Sampled-data Control Research Articles

Tracking Control of Unicycle Mobile Robots With Event-Triggered and Self-Triggered Feedback

This paper studies the tracking control problem for unicycle mobile robots with event-triggered and self-triggered feedback. Based on a modified dynamic feedback linearization technique and a refined stability analysis, we first propose a new class of saturated sampled-data controllers for unicycle mobile robots of which the state is subject to sampling (measurement) errors. It is guaranteed that the generated control inputs are restricted to within desired ranges, and the unicycle trajectory practically converges towards a time-varying trajectory as long as the sampling errors satisfy a saturated sector bound condition with a nonnegative offset. The proposed robust controller gives rise to a novel event-triggered sampling mechanism with a saturated threshold signal, which adjusts the sampling errors online to steer the tracking error to a desired neighborhood of the origin and guarantees a positive lower bound for the intersampling intervals. As a special case, by designing appropriately the controller and the event-triggered sampling mechanism, asymptotic tracking is achievable. New self-triggered and periodic sampling mechanisms are also developed as natural extensions of the ev

Intermittent sampled-data control for exponential synchronization of chaotic delayed neural networks via an interval-dependent functional

This paper focuses on the exponential synchronization of chaotic delayed neural networks (CDNNs) via the intermittent sampled-data control (ISC). To save the control cost and limited bandwidth, an ISC strategy which integrates the merits of the intermittent control (IC) scheme and the sampled-data control (SC) scheme is proposed. With the proposed ISC scheme, an interval-dependent Lyapunov functional (IDLF) is established for the synchronization control systems. The main characteristic of this functional is that it takes full advantage of the available state information of both working intervals and sleeping intervals. Due to the continuity of the proposed functional, some restrictive conditions on Lyapunov matrices are removed. In addition, some less conservative synchronization criteria are established by means of a combination of the Lyapunov stability theory, the reciprocally convex inequality and the Wirtinger inequality. Meanwhile, an algorithm for the ISC gain is effectively designed to realize the synchronization of master and slave CDNNs. Furthermore, a qualitative relationship between the duty ratio (DR) and the system decaying rate is analyzed. In the end, two examples are given to reveal that the proposed results are feasible and reasonable.

Practical consensus for heterogeneous multi-agent systems with gain fluctuations via resilient sampled-data control

This study proposes a sampled-data-based practical consensus control method for heterogeneous multi-agent systems with gain fluctuations. First, the heterogeneous multi-agent system is formulated together with randomly occurring nonlinear dynamics. Second, unlike the existing studies, a more general retarded sampled-data control approach is designed, which involves the gain fluctuations along with the actual sampling pattern and constant time delay, to achieve the practical consensus of the considered system. By utilizing the aperiodic sampling information, and looped functional approach, a Wirtinger’s inequality-based discontinuous Lyapunov-Krasovskii functional is constructed to derive the delay-dependent stability condition of the closed-loop system in the form of linear matrix inequality. Finally, numerical simulation is presented to illustrate the derived theoretical results.

Output Regulation of Switched Stochastic Systems with Sampled-Data Control

This paper studies the output regulation problem for a class of switched stochastic systems with sampled-data control. Solutions to the output regulation problem are given in two situations. On the one hand, the exogenous signal is assumed to be a constant. By designing a sampled-data state feedback controller, we obtain that the closed-loop system is mean-square exponentially stable and the regulation output tends to zero. On the other hand, the exogenous signal is assumed to be time-varying with bounded derivative. By constructing a class of Lyapunov-Krasovskii functional and a switching rule which satisfies the average dwell time, sufficient conditions for the solvability of practical output regulation problem are given for switched stochastic systems. Finally, numerical examples are given to illustrate the effectiveness of the method.

Improved criteria of sampled-data master-slave synchronization for chaotic neural networks with actuator saturation

This paper investigates the sampled-data master-slave synchronization problem for chaotic neural networks with actuator saturation by constructing novel Lyapunov-Krasovskii functionals. The proposed functionals exploit the sampling interval from the recent sampling instant tk to the next sampling instant tk+1 by using the integral vectors ∫tkte(s)ds, 2t−tk∫tkt∫tkse(u)duds, ∫ttk+1e(s)ds, and 2tk+1−t∫ttk+1∫stk+1e(u)duds. Based on the proposed functionals, this paper derives sufficient criteria for the sampled-data master-slave synchronization of chaotic neural networks with actuator saturation represented using a dead zone nonlinearity. Also, the controller gain matrix of the sampled-data controller can be obtained by solving linear matrix inequalities (LMIs). The superiority and validity of the proposed criterion are verified through the numerical example obtained from the literature.

Lyapunov-based sampled-data set stabilisation of boolean control networks with time delay and state constraint

Lyapunov-based approach to sampled-data set stabilisation of constrained delayed Boolean control networks (DBCNs) is investigated in this paper. The main mathematical tool is semi-tensor product (STP) of matrices. Since the sampling interval is selected from a finite set, the STP method is adopted to convert the dynamics of constrained DBCNs under nonuniform sampled-data control into a switched Boolean network (SBN). It is worth noting that the switches can only occur at the sampling instant. Using the techniques of Lyapunov function and average dwell time, several sufficient conditions are proposed for the global stability of SBN. Moreover, by virtue of reachable set approach, a procedure is established to design state feedback sampled-data stabilisers for constrained DBCNs. The obtained results are applied to the cell survival regulation of apoptosis networks.

Induced $\mathcal {L}_\infty$ Quantized Sampled-Data Control for T–S Fuzzy System With Bandwidth Constraint

This article proposes an induced <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {L}_\infty$</tex-math></inline-formula> sampled-data control problem for the Takagi–Sugeno (T–S) fuzzy system with dynamic quantization, in which the communication channel is assumed to be bandwidth-constrained. First, according to the input delay approach, the dynamics of the considered closed-loop system is modeled by a delay system with constrained nonlinear term. Then, for the bandwidth-constrained communication channel, a constraint condition is introduced to ensure that the adjustable parameter of the dynamic quantization strategy is limited by a bounding region. The main purpose of the problem addressed is to design a controller, such that the closed-loop system guarantees the asymptotic stability with an induced <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {L}_\infty$</tex-math></inline-formula> performance index. The sufficient conditions of stability with induced <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {L}_\infty$</tex-math></inline-formula> control performance are given as the basis of controller design. Furthermore, the induced <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {L}_\infty$</tex-math></inline-formula> sampled-data control scheme and the improved updating rule of dynamic parameter are proposed. Finally, an example shows the effectiveness of the the proposed controller design scheme.

Sampling-Based Event-Triggered Exponential Synchronization for Reaction-Diffusion Neural Networks.

In this article, the exponential synchronization control issue of reaction-diffusion neural networks (RDNNs) is mainly resolved by the sampling-based event-triggered scheme under Dirichlet boundary conditions. Based on the sampled state information, the event-triggered control protocol is updated only when the triggering condition is met, which effectively reduces the communication burden and saves energy. In addition, the proposed control algorithm is combined with sampled-data control, which can effectively avoid the Zeno phenomenon. By thinking of the proper Lyapunov-Krasovskii functional and using some momentous inequalities, a sufficient condition is obtained for RDNNs to achieve exponential synchronization. Finally, some simulation results are shown to demonstrate the validity of the algorithm.

Stability and Robustness Analysis of Finite-Time Consensus Algorithm for Second-Order Multiagent Systems Under Sampled-Data Control

The consensus problem for second-order multiagent systems based on nonsmooth sampled-data control is considered. First, a continuous-time nonsmooth consensus protocol is proposed, which can realize the consensus of systems in a finite time when the external disturbance is absent. Next, based on the sampled data and the zero-order holder, a new discrete-time nonsmooth protocol is proposed. Considering external disturbances, the explicit relationship between the ultimate boundary of errors of any two agents and the sampling period and external disturbance is given with the Lyapunov method and graph theory, which theoretically shows that the nonsmooth control algorithm has a stronger ability to resist external disturbance than the smooth control algorithm. Finally, a simulation example shows the superiority of the nonsmooth consensus algorithm over a smooth consensus algorithm.

Aperiodic Sampled-Data Control for Stabilization of Memristive Neural Networks With Actuator Saturation: A Dynamic Partitioning Method.

This article is concerned with the local stabilization of memristive neural networks subject to actuator saturation via aperiodic sampled-data control. A dynamic partitioning point is elegantly introduced, which is placed between the latest sampling instant and the present time to utilize more information of the inner sampling. To analyze the stability of the closed-loop system, a time-dependent two-side looped functional, which fully utilizes the state information on the entire sampling interval as well as at the dynamic partitioning point, is constructed. It relaxes the positive definiteness of traditional Lyapunov functional inside the sampling interval and therefore, provides the possibility to derive less conservative stability results. Besides, an auxiliary system is established to describe the dynamics at the partitioning point. On the basis of the constructed looped functional, the discrete-time Lyapunov theorem, and some estimation approaches, a linear matrix inequalities-based stability criterion is developed, and then, the sampled-data saturated controller is designed to ensure the local asymptotic stability of the closed-loop system. Thereafter, two optimization problems are developed to seek the desired feedback gain and to expand the estimation of the region of attraction or to enlarge the upper bound of the sampling interval. Eventually, a numerical example is given to demonstrate the effectiveness and the superiority of the proposed results.

Predictor-Based Extended State Observer for Disturbance Rejection Control of Multirate Systems With Measurement Delay

This article investigates the multirate disturbance rejection control problem for linear control systems with mismatched disturbance and measurement delay using predictor-based extended state observer. A new extended state observer together with output predictor is first designed to obtain the estimation values of system state and mismatched disturbance, where output predictor is used to compensate the influences of measurement delay and sampling of output. To attenuate the undesirable influence of mismatched disturbance, we then design a new sampled-data robust controller with disturbance compensation, and the updating rate of the proposed controller is allowed to be different from that of the sensor. Thanks to prediction and disturbance/uncertainty estimation and attenuation techniques, the disturbance rejection property of the resultant closed-loop control systems is enhanced despite the multirate and measurement delay. Some sufficient conditions are presented to ensure the stability property of the resultant control systems. We finally consider the application of the visual servoing control system for an inertially stabilized platform, and the experiment results verify superiorities of the predictor-based disturbance rejection control method proposed in the article.

Non-fragile sampled-data control for synchronization of chaotic fractional-order delayed neural networks via LMI approach

This study addresses the master and slave synchronization problem of chaotic fractional-order delayed neural networks using a non-fragile sampled-data control (NFSDC) scheme which includes uncertainty information in the control gain matrix. An appropriate Lyapunov functional is constructed with information about sampling instants. A new, improved fractional-order inequality is developed to estimate the integral term. Then, based on the new integral inequality, the delay-dependent stability criteria are derived in the form of linear matrix inequality, which guarantees the asymptotic stability of the fractional-order error systems. This implies that the proposed NFSDC can synchronize the fractional-order master and slave systems. Moreover, numerical simulation results illustrate the synchronization nature and the influence of fractional derivatives in the system dynamics. Finally, it can be concluded that the proposed method and control scheme are effective.

Distributed optimization for multi-agent systems with communication delays and external disturbances under a directed network

This article studies the distributed optimization problem for multi-agent systems with communication delays and external disturbances in a directed network. Firstly, a distributed optimization algorithm is proposed based on the internal model principle in which the internal model term can effectively compensate for external environmental disturbances. Secondly, the relationship between the optimal solution and the equilibrium point of the system is discussed through the properties of the Laplacian matrix and graph theory. Some sufficient conditions are derived by using the Lyapunov–Razumikhin theory, which ensures all agents asymptotically reach the optimal value of the distributed optimization problem. Moreover, an aperiodic sampled-data control protocol is proposed, which can be well transformed into the proposed time-varying delay protocol and analyzed by using the Lyapunov–Razumikhin theory. Finally, an example is given to verify the effectiveness of the results.

Stabilization of PMSG-based wind turbine systems with sampling information: Dynamic delay partition method

This paper addresses the novel stabilization criteria for a nonlinear permanent magnet synchronous generator (PMSG)-based wind turbine systems (WTS) with sampled-data information, subject to the uncertainty and controller gain variations. In this regard, the nonlinearity in PMSG-based WTS is conferred by the Takagi–Sugeno (T–S) fuzzy systems. Next, by employing the full advantages of the variable characteristic related to the sampling pattern, a novel looped-type asymmetric augmented Lyapunov-Krasovskii functional (LKF) is developed. Then, the dynamic delay partition method is the first time to be applied for the non-fragile sampled-data control design of proposed T–S fuzzy systems. Also, the less conservativeness stabilization criteria for T–S fuzzy systems are obtained in the form of linear matrix inequality. In the end, the numerical examples confirm the applicability and efficiency of the presented results.

Mixed-Delay-Dependent Augmented Functional for Synchronization of Uncertain Neutral-Type Neural Networks with Sampled-Data Control

In this paper, the synchronization problem of uncertain neutral-type neural networks (NTNNs) with sampled-data control is investigated. First, a mixed-delay-dependent augmented Lyapunov–Krasovskii functional (LKF) is proposed, which not only considers the interaction between transmission delay and communication delay, but also takes the interconnected relationship between neutral delay and transmission delay into consideration. Then, a two-sided looped functional is also involved in the LKF, which effectively utilizes the information on the intervals [tk,t], [tk−τ,t−τ],[t,tk+1),[t−τ,tk+1−τ). Furthermore, based on the suitable LKF and a free-matrix-based integral inequality, two synchronization criteria via a sampled-data controller considering communication delay are derived in forms of linear matrix inequalities (LMIs). Finally, three numerical examples are carried out to confirm the validity of the proposed criteria.

Further Results on Dissipativity Analysis for T–S Fuzzy Systems Based on Sampled-Data Control

This article investigates the dissipative stability and stabilization problems of Takagi–Sugeno fuzzy systems by employing sampled-data control. First, in order to enhance the adaptability of the controller, the internal and external influence factors, such as communication time delay and aperiodic sampling pattern, are taken into consideration in the design process. Then, some new terms are proposed to construct the looped-functional-like Lyapunov functional, which can improve the dissipative performance, enlarge the admissible upper bound of the aperiodic sampling periods, and reduce the occupation of control signals in the communication channel. Next, based on the free-matrix-based integral inequalities, some novel dissipative criteria are presented in terms of linear matrix inequalities. Finally, the superiority of the provided criteria is demonstrated through a truck–trailer system.

Asynchronous Sampled-Data Controller Design for Switched Markov Jump Systems and Its Applications

This article is dedicated to design asynchronous aperiodic sampled-data controller for a class of Markov jump systems with switching transition rate. The sampling controller corresponding switching transition rate matrix mode is not synchronized with the system corresponding switching transition rate matrix mode due to the possible switching of the transfer rate matrix in the sampling interval. With the help of T–S fuzzy models, the state-space representation of the system is turned into a fuzzy Itô stochastic switched Markov jump systems. By constructing novel Lyapunov functionals, mean square exponential stability criteria, and dissipativity criteria are presented. Furthermore, an asynchronous aperiodic sampled-data controller is designed for fuzzy Itô stochastic Markov jump systems. At last, by fuzzing the nonlinear tunnel diode circuit model and nonlinear mass-spring-damper mechanical model, the effectiveness and lower conservativeness of the proposed method are illustrated.

Sampled-data control through model-free reinforcement learning with effective experience replay

Reinforcement Learning (RL) based control algorithms can learn the control strategies for nonlinear and uncertain environment during interacting with it. Guided by the rewards generated by environment, a RL agent can learn the control strategy directly in a model-free way instead of investigating the dynamic model of the environment. In the paper, we propose the sampled-data RL control strategy to reduce the computational demand. In the sampled-data control strategy, the whole control system is of a hybrid structure, in which the plant is of continuous structure while the controller (RL agent) adopts a discrete structure. Given that the continuous states of the plant will be the input of the agent, the state–action value function is approximated by the fully connected feed-forward neural networks (FCFFNN). Instead of learning the controller at every step during the interaction with the environment, the learning and acting stages are decoupled to learn the control strategy more effectively through experience replay. In the acting stage, the most effective experience obtained during the interaction with the environment will be stored and during the learning stage, the stored experience will be replayed to customized times, which helps enhance the experience replay process.The effectiveness of proposed approach will be verified by simulation examples.

Stochastic Sampled-Data Exponential Synchronization of Markovian Jump Neural Networks With Time-Varying Delays.

In this article, the exponential synchronization of Markovian jump neural networks (MJNNs) with time-varying delays is investigated via stochastic sampling and looped-functional (LF) approach. For simplicity, it is assumed that there exist two sampling periods, which satisfies the Bernoulli distribution. To model the synchronization error system, two random variables that, respectively, describe the location of the input delays and the sampling periods are introduced. In order to reduce the conservativeness, a time-dependent looped-functional (TDLF) is designed, which takes full advantage of the available information of the sampling pattern. The Gronwall-Bellman inequalities and the discrete-time Lyapunov stability theory are utilized jointly to analyze the mean-square exponential stability of the error system. A less conservative exponential synchronization criterion is derived, based on which a mode-independent stochastic sampled-data controller (SSDC) is designed. Finally, the effectiveness of the proposed control strategy is demonstrated by a numerical example.

Explaining the “Mystery” of Periodicity in Inter-Transmission Times in Two-Dimensional Event-Triggered Controlled Systems

Motivated by scenarioswhere the communication or the computation resources are limited, event-triggered control consists of transmitting data between the plant and the controller according to the actual system needs and not the elapsed time since the last transmission instant as in traditional sampled-data control, so that the desired control objective is achieved. A range of techniques are nowadays available to design event-triggered controllers. However, we generally have only very little information about the actual behavior of the transmission instants and thus about the amount of transmissions being actually generated, though this is a key feature of the design. In this article, we analyze the inter-event times, i.e., the times between two successive transmission instants, when the plant is modeled as a two-dimensional linear time-invariant system. The controller is a state-feedback law and the triggering rule is the relative threshold policy, which is allowed to be time-regularized. One of the main results in this article is the explanation of the oscillatory behavior of the inter-event times when the constant used to define the threshold is small relative to 1, a phenomenon commonly observed in simulations but never explained so far. More generally, the presented results help to understand the behavior of the inter-event times, instead of solely relying on numerical simulations, and thereby can be exploited to rigorously evaluate the performance of the considered triggering condition in terms of (average) inter-transmission times.