derived in terms of linear matrix inequalities by constructing piecewise Lyapunov–Krasovskii functional based on the Wirtinger's inequality. Also, the controller gain matrix is designed by applying an input-delay approach. Further convex combination technique and some integral inequalities are used to derive less conservative results. The effectiveness of the derived results is validated through numerical examples.     

Robust sampled-data control with random missing data scenario

The problem of robust sampled-data control for uncertain dynamic systems in the presence of missing data has been investigated. By using stochastic variables with a Bernoulli distributed white sequence to model missing data, along with time-varying norm-bounded uncertainties, and the input delay approach for sampled-data systems, two models for the considered sampled-data control system are proposed as the consecutive missing data scenario. Moreover, when data are missing, the control signals are held as the last received data. Sufficient conditions for the existence of desired robust sampled-data controllers are presented in the form of a linear matrix inequality. A numerical example is given to illustrate the validity of the proposed methods and to compare the results between the two proposed models of the sampled-data control system.     

Asymptotic stabilisation of a class of nonlinear systems via sampled-data output feedback control

This article considers sampled-data output feedback control of a class of nonlinear systems in output feedback form. The underlying continuous-time controller is designed based on backstepping technique, employing a linear dynamic filter, and globally asymptotically stabilises the system. Rigorous analysis shows that when implemented with a sampling and zero-order hold device, the sampled-data version of the continuous-time controller semi-globally asymptotically stabilises the original system, given that the sampling period is smaller than a specific value, which depends on the initial values and nonlinearity of the system. Simulation results of a physical system are included in the end.     

Computer control under time-varying sampling period: An LMI gridding approach

This paper addresses computer control under time-varying sampling period and delayed actuation. The proposed approach uses time-varying observers and state-feedback controllers designed by means of linear matrix inequalities (LMI) and quadratic Lyapunov functions. The use of non-stationary Kalman filters is also discussed. A separation principle applies in some cases. A DC motor control setup shows the applicability of the approach in a real implementation.     

Allowable sampling period for consensus control of multiple general linear dynamical agents in random networks

This article studies the consensus problem for a group of sampled-data general linear dynamical agents over random communication networks. Dynamic output feedback protocols are applied to solve the consensus problem. When the sampling period is sufficiently small, it is shown that as long as the mean topology has globally reachable nodes, the mean square consensus can be achieved by selecting protocol parameters so that n???1 specified subsystems are simultaneously stabilised. However, when the sampling period is comparatively large, it is revealed that differing from low-order integrator multi-agent systems the consensus problem may be unsolvable. By using the hybrid dynamical system theory, an allowable upper bound of sampling period is further proposed. Two approaches to designing protocols are also provided. Simulations are given to illustrate the validity of the proposed approaches.     

交换式以太网控制系统传感器变采样调度研究

针对基于交换式以太网的网络化控制系统的数据传输和控制性能优化问题,提出了传感器根据给定值与实测值差额的绝对值对照静态调度表变采样周期的调度优化方法.使用TrueTime 2.0工具箱搭建了交换式以太网控制系统仿真平台进行仿真研究,并与定采样周期方法进行了对比,仿真结果验证了其可行性.此方法在实际的工程应用中具有一定的参考价值.     

Decentralised sampled-data control for large-scale systems with nonlinear interconnections

This paper presents a decentralised sampled-data control technique for a class of large-scale systems, which are considered to consist of linear subsystems and nonlinear interconnections. The decentralised sampled-data controller design problem is established using a closed-loop subsystem. Based on the controller design problem, the stability condition is derived for a closed-loop large-scale system, and the maximum interconnection bound is guaranteed to satisfy the stability condition. Also, its sufficient condition is formulated in terms of linear matrix inequalities. Finally, the effectiveness of the proposed technique is verified by using an example of the multi-machine power system.     

Robust reliable control design for networked control system with sampling communication

In this article, the problem of robust exponential stability and reliable stabilisation for a class of continuous-time networked control systems (NCSs) with a sample-data controller and unknown time-varying sampling rate is considered. The analysis is based on average dwell-time, Lyapunov–Krasovskii functional and linear matrix inequality (LMI) technique. The delay-dependent criteria are developed for ensuring the robust exponential stability of the considered NCSs. The obtained conditions are formulated in terms of LMIs that can easily be solved by using standard software packages. Furthermore, the result is extended to study the robust stabilisation for NCS with parameter uncertainties. A state feedback controller is constructed in terms of the solution to a set of LMIs, which guarantee the robust exponential stabilisation of NCS and the controller. Finally, numerical examples are presented to illustrate the effectiveness of the obtained results.     

Non-fragile sampled-data control of network systems subject to time-delay

This paper studies the consensus problem of non-linear network systems subject to time-delay through aperiodic sampled-data control, which is more desirable and flexible than periodic sampling control. By receiving the relative information of the neighboring nodes, each node can obtain control input signals at the discrete sampling instants. A new stability criterion is established for network systems via using a time-dependent Lyapunov functional and the free-weighting matrix method. The maximum upper bound of sampling interval can be achieved by solving Linear matrix inequality optimization problem. Under the basic work of a non-fragile sampled-data controller, network systems with time-delay are asymptotically stable. In the end, two numerical simulation examples can be provided to illustrate the validity of the application of the proposed algorithm.     

Observer-based output feedback control of networked control systems with non-uniform sampling and time-varying delay

This paper investigates the problem of observer-based output feedback control for networked control systems with non-uniform sampling and time-varying transmission delay. The sampling intervals are assumed to vary within a given interval. The transmission delay belongs to a known interval. A discrete-time model is first established, which contains time-varying delay and norm-bounded uncertainties coming from non-uniform sampling intervals. It is then converted to an interconnection of two subsystems in which the forward channel is delay-free. The scaled small gain theorem is used to derive the stability condition for the closed-loop system. Moreover, the observer-based output feedback controller design method is proposed by utilising a modified cone complementary linearisation algorithm. Finally, numerical examples illustrate the validity and superiority of the proposed method.     

Delay-dependent resilient-robust stabilisation of uncertain networked control systems with variable sampling intervals

This work is concerned with the robust resilient control problem for uncertain networked control systems (NCSs) with variable sampling intervals, variant-induced delays and possible data dropouts, which is seldom considered in current literature. It is mainly based on the continuous time-varying-delay system approach. Followed by the nominal case, delay-dependent resilient robust stabilising conditions for the closed-loop NCS against controller gain variations are derived by employing a novel Lyapunov–Krasovskii functional which makes good use of the information of both lower and upper bounds on the varying input delay, and the upper bound on the variable sampling interval as well. A feasible solution of the obtained criterion formulated as linear matrix inequalities can be gotten. A tighter bounding technique is presented for acquiring the time derivative of the functional so as to utilise many more useful elements, meanwhile neither slack variable nor correlated augmented item is introduced to reduce overall computational burden. Two examples are given to show the effectiveness of the proposed method.     

Improved results on synchronisation of delayed complex dynamical networks via sampled-data control

This paper focuses on the synchronisation problem of delayed complex dynamical networks via sampled-data control. A novel input-delay-dependent Lyapunov–Krasovskii functional (LKF) is constructed for the first time, which can make full use of the information on the input delay. To strengthen the combinations of the vectors in the resulting augmented vector, a new zero value equality is founded. Based on the input-delay-dependent LKF and zero value equality, synchronisation criteria are established. In comparison with some existing synchronisation criteria, the criteria in this paper are less conservative. The desired sampled-data controller is designed by solving a set of linear matrix inequalities. Finally, numerical examples are given to demonstrate the superiorities of proposed results.     

Further results on sampled-data design for robust control of a single qubit

This paper presents further results on the robust control method for qubit systems in Dong et al. (2013) Dong, D., Petersen, I.R., &; Rabitz, H. (2013). Sampled-data design for robust control of a single qubit. IEEE Transactions on Automatic Control, 58, 2654–2659.[Crossref], [Web of Science ®] , [Google Scholar]. Based on the properties of an antisymmetric system, an alternative method is presented to analyse and exclude singularity intervals in the proof of partial original results. For the case of amplitude damping decoherence, a larger sampling period is presented when the upper bound of the probability of failure is small enough. For the case of phase damping decoherence, a larger sampling period is given when the lower bound of the target coherence is large enough. Furthermore, we provide improved sampling periods for amplitude damping decoherence and phase damping decoherence without the above prior constraints.     

Fault-tolerant control for a class of nonlinear sampled-data systems via a Euler approximate observer

In this paper, a fault-tolerant control (FTC) scheme is developed for a class of nonlinear sampled-data systems. First, a Euler approximate discrete model is used to describe the plant under the sampling. Under this model, an observer-based fault estimation method is proposed. To guarantee the accuracy of both the state and fault estimation values, the conditions to make the approximate model consistent with the exact model are presented. Then, an active fault-tolerant controller, which has a constraint condition for the sampling time, is designed to make the faulty system stable. Finally, an inverted pendulum is used to show the efficiency of the proposed method.     

Lag synchronization of complex dynamical networks with randomly occurring parameter uncertainties and control packet loss via stochastic sampled-data control

ABSTRACT

This paper focuses on the lag synchronization of two general complex dynamical networks with randomly occurring parameter uncertainties and control packet loss. The randomly occurring uncertainties are adopted to reflect more realistic dynamical behaviours of complex networks that are caused by noisy environment. By introducing a Bernoulli distributed stochastic variable, the information of probabilistic time-varying delay is transformed into the deterministic time-varying delay with stochastic parameters. Sampled-data controllers with stochastically varying sampling intervals are considered and a switched system is used to describe packet dropouts in a deterministic way. Some sufficient conditions for the lag synchronization in the mean square are derived in terms of constructing an appropriate Lyapunov function and using linear matrix inequalities. Finally, a numerical example is given to show the effectiveness of the theoretical results.     

Non-uniform sampled-data control of MIMO systems

In this paper, the problem of controlling MIMO plants where the pattern of measurements sampling and control actions delivering is not regular is tackled. Multirate control, time delay systems, missing data environments as well as limited computing and communication resources are on the grounds of these problems. There is an extensive literature on these topics. Different models are reviewed and, from the control viewpoint, model-based control design techniques are reported and new algorithms are proposed. Among the main challenges are the achievement of good performance and the avoidance of intersampling ripple. Both issues are considered and some results are discussed.     

Decentralised output feedback for a class of nonlinear systems via quantised sampled-data control

We design a decentralised observer-based sampled-data controller with quantised output for a class of interconnected nonlinear systems. Instead of quantising the output directly, we quantise the sampled output to avoid sudden jump. It can be proved that by choosing suitable design parameters, global stability of the system is achieved. An example is given to illustrate the effectiveness of the proposed method.