Aperiodic Sampled-data Control Research Articles

Aperiodic dynamic event-triggered control for linear systems: A looped-functional approach

The recent literature on event-triggered control has demonstrated the potential of dynamic periodic event-triggered control. Compared to continuous-time event-triggering rules, the benefit of considering periodic event-triggered control is to avoid the Zeno phenomenon, which refers to the situation when there are an infinite number of updates in a bounded interval of time. The idea of periodic event-triggered control is to trigger the control law only at known allowable periodic sampling instants. In this paper, our objective is to relax the constraint on the periodicity of the allowable sampling instants and to adapt this framework to the dynamic event-triggered control, which has not been considered in the literature, as far as we are aware of. Following the successful efforts to assess the stability of aperiodic sampled-data control, here we propose a generic framework to emulate aperiodic dynamic event-triggered control law for linear systems, for which the allowable sampling instants are not necessarily equidistant. Such an analysis is made possible thanks to the looped-functionals framework, which gives the flexibility to consider the periodic/aperiodic static/dynamic event-triggered control in a single formulation. Finally, the efficiency of the proposed results is illustrated through the study of two academic examples.

Formula omitted]-[formula omitted]-dissipative control of T-S fuzzy systems via aperiodic sampling control with communication delay

This article concerns the strict (Q,S,R)-γ dissipativity of Takagi–Sugeno fuzzy systems (TSFSs) via aperiodic sampled-data control with communication delay. The motivations of this paper are that the transmission channels have communication delay and the original dissipative analysis method may be conservative. In order to consider the impact of communication delays, first of all, a sampled-data controller (SDC) with a constant communication delay is conceived to analyze the dissipativity of TSFSs. Next, the overall closed-loop system model is established stemming from the designed controller. In order to attain less conservative results, a new looped-functional which can take advantage of the available information of the sampling instants is formed. Then, strict (Q,S,R)-γ dissipativity can be guaranteed by a criterion obtained by using the looped-functional and the modified free-matrix-based inequality (FMBI) technique. By working out the obtained linear matrix inequalities (LMIs), the controller gain matrix that meets the requirement can be determined. Finally, the truck trailer and the mass–spring systems are showcased as simulation examples to provide evidence of the effectivity and superiority of the devised approach. In the presence of 0.1 s communication delay in the truck trailer system controller, the maximum γ can reach 0.9751 when sampling interval h takes 0.15 s, which makes the system can achieve strict (Q,S,R)-γ dissipativity.

Sampled-data exponential consensus of multi-agent systems with Lipschitz nonlinearities

In this paper, the exponential consensus of leaderless and leader-following multi-agent systems with Lipschitz nonlinear dynamics is illustrated with aperiodic sampled-data control using a two-sided loop-based Lyapunov functional (LBLF). Firstly, applying input delay approach to reformulate the resulting sampled-data system as a continuous system with time-varying delay in the control input. A two-sided LBLF which captures the information on sampled-data pattern is constructed and the symmetry of the Laplacian matrix together with Newton–Leibniz formula have been employed to obtain reduced number of decision variables and decreased LMI dimensions for the exponential sampled-data consensus problem. Subsequently, an aperiodic sampled-data controller was designed to simplify and enhance stability conditions for computation and optimization purposes in the proposed approach. Finally, based on the controller design, simulation examples including the power system are proposed to illustrate the theoretical analysis, moreover, a larger sampled-data interval can be acquired by this method than other literature, thereby conserving bandwidth and reducing communication resources.

Improved aperiodic sampled-data control for singular Markov jump systems under incomplete transition descriptions

This paper studies the aperiodic sampled-data control problem of singular Markov jump systems under uncertain and unknown transition rates. First, taking into account the system information from x(tk) to x(tk+1), a novel two-sided looped mode-dependent Lyapunov–Krasovskii function (LKF) is constructed, which provides more freedom to test the feasibility of the LMI condition in the criterion. Based on this LKF and an improved integral inequality, a stochastic admissibility condition is given by linear matrix inequalities (LMIs), which is less conservative. Then, by using a lemma of equivalent set, a controller algorithm without equality constraint is proposed by LMIs to ensure the stability of the system. Finally, several examples are provided to verify the validity of the main results.

Aperiodic Sampled-Data Control for Anti-Synchronization of Chaotic Nonlinear Systems Subject to Input Saturation

This paper studies the aperiodic sampled-data (SD) control anti-synchronization issue of chaotic nonlinear systems under the effects of input saturation. At first, to describe the simultaneous existence of the aperiodic SD pattern and the input saturation, a nonlinear closed-loop system model is established. Then, to make the anti-synchronization analysis, a relaxed sampling-interval-dependent Lyapunov functional (RSIDLF) is constructed for the resulting closed-loop system. Thereinto, the positive definiteness requirement of the RSIDLF is abandoned. Due to the indefiniteness of RSIDLF, the discrete-time Lyapunov method (DTLM) then is used to guarantee the local stability of the trivial solutions of the modeled nonlinear system. Furthermore, two convex optimization schemes are proposed to expand the allowable initial area (AIA) and maximize the upper bound of the sampling period (UBSP). Finally, two examples of nonlinear systems are provided to illustrate the superiority of the RSIDLF method over the previous methods in expanding the AIA and enlarging the UBSP.

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.

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.

Resilient Control for Multiagent Systems With a Sampled-Data Model Against DoS Attacks

To reduce the computational burden and resist the denial-of-service (DoS) attacks, a resilient distributed sampled-data control scheme is proposed for multiagent systems. The agent states are sampled periodically by the sensors. DoS attacks disrupt the data communication from transmitters to controllers randomly or periodically with a limited duration time. Information on DoS attacks can be obtained by introducing novel logic processors embedded in corresponding controllers. Next, the problem of resilient control can be converted into one concerned with the upper and lower bound of the sampling interval of an aperiodic sampled-data control system. Some sufficient criteria for developing resilient distributed controllers are derived using the novel looped Lyapunov functional approach and the free-matrix-based inequality method. Finally, two illustrative examples, unmanned aerial vehicles and the two-mass-spring systems, are provided to demonstrate the efficiency of the proposed resilient distributed sampled-data control protocols against the DoS attacks.

Stability analysis of sampled-data systems with sector-bounded input nonlinearity

This work proposes a method for the stability analysis of aperiodic sampled-data control systems with sector and slope bounded input nonlinearities. The stability conditions are derived by using a hybrid system representation and a timer-dependent Lur'e type Lyapunov function. Considering a polynomial timer-dependence, the stability conditions are cast in sum-of-squares optimization problems aiming at computing the largest range of sampling intervals or the largest sector bounds on the nonlinearity for which the origin of the closed-loop system is globally asymptotically stable.

Asymptotic synchronization of delayed Lur’e systems via non-fragile sampled-data control

This paper is dedicated to investigating the asymptotic synchronization of delayed Lur’e systems via non-fragile aperiodic sampled-data control. Two different kinds of gain fluctuations are taken into consideration. A time-dependent two-sided looped functional is proposed, which makes efficient use of the obtainable information not only of the whole sampling intervals, but also of the nonlinear functions of the considered systems. A criterion on global asymptotic stability is derived by means of the constructed looped functional and using the free-weighting matrix approach. Then, a non-fragile aperiodic sampled-data controller, which allows both additive and multiplicative gain fluctuations, is designed to ensure the asymptotic synchronization based on solutions of a set of linear matrix inequities. Finally, an example with simulations is presented, which shows that the designed controller allows a larger sampling period in comparison with the existing results.

Guest Editorial: Learning, optimisation and control of cyber‐physical systems

Guest Editorial: Learning, optimisation and control of cyber‐physical systems

Sampled‐data synchronization of singular Markovian jump system: Application to DC motor model

Sampled-data synchronization problem for singular Markovian jump systems (SMJSs) subject to aperiodic sampled-data control is investigated. Firstly, via constructing mode-dependent one-sided loop-based Lyapunov functional (LBLF) and two-sided LBLF, two different stochastically admissible conditions are suggested for error SMJSs with aperiodic sampled-data. It is guaranteed that the slave system is stochastically synchronized to the master system on the basis of the proposed stochastically admissible conditions. Secondly, two corresponding mode-dependent aperiodic sampled-data controller design approaches are provided for error SMJSs based on two different conditions, separately. Finally, the validity of these approaches is demonstrated by a direct current (DC) motor model. It also demonstrated that the two-sided LBLF method possesses a larger upper bound of sampled-data period than the one-sided LBLF method.

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

In this article, sampled-data synchronization problem for stochastic Markovian jump neural networks (SMJNNs) with time-varying delay under aperiodic sampled-data control is considered. By constructing mode-dependent one-sided loop-based Lyapunov functional and mode-dependent two-sided loop-based Lyapunov functional and using the Itô formula, two different stochastic stability criteria are proposed for error SMJNNs with aperiodic sampled data. The slave system can be guaranteed to synchronize with the master system based on the proposed stochastic stability conditions. Furthermore, two corresponding mode-dependent aperiodic sampled-data controllers design methods are presented for error SMJNNs based on these two different stochastic stability criteria, respectively. Finally, two numerical simulation examples are provided to illustrate that the design method of aperiodic sampled-data controller given in this article can effectively stabilize unstable SMJNNs. It is also shown that the mode-dependent two-sided looped-functional method gives less conservative results than the mode-dependent one-sided looped-functional method.

Polyhedral Regions of Stability for Aperiodic Sampled-Data Linear Control Systems With Saturating Inputs

This work proposes a method to assess the local asymptotic stability and to provide polyhedral estimates of the region of attraction of the origin (RAO) of linear systems under aperiodic sampled-data control and saturating inputs. The approach is based on a discrete-time model that describes the behavior of the system state between consecutive sampling instants. It corresponds to a difference inclusion defined from a partition of the intersampling interval and from the saturated and nonsaturated (SNS) embedding of saturation functions. A method to construct a contractive polyhedral set for this model is proposed. It is shown that this set induces a local Lyapunov function strictly decreasing at the sampling instants and that it is an estimate of the RAO of the continuous-time closed-loop system.

Some new results on the consensus of coupled harmonic oscillators with impulsive control

AbstractWe consider the consensus of coupled harmonic oscillators with impulsive control via sampled position data in this article. Leader‐following consensus problem and leaderless consensus problem are investigated by unified analysis. Using joint spectral radius of the set of matrix, the consensus problem is solved without the assumption that the sampling interval is fixed. Some sufficient conditions which are valid for both cases of periodic and aperiodic sampled data control are obtained under a directed network topology. At last, some simulations are provided to support the theoretical analysis.

Aperiodic sampled-data controller design for switched Itô stochastic Markovian jump systems

In this paper, aperiodic sampled-data control for a class of Itô stochastic Markovian jump systems with switching transition rate matrix containing partially known elements is investigated. By introducing a loop-based Lyapunov functional, mean square exponential stability criteria are presented and mode-dependent aperiodic sampled-data controllers are designed. Due to the constraint on the upper bound of the sampling interval is no greater than the dwell time, the transition rate matrix may switch in a sampling interval. The issue concerning the asynchronization between the sampled-data controller mode and the system mode is hence considered. A practical RLC electrical circuit example is presented to illustrate the effectiveness of the method.

Decentralized Resilient $H_{\infty}$ Load Frequency Control for Cyber-Physical Power Systems Under DoS Attacks

This paper designs a decentralized resilient H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> load frequency control (LFC) scheme for multi-area cyber-physical power systems (CPPSs). Under the network-based control framework, the sampled measurements are transmitted through the communication networks, which may be attacked by energy-limited denial-of-service (DoS) attacks with a characterization of the maximum count of continuous data losses (resilience index). Each area is controlled in a decentralized mode, and the impacts on one area from other areas via their interconnections are regarded as the additional load disturbance of this area. Then, the closed-loop LFC system of each area under DoS attacks is modeled as an aperiodic sampled-data control system with external disturbances. Under this modeling, a decentralized resilient H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> scheme is presented to design the state-feedback controllers with guaranteed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance and resilience index based on a novel transmission interval-dependent loop functional method. When given the controllers, the proposed scheme can obtain a less conservative H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance and resilience index that the LFC system can tolerate. The effectiveness of the proposed LFC scheme is evaluated on a one-area CPPS and two three-area CPPSs under DoS attacks.

Aperiodic sampled-data control for local stabilization of memristive neural networks subject to actuator saturation: Discrete-time Lyapunov approach

In this paper, the local stabilization of memristive neural networks (MNNs) with actuator saturation is investigated via aperiodic sampled-data control. Inspired by the characteristic of the control scheme, a novel sampling-interval-dependent Lyapunov functional (SIDLF) is constructed. The main contribution of the developed Lyapunov functional lies in that the requirement on its positive definiteness is replaced by a looped condition. Then, using some inequality techniques and the discrete-time Lyapunov approach, two sufficient criteria are derived to ensure the locally asymptotical stability of the trivial solutions of closed-loop systems. A unified work is developed that can deal with the presence of the saturation nonlinearity effects, aperiodic sampled-data control, as well as SIDLF. Additionally, two convex optimization schemes, aiming at enlarging the admissible initial region (AIR) and maximizing the upper bound of sampling interval, are respectively presented for designing the desired saturated sampled-data controller gains. A quantitative relationship between the maximum sampling interval and AIR is revealed. Finally, two numerical examples are given to illustrate the advantages and effectiveness of the derived theoretical conclusions.

Aperiodic Sampled-Data Control for Chaotic System Based on Takagi–Sugeno Fuzzy Model

This paper investigates the aperiodic sampled-data control for a chaotic system. Firstly, Takagi–Sugeno (T-S) fuzzy models for the chaotic systems are established. The lower and upper bounds of the sampling period are taken into consideration. Then, the criteria for mean square exponential stability analysis and aperiodic sampled-data controller synthesis are provided by means of linear matrix inequalities. And the real sampling patterns can be fully captured by constructing suitable Lyapunov functions. Finally, an illustrative example shows that the proposed method is effective to guarantee that the system’s states are stable with aperiodic sampled data.

Robust Sampled-Data Control for Switched Complex Dynamical Networks With Actuators Saturation.

In this article, an aperiodic sampled-data control problem is investigated for polytopic uncertain switched complex dynamical networks subject to actuator saturation. Due to the constraint on the upper bound of the sampling interval being no greater than the dwell time, the issue concerning the asynchronization between the sampled-data controller mode and the system mode is hence considered to be caused by subsystems that may switch in a sampling interval. By considering the sampling interval without switching and the sampling interval with switching, the parameters-dependent loop-based Lyapunov functionals are constructed, respectively. With the help of the constructed functional, mean-square exponential stability criteria for the error polytopic uncertain switched complex dynamical networks are presented under the definition of average dwell time. Furthermore, based on the stability criteria, the asynchronous aperiodic sampled-data controller is designed for polytopic uncertain switched complex dynamical networks subject to actuator saturation. The polytopic uncertain switched complex dynamical networks can be guaranteed to exponentially synchronize with the target node based on the proposed stability conditions and aperiodic sampled-data controller design method. Finally, by transforming the proposed theoretical conditions into the LMI-based objective optimization problem, the domain of attraction of polytopic uncertain switched complex dynamical networks is estimated. An example based on switched Chua's circuit is applied to verify the effectiveness of the proposed method.