Sampled-data Feedback Research Articles

Sampled-data control of a class of stochastic feedforward nonlinear systems with large delays and sparse sampling

This paper investigates the problem of sampled-data control for a class of stochastic nonlinear systems with delays in the input and state. It is shown that under an upper-triangular linear growth condition, a linear memoryless sampled-data feedback controller is able to globally stabilise the stochastic nonlinear time-delay systems, no matter how large the time delay and sampling period are. The memoryless sampled-data feedback controller is designed by using the emulation method together with the feedback domination technique. With the aid of Lyapunov-Krasovskii functional method, the constructed memoryless sampled-data feedback controller achieves global exponential stability (GES) in mean square of the hybrid closed-loop systems. Application of the sampled-data control scheme is demonstrated through a practical example with simulation.

Decentralized Predictor Stabilization for Interconnected Networked Control Systems with Large Uncertain Delays and Event-Triggered Input

In this article, we propose a control scheme with predictors in a decentralized manner for coupled networked control systems (NCSs) under uncertain, large time-delays and event-triggered inputs. The network-induced delays are handled via the prediction; thus, the delay value is allowed to be large, and the burden of the network is relieved by the event-triggered input. Two methods are employed to deal with the large delay issue: the state and output feedback. When the state of each subsystem is measurable, full-state feedback is used, whereas when the plant state cannot be measured, output feedback is employed with the help of an observer, which is more common in practice. Instead of treating the interactive plants like a global system, the exponential stability of the coupled systems, under decentralized predictors with asynchronous sampled-data feedback, is analyzed in a decentralized way. Finally, the proposed methods are verified via an example of three interconnected cart–pendulum systems, while such systems would not be stabilizable by the traditional approach when the network-induced delays are relatively large.

Sampled-Data Feedback Stabilization in Mean Square for Stochastic Homogeneous Systems

Sampled-Data Feedback Stabilization in Mean Square for Stochastic Homogeneous Systems

Event-Triggered Control of Stochastic Functional Differential Systems via Degenerate Lyapunov Functionals

This article discusses the problem of event-triggered controls (ETCs) for stochastic functional differential systems (SFDSs). For the stabilization of SFDSs, we design a proper degenerate Lyapunov functional and propose a novel ETC. The degenerate Lyapunov functional is more general than the traditional positive definitive Lyapunov functionals and ETC has a prominent advantage of reducing communication resources compared with periodic sampled-data feedback controls because time updating is based on a certain event. Also, a fixed positive lower bound on the stochastic interexecution times is guaranteed by this novel event-triggering mechanism. Together with ETC and the degenerate Lyapunov functional, the boundedness, mean square exponential stabilization, and globally asymptotical stabilization of SFDSs can be established for different choices of parameters. Finally, the obtained results are validated through numerical simulations.

Perception-Based Sampled-Data Optimization of Dynamical Systems

Motivated by perception-based and sensing-based control problems in autonomous systems, this paper addresses the problem of developing feedback controllers to regulate the inputs and the states of a dynamical system to optimal solutions of an optimization problem when one has no access to exact measurements of the system states. In particular, we consider the case where the states need to be estimated from high-dimensional sensory data received only at some time instants. We develop a sampled-data feedback controller that is based on adaptations of a projected gradient descent method and includes neural networks as integral components to estimate the state of the system from perceptual information. We derive sufficient conditions to guarantee (local) input-to-state stability of the control loop. Moreover, we show that the interconnected system tracks the solution trajectory of the underlying optimization problem up to an error that depends on the approximation errors of the neural network and on the time-variability of the optimization problem; the latter originates from time-varying safety and performance objectives, input constraints, and unknown disturbances.

Event-triggered stabilisation of sampled-data singular systems: a hybrid control approach

This paper provides a design of event-triggered feedback stabilisation scheme for a class of sampled-data singular systems, in which the input matrix corresponding to the algebraic equation is not full column rank. First, unlike the conventional piecewise-constant sampled-data feedback controller, a novel hybrid impulsive and sampled-data state feedback controller is designed, which can effectively match with the algebraic equation at sampling instants. An improved discrete event-triggering mechanism with checking period is proposed to achieve exponential stabilisation. Based on these, by applying the input delay approach and defining a new input-delay dependent Lyapunov functional, a sufficient stability condition is presented which ensures that the solution of the event-triggered control system exists and is unique, and the system is exponentially stable with definite decay rate. The estimate of decay coefficient is also given explicitly. Then, an optimisation-based method is developed to jointly design the hybrid controller gains and the event parameters. Finally, two simulation examples including a linearised 2-generator and 6-bus power network system are given to illustrate the validity of the new approach.

Asymptotical feedback controllability of continuous-time probabilistic logic control networks

In this article, we study the controllability of continuous-time probabilistic logic control networks (CT-PLCNs) under sampled-data feedback controls (SDFCs). First, we demonstrate that the concept of finite-time controllability with probability one for discrete-time probabilistic logic control networks cannot be generalized to CT-PLCNs. Then, we propose the concepts of asymptotical feedback reachability and asymptotical feedback controllability for CT-PLCNs. Based on the invariant subsets, we prove that a target state is asymptotically feedback reachable if and only if the target state is a control equilibrium point and any initial state has an admissible path to the target state. Moreover, we introduce the concept of reachability matrix and propose an easily verifiable criterion for asymptotical feedback reachability expressed in terms of the reachability matrix. Based on these, we prove that a CT-PLCN is asymptotically feedback controllable if and only if every state is a control equilibrium point and there is an admissible path between any pair of initial and target states. The relation between controllability and stabilizability is also discussed. We prove that a CT-PLCN is asymptotically feedback controllable if and only if every state is asymptotically feedback stabilizable. For a controllable CT-PLCN, we propose an algorithm of designing a stabilizing SDFC for any given target state. Additionally, we discuss the asymptotical feedback controllability of CT-PLCNs under time-varying nonuniform SDFCs. Finally, an illustrative example is presented to explain the proposed methods and verify the controllability criteria.

Sampled-data-based uncertainty compensation control for a class of continuous-time nonlinear MIMO systems

This paper proposes a sampled-data-based uncertainty compensation control strategy for a class of continuous-time multi-input multi-output nonlinear systems with strong coupling uncertainties. Unlike observer-based uncertainty compensation control methods, this paper utilizes the true value of the total disturbance at an instant in the previous sampling interval rather than its observed value in the last sampling time to compensate for the total disturbance. The total disturbance considered in this paper is composed of the unmodeled nonlinear coupling dynamics and external disturbance. The continuous-time systems and the sampled-data feedback control make up a hybrid closed-loop control system, which, together with the strongly coupled nonlinear uncertainties of the system, brings a significant hurdle to verifying the stability and convergence of the closed-loop control system. A new eigenvalue-and-series-based analysis method is proposed to overcome this hurdle. It is proved that when the tracking target is a bounded function, the tracking error can be arbitrarily small when the sampling period is small enough. Furthermore, when the tracking target is a constant and the nonlinear term is time-invariant, the tracking error converges to zero as time tends to infinity. Numerical results on the attitude control for a 2-DOF UAV validate the effectiveness and merits of the proposed method.

Communication Topology Assignment and Control Co-design for Vehicle Platoons in LTE-V2V Network

In this study, we investigate the problem of inter-vehicle communication topology (IVCT) assignment and control for vehicular platoons in LTE-V2V networks based on the cooperative awareness message dissemination mechanism. A sampled-data feedback controller is proposed for platoons to eliminate the effect of stochastic packet dropouts and external disturbance, where the controller gain depends on the IVCT. To guarantee the stability requirement of a platoon with the minimized cost function, a unified control framework is established to jointly determine the optimal IVCT from all the available ones and the associated feedback controller gain. This co-design procedure is based on the optimal control and dynamic programming technique, where both fixed and periodic switching IVCTs are available. A useful algorithm is proposed to implement the established co-design framework. Furthermore, we present numerical examples to demonstrate the effectiveness of the proposed method.

Sampled-data control of a class of time-delay nonlinear systems via memoryless feedback

We prove that under a linear growth condition, a family of time-delay nonlinear systems is globally stabilizable by memoryless sampled-data state and output feedback, respectively, if the input delay and sampling period are not too big although the state delays are permitted to be large. The proofs rely on the construction of sampled-data feedback controllers and the Lyapunov–Krasovskii functional method. The designed memoryless controllers achieve global asymptotic stabilization of the hybrid closed-loop systems with time-delay and are easily implementable by computers owing to their discrete-time and delay-free nature.

Asymptotical Stability and Stabilization of Continuous-Time Probabilistic Logic Networks

Discrete-time probabilistic logic networks (DT-PLNs), of which probabilistic Boolean networks (PBNs) are a special type, are an important qualitative model for gene regulatory networks (GRNs). Although a DT-PLN can predict the long-term behavior of a GRN, using it to describe the transient kinetics at the microtimescale level remains inconvenient. In this article, we investigate the problems associated with the stability and stabilization of continuous-time probabilistic logic networks (CT-PLNs). First, we demonstrate that the concept of finite-time stability for DT-PLNs cannot be extended to CT-PLNs owing to the nonsingularity of transitional probability matrices. Thus, we introduce the concept of asymptotical stability, which is defined as the convergence in distribution of the network state. Second, by developing the theory of invariant subsets for CT-PLNs, a necessary and sufficient condition for asymptotical stability with respect to a subset is proposed, which is expressed in terms of the transition rate matrix of probability. Third, for a CT-PLN with input nodes, termed a continuous-time probabilistic logic control network, we discuss the subsets that are invariant under piece-wise constant input. Based thereupon, we propose a necessary and sufficient condition under which asymptotically stabilizing sampled-data feedback exists. A method for designing sampled-data feedback is proposed. Last, Monte Carlo simulation algorithms are proposed to efficiently simulate a CT-PLN in the time domain. Examples are provided to demonstrate the methods proposed in this article.

Digital tracking control of the boost converter: prediction-based digital redesign approach

Several continuous-time tracking controllers of the DC-to-DC boost converters had been addressed, but few literature touched the digital tracking control because that was a challenging theoretical problem which consists of nonlinear, non-minimum phase and saturated control. Given a continuous-time nonlinear boost converter with continuous tracking control, this paper proposes a new sampled-data feedback laws from the available analog counterpart via digital redesign such that the state trajectories of the sampled-data closed-loop systems close to the continuous-time one in the sense of state-matching. An existing boost converter circuit has been demonstrated to visualize the feasibility of the proposed methodology.

Sampled-Data Consensus for Networked Euler-Lagrange Systems With Differentiable Scaling Functions

This paper is concerned with the sampled-data consensus of networked Euler-Lagrange systems. The Euler-Lagrange system has enormous advantages in analyzing and designing dynamical systems. Yet, some problems arise in the Euler-Lagrange equation-based control laws when they contain sampled-data feedback. The control law differentiates the discontinuous sampled-data signals to generate its control input. In this process, infinities in the control input are inevitable. The main goal of this work is to eliminate these infinities. To reach this goal, a class of differentiable scaling functions is designed to replace the conventional zero-order-hold and ensure a smooth transition between sampled states. The scaling functions work as multipliers on the sampled-data signals to make them differentiable, hence avoid the infinities. A consensus criterion compatible with the differentiable scaling functions is also obtained. It is shown in numerical examples that the proposed differentiable scaling functions approach both eliminates the infinities and ensures consensus under the criterion.

Time-Delayed Sampled-Data Feedback Control of Differential Systems Undergoing Hopf Bifurcation

In this paper, time-delayed sampled-data feedback control technique is used to asymptotically stabilize a class of unstable delayed differential systems. Through the analysis for the distribution change of eigenvalues, an effective interval of the control parameter is obtained for a given sampling period. Here an indirect strategy is taken. Specifically, the system of continuous-time delayed feedback control is studied first by Hopf bifurcation theory. And then, the result and implicit function theorem are used to analyze the system of time-delayed sampled-data feedback control with a sufficiently small sampling period. Considering the practical criterion for the size of sampling period, the upper bound of sampling period is estimated. Finally, an application example, an unstable Mackey–Glass model, is asymptotically stabilized by introducing a blood transfusion item with time-delayed sampled-data feedback control. The blood transfusion speed and blood collection test period are derived from the main results. Some simulations and comparisons show the correctness and advantages of the main theoretical results.

A General Class of Control Lyapunov Functions and Sampled-Data Stabilization

Several important contributions toward sampled-data and hybrid feedback stabilization have appeared in the literature. This article extends recent results by second author concerning sampled-data feedback stabilization for affine in the control of nonlinear systems with a nonzero drift term, under the presence of a generalized control Lyapunov function associated with appropriate Lie algebraic hypotheses concerning the dynamics of the system. The main results of this article constitute a generalization of the well-known “Artstein-Sontag” theorem on asymptotic stabilization by means of an almost smooth feedback controller. The analysis is limited to the affine single-input nonlinear systems with nonzero drift term; however, the results can easily be extended to the multi-input case. An illustrative example of the derived results is included.

Sampled-data general partial synchronization of Boolean control networks

In this manuscript, the general partial synchronization of a type of drive-response Boolean control networks (BCNs) is proposed for the first time and is addressed by sampled-data feedback control (SDFC). Different from all previous synchronization in the field of BCNs, the general partial generalization requires that the total number of the synchronized nodes exactly maintains at a pre-special value after finite-time step, and it removes the requirement on the anticipated synchronized nodes. To begin with, we define the general partial synchronization of derive-response BCNs based on the Hamming distance of two Boolean vectors. Subsequently, by utilizing the semi-tensor product (STP) of matrices, we obtain a series of criteria for BCNs to achieve general partial synchronization by SDFC. Then, the corresponding SDFC strategy is designed, under which the considered BCNs achieve general partial synchronization. Finally, these results are demonstrated by an illustrative numerical example.

Exponential stabilisation for nonlinear PDE systems via sampled-data static output feedback control

ABSTRACT This paper focuses on the problem of exponential stabilisation for nonlinear partial differential equation (PDE) systems by designing sampled-data static output feedback controller. First, the nonlinear PDE systems are reconstructed by Takagi-Sugeno (T-S) fuzzy model. Subsequently, the closed-loop systems are obtained by introducing sampled-data static output feedback fuzzy controller. Then, stability conditions of the closed-loop system are obtained based on Lyapunov function approach, which can guarantee that the considered systems are exponential stabilisation and satisfy dissipative performance. Finally, the effectiveness of the developed method is demonstrated by a simulation study.

Robust perimeter control design for two urban regions with sampled-data and input saturation

This paper investigates the robust perimeter control for two urban regions with sampled-data and input saturation. Based on the macroscopic fundamental diagram, an uncertain network vehicle balance model is established for two urban regions. Instead of the continued feedback control, this paper designs a sampled-data feedback control law to stabilize the traffic accumulations at the desired state. Based on the Lyapunov function theory, the stability condition of two urban regions is given in the form of linear matrix inequalities (LMIs), which ensures that the traffic accumulation for each region is stabilized at the desired state. Moreover, for the inevitable disturbances, the robust saturation control strategy is designed such that the traffic accumulation for each region is robustly stabilized at the desired state, and meanwhile a less disturbance attenuation level is guaranteed. Numerical examples are given to illustrate the effectiveness of the proposed methods.

Filtered adaptive constrained sampled-data output feedback control for uncertain multivariable nonlinear systems

This paper synthesises a constrained sampled-data output feedback controller for uncertain multivariable nonlinear systems in the presence of various constraints, using the filtered adaptive control architecture. Nonlinear uncertainties are estimated online by solving the error dynamics between the output predictor and the real system with the neglection of unknowns, the yielded adaptive parameters are piecewise constant. In the proposed control scheme, the nonlinear uncertainties are compensated for within the bandwidth of low-pass filters, while the trade-off between tracking and constraints violation avoidance is formulated as a numerical constrained optimisation problem which is solved periodically. Priority is given to constraints violation avoidance at the cost of deteriorated tracking performance. System transformations are performed to find the sufficient conditions that can guarantee the stability of the closed-loop system with the sampled-data controller, where both the states and control inputs are held constant over the sampling period.

Stability and Stabilization for T–S Fuzzy Large-Scale Interconnected Power System With Wind Farm via Sampled-Data Control

This article focuses on the stability and stabilization analysis of large-scale multiarea interconnected power systems (LSMAIPSs) involving the wind farm through the Lyapunov stability theory. Instead of linearizing the nonlinear model at a certain operating point the Takagi-Sugeno (T-S) fuzzy model is able to achieve better performance. In this article, a doubly fed induction generator (DFIG)-based wind turbine systems (WTSs) are integrated into each area of the power system. The main reason behind the integration is because the power factor has the ability to destabilize the performance of the power supply. To ensure the stability of the LSMAIPS, a decentralized sampled-data feedback load frequency control is designed. The stability and stabilization conditions are derived through constructing suitable Lyapunov function which contains the sampling information and the solvable linear matrix inequalities (LMIs) along with an evaluation of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. To an evident, the simulation results are performed based on experimental values of two-area large-scale interconnected power system with DFIG-based wind farm, which guarantees the asymptotic stability of the proposed T-S fuzzy system under the sampled-data controller.