Sampled-data Feedback Control Research Articles

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.

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.

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.

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.

Sampled-Data Set Stabilization of Switched Boolean Control Networks

In this paper, the set stabilization of switched Boolean control networks (SBCNs) under sampled-data feedback control is addressed. Here, the control input is switching signal-dependent, and SBCNs can switch only at the sampling instants. First, the sampled point control invariant subset (SPCIS) of SBCNs is defined, and an algorithm is provided to obtain the largest SPCIS under arbitrary switching signal. Based on the largest SPCIS, some necessary and sufficient conditions are presented for the set stabilization of SBCNs by switching signal-dependent sampled-data (SSDSD) state feedback control. Furthermore, a constructive procedure is given to design all possible SSDSD state feedback controllers. Finally, some examples are presented to illustrate the effectiveness of the obtained results.

Sampled-data output feedback controllers for nonlinear systems with time-varying measurement and control delays

Abstract In this paper, we propose sampled-data output feedback controllers for nonlinear systems with time-varying measurement and input delays. A state prediction is generated by chains of saturated high-gain observers with switching error-correction terms and the state prediction is used to stabilize the system with saturated controls. The observers reconstruct the unmeasurable states at different delayed time-instants, which partition the maximal variation interval of the time-varying delays. The density of these delayed time instant depend both on the magnitude of the delays and the growth rate of the nonlinearities. Our sampled-data feedback controllers are obtained as zero-order discretizations of continuous time controllers.

Stabilization of Stochastic Retarded Systems Based on Sampled-Data Feedback Control

Throughout this article, we study the mean square exponential stabilization of stochastic retarded systems described by stochastic functional differential equations (SFDEs). Different from the traditional feedback controls with continuous observation of state, we put forward a novel sampled-data feedback control depending on the discrete observation of state and time delay. It greatly enlarges the probability of finding discrete-time feedback controls for stochastic retarded systems. In addition, the novel sampled-data feedback control succeeds in handling the delays involved in SFDEs. As applications, we provide two examples with simulation figures to illustrate the main result.

Networked Output Feedback Control for a Class of Uncertain Nonlinear Time-Delay Systems

This paper studies the global stabilization problem for a class of uncertain time-delay nonlinear systems by designing a sampled-data output feedback controller via network. Under a lower triangular linear growth condition, when only the output is measurable, a sampled-data output feedback network controller, whose observer and control law are both linear, is constructed to solve the stabilization problem. Using a feedback domination design approach which substantially differs from the separation principle, we explicitly construct a Lyapunov–Krasovskill functional to prove the global asymptotic stability with the help of inductive proof method. The control law is discrete-time and linear, hence simulation examples be easily implemented with computers to show the effectiveness of our proposed method.

Disturbance-observer-based sampled-data adaptive output feedback control for a class of uncertain nonlinear systems

ABSTRACTIn this paper, a sampled-data adaptive output feedback controller is proposed for a class of uncertain nonlinear systems with unmeasured states, unknown dynamics and unknown time-varying external disturbances. To approximate uncertain nonlinear functions, radial basis function neural networks (RBFNNs) are employed. The state observer and the disturbance observer (DO) are constructed to estimate the unmeasured state and the external disturbance, respectively. Then, the sampled-data adaptive output feedback controller and adaptive laws are designed by using the backstepping design technique. The allowable sampling period T is derived to guarantee that all states of the resulting closed-loop system are semi-globally uniformly ultimately bounded. Finally, two simulation examples are presented to illustrate the effectiveness of the proposed approach.

Cooperative Adaptive Cruise Control of Vehicles Using a Resource-Efficient Communication Mechanism

In this study, a resource-efficient communication mechanism is investigated for the cooperative adaptive cruise control (CACC) of vehicles subject to actuator delay and disturbances. Specifically, a dynamic event-triggered communication mechanism (DECM) is designed for a tracking error (spacing error, velocity error, and acceleration error) based sampled-data feedback controller. Under the DECM, the transmissions of sampled velocity and acceleration from a preceding vehicle to the controller can be significantly reduced. Sufficient conditions for the stability of the CACC system are obtained for the DECM-based sampled-data feedback controller. According to the obtained conditions, parameter design criteria are established for the DECM to guarantee the stable performance of CACC systems. Simulation studies illustrate that the proposed DECM-based CACC system can not only save inter-vehicle communication resources, but also guarantee stable performance.

Mixed [formula omitted] sampled-data output feedback control design for a semi-linear parabolic PDE in the sense of spatial [formula omitted] norm

This paper addresses distributed mixed H2∕H∞ sampled-data output feedback control design for a semi-linear parabolic partial differential equation (PDE) with external disturbances in the sense of spatial L∞ norm. Under the assumption that a finite number of local piecewise measurements in space are available at sampling instants, a static sampled-data output feedback controller is suggested, where the sampling interval in time is bounded. The local piecewise measurements bring additional difficulty for the exponential stability and performance analysis since the existing Poincaré-Wirtinger inequality in 1D spatial domain is not applicable. By constructing an appropriate Lyapunov–Krasovskii functional candidate and employing Wirtinger’s inequalities, a variant of Poincaré-Wirtinger inequality in 1D spatial domain, as well as Agmon’s inequality, it is shown that the suggested static sampled-data output feedback controller not only guarantees the output exponential stability of the resulting closed-loop PDE in the spatial L∞ norm but also ensures the mixed H2∕H∞ performance index defined in the spatial L∞ norm, if the sufficient conditions presented in terms of standard linear matrix inequalities (LMIs) are fulfilled. The satisfactory and better performance of the suggested sampled-data feedback controller is demonstrated by numerical simulation results of an illustrative example.

An Observer Based Sampled-data Control for Class of Scalar Nonlinear Systems Using Continualized Discretization Method

A new observer based sampled-data feedback control is proposed for a class of scalar nonlinear affine systems, where the control distribution is constant, in the presence of noise. The discrete-time states are estimated by a nonlinear state observer, and used for designing the sampled-data control. The discrete-time model used for controller and state observer design is derived using continualizated discretization method. This discretization method is based on the new concept of continualization of discrete-time models, and is applicable to any system whose Jacobian matrix is defined. In this work, it is shown that for the system without the presence of noise, the proposed sampled-data control preserves the equilibria and dynamics of the desired system, while the conventional control, which is based on forward difference method, does not. Simulations are carried out for the scalar Riccati system with the presence of noise to demonstrate the better performances of the proposed method not only in sampled-data control design, but also in system states estimation than the conventional method for both high and low sampling frequencies.

Transmission power scheduling and control co-design for wireless sensor networks

This paper discusses transmission power scheduling and control co-design in wireless sensor networks (WSNs) under communication energy constraints, in which the dynamics of all mobile sensor nodes (MSNs) are assumed to be nonlinear. A most regular code sequence (MRCS) is introduced as the transmission power scheduling policy to automatically allocate the transmission power levels to MSNs thereby adhering to the given communication energy budget. The effects of the different transmission power levels on data transmission is explicitly characterized in this paper. By using a stochastic system analysis approach and average dwell time technique, a framework for the transmission power scheduling and control co-design is established. The control co-design algorithm is proposed to simultaneously determine the gain of the sampled-data feedback controller and the parameters of the generated MRCS. A numerical simulation is conducted to verify the effectiveness of the proposed algorithm.

Synchronization of memristive BAM neural networks with leakage delay and additive time-varying delay components via sampled-data control

In this paper, the global asymptotic stability of memristive bidirectional associative memory neural networks with leakage delay and two additive time-varying delays is firstly studied. Then, we propose a novel sampled-data feedback controller to guarantee the synchronization of system based on drive/response concept. In particular, taking full advantage of the input delay approach, the Lyapunov function method and the Jensen’s inequality theory, several sufficient conditions are obtained. Finally, two numerical simulation examples show the effectiveness of the designed sampled-data control strategy. Furthermore, our results can be applied to simulate the associative memory function of brain-like robots, large-scale information storage, etc.