Discrete Instants Research Articles

Energy-to-Peak State Estimation for Switched Neutral-Type Neural Networks With Sector Condition via Sampled-Data Information.

In this article, the energy-to-peak state estimation problem is investigated for a class of switched neutral neural networks subject to the external perturbations with bounded energy. Both the values of the measurement outputs and switching signal of the subsystems are only available for the controllers at the discrete sampling instants. Unlike the results for nonswitched neural networks, the coexistence of the switching and sampling actions directly causes the asynchronous phenomena between the indexes of subsystems and their corresponding controllers. To address this situation, the piecewise time-dependent Lyapunov-Krasovskii functional and slow switching mechanism are introduced. Under the developed theorem conditions, we prove that the designed state estimator exponentially tracks the true value of the neural state with the accessible sampled-data information. Also, the influence of the exogenous perturbations on the peak value of the estimation error is constrained at a prescribed level. Finally, a neutral cellular neural network with switching parameters is employed to substantiate the effectiveness and applicability of the theoretical results.

Novel Techniques for a Verified Simulation of Fractional-Order Differential Equations

Verified simulation techniques have been investigated intensively by researchers who are dealing with ordinary and partial differential equations. Tasks that have been considered in this context are the solution to initial value problems and boundary value problems, parameter identification, as well as the solution of optimal control problems in cases in which bounded uncertainty in parameters and initial conditions are present. In contrast to system models with integer-order derivatives, fractional-order models have not yet gained the same attention if verified solution techniques are desired. In general, verified simulation techniques rely on interval methods, zonotopes, or Taylor model arithmetic and allow for computing guaranteed outer enclosures of the sets of solutions. As such, not only the influence of uncertain but bounded parameters can be accounted for in a guaranteed way. In addition, also round-off and (temporal) truncation errors that inevitably occur in numerical software implementations can be considered in a rigorous manner. This paper presents novel iterative and series-based solution approaches for the case of initial value problems to fractional-order system models, which will form the basic building block for implementing state estimation schemes in continuous-discrete settings, where the system dynamics is assumed as being continuous but measurements are only available at specific discrete sampling instants.

Static and Dynamic Event-Triggered Mechanisms for Distributed Secondary Control of Inverters in Low-Voltage Islanded Microgrids.

Due to the high resistance/reactance (R/X) ratio of a low-voltage microgrid (LVMG), virtual complex impedance-based P-· V/Q-ω droop control is adopted in this article as the primary control (PC) technique for stabilizing the system. A distributed event-triggered restoration mechanism (ETSM) is proposed as the secondary control (SC) technique to restore the output-voltage frequency and improve power sharing accuracy. The proposed ETSM ensures that neighboring communication happens only at some discrete instants when a predefined event-triggering condition (ETC) is fulfilled. In general, the design of the ETC is the crucial challenge of an event-triggered mechanism (ETM). Thus, in this article, a static ETM (SETM) is proposed as the ETC at first, where two static parameters are utilized to reduce the triggering frequency. Bounded stability is ensured under the SETM, which means that the output-voltage frequency is restored to the vicinity of its nominal value, and close to fair utilization of the distributed generators (DGs) is achieved. To further improve the power sharing accuracy and accelerate the regulation process, a dynamic ETM (DETM) is then introduced. In the DETM, two dynamic parameters that converge to zero in the steady state are designed, which promises asymptotic stability of the system. Besides, Zeno behavior is excluded in both mechanisms. An LVMG consisting of four DGs is constructed in MATLAB/Simulink to illustrate the effectiveness of the proposed methods, and the simulations correspond with our theoretical analysis.

Fuzzy-logic-based adaptive event-triggered sliding mode control for spacecraft attitude tracking

The attitude tracking control problem for spacecraft with limited communication is investigated in this paper by employing event-triggered based sliding mode control theory. Considering model uncertainties and external disturbances, the attitude dynamics are developed on the special orthogonal group SO(3) directly, avoiding singularities and ambiguities associated with other attitude representations. Based on the developed model, a coordinate-free adaptive event-triggered sliding mode controller is proposed to ensure the closed-loop system to be uniformly ultimately bounded, in which an adaptive fuzzy logic system is utilized to compensate the disturbance. The control signal is only updated and transmitted at some discrete instants generated by the designed event-triggering strategy, such that the communication burden can be decreased significantly. Finally, the effectiveness of the designed control method is demonstrated by numerical examples.

Model-Free Event-Triggered Optimal Consensus Control of Multiple Euler-Lagrange Systems via Reinforcement Learning

This paper develops a model-free approach to solve the event-triggered optimal consensus of multiple Euler-Lagrange systems (MELSs) via reinforcement learning (RL). Firstly, an augmented system is constructed by defining a pre-compensator to circumvent the dependence on system dynamics. Secondly, the Hamilton-Jacobi-Bellman (HJB) equations are applied to the deduction of the model-free event-triggered optimal controller. Thirdly, we present a policy iteration (PI) algorithm derived from RL, which converges to the optimal policy. Then, the value function of each agent is represented through a neural network to realize the PI algorithm. Moreover, the gradient descent method is used to update the neural network only at a series of discrete event-triggered instants. The specific form of the event-triggered condition is then proposed, and it is guaranteed that the closed-loop augmented system under the event-triggered mechanism is uniformly ultimately bounded (UUB). Meanwhile, the Zeno behavior is also eliminated. Finally, the validity of this approach is verified by a simulation example.

Event-Triggered Tracking Control With Filtered Outputs and Impulsive Observers.

This article studies an event-triggered tracking control problem for linear systems subject to output feedback and disturbances, where a new configuration incorporating filtered outputs and impulsive observers is proposed. The transmissions in the sensor-to-controller and controller-to-actuator channels are scheduled by dynamic event-triggered control (ETC) mechanisms to save communication resources. To eliminate the effects of the derivatives of output noises on the tracking and transmission performance, a low-pass filter is introduced to preprocess the raw output signals. Both the filter state and raw output will be transmitted to the controller node while the latter is only utilized by an impulsive observer at some discrete instants. Then, it is proved that the proposed dynamic ETC schemes can solve the practical tracking control problem with fixed reference points and avoid Zeno behavior in both channels. Meanwhile, when some user-specified parameters in the event-triggering conditions are small enough, the tracking control problem can be solved asymptotically for disturbance-free systems. In addition, to further improve the transient performance, reduced-order impulsive observers and optimization of impulsive gain matrices are studied. Finally, simulation results are provided to illustrate the efficiency and feasibility of the obtained results.

Periodic event-triggered output regulation for linear multi-agent systems

This study considers the problem of periodic event-triggered (PET) cooperative output regulation for a class of linear multi-agent systems. The advantage of the PET output regulation is that the data transmission and triggered condition are only needed to be monitored at discrete sampling instants. It is assumed that only a small number of agents can have access to the system matrix and states of the leader. Meanwhile, the PET mechanism is considered not only in the communication between various agents, but also in the sensor-to-controller and controller-to-actuator transmission channels for each agent. The above problem set-up will bring some challenges to the controller design and stability analysis. Based on a novel PET distributed observer, a PET dynamic output feedback control method is developed for each follower. Compared with the existing works, our method can naturally exclude the Zeno behavior, and the inter-event time becomes multiples of the sampling period. Furthermore, for every follower, the minimum inter-event time can be determined a prior, and computed directly without the knowledge of the leader information. An example is given to verify and illustrate the effectiveness of the new design scheme.

Leader-following consensus for multi-agent systems with nonlinear dynamics subject to additive bounded disturbances and asynchronously sampled outputs

This paper is concerned with the leader-following consensus problem for a class of Lipschitz nonlinear multi-agent systems with uncertain dynamics, where each agent only transmits its noisy output, at discrete instants and independently from its neighbors. The proposed consensus protocol is based on a continuous-discrete time observer, which provides a continuous time estimation of the state of the neighbors from their discrete-time output measurements, together with a continuous control law. The stability of the multi-agent system is analyzed with a Lyapunov approach and the exponential practical convergence is ensured provided that the tuning parameters and the maximum allowable sampling period satisfy some inequalities. The proposed protocol is simulated on a multi-agent system whose dynamics are ruled by a Chua’s oscillator.

Adaptive Neural Network Model-based Event-triggered Attitude Tracking Control for Spacecraft

This article investigates the problem of attitude tracking control for spacecraft with limited communication, unknown system parameters, and external disturbances. An adaptive control scheme with an event-triggered mechanism (ETM) is proposed to alleviate the communication burden. Radial Basis Function Neural Network (RBFNN) estimation model is developed to provide the input signals for the control module in this control scheme. Estimated attitude information of the spacecraft generated from the estimation model will only be transmitted to the control module at the instants when the ETM is violated. The neural network (NN) and the estimation model will be updated complying with an adaptive algorithm at the discrete triggering instants. It’s substantiated that all the errors of attitude tracking converge towards corresponding residuals and there are no accumulated triggering instants. Numerical simulation also demonstrates the effectiveness of the proposed control method.

Efficient parametric estimation for a signal-plus-noise Gaussian model from discrete time observations

This paper deals with the parametric inference for integrated continuous time signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter ismultidimensional and compounded of a signal-of-interest parameter and a variance parameter of the noise.We state the consistency and the minimax efficiency of the maximum likelihood estimator and of the Bayesian estimator when the time of observation tends to infinity and the delays between two consecutive observations tend to 0 or are only bounded. The class of signals in consideration contains among others, almost periodic signals and also non-continuous periodic signals. However the problem of frequency estimation is not considered here. Furthermore, in this paper the signal-plus-noise discretely observed in time model is considered as a particular case of a more general model of independent Gaussian observations forming a triangular array.

Formation Tracking of Second-Order Multi-Agent Systems With Multiple Leaders Based on Sampled Data

This brief investigates formation tracking of second-order multi-agent systems with multiple leaders on a directed communication topology based on sampled data. Specifically, with communication among agents only occurring at discrete instants, a formation control protocol based on sampled information is proposed to reduce communication consumption. Then, a sufficient condition regarding the sampling period and the gain is derived to guarantee that the followers ultimately achieve the desired formation, the reference function of the followers is in the convex hull formed by the leaders, and the velocities of all agents asymptotically reach the desired one. Finally, simulations are presented to verify the effectiveness of the theoretical result.

Adaptive Event-Triggered Consensus of Multiagent Systems on Directed Graphs

This article systematically studies consensus of linear multiagent systems (MASs) on directed graphs through adaptive event-triggered control. It presents innovative adaptive event-triggered state-feedback protocols with novel composite event-triggering conditions. Two specific designs in terms of different event-triggering conditions and laws of adaption are first discussed for linear MASs on strongly connected directed graphs, which are then extended to general directed graphs that contain a spanning tree. Moreover, another adaptive event-triggered protocol is proposed for solving leader-follower consensus that tracks a leader of a bounded control input. The protocols inherit the merits of both adaptive control and event-triggered control: the protocols can be implemented in a fully distributed way, since the Laplacian is avoided in design, and each agent only needs to know the relative information between neighbors at discrete instants determined by event-triggering conditions. Compared with the existing related results, the proposed protocols are applicable for linear MASs on general directed graphs, and moreover, the time-dependent term in the event-triggering conditions is allowed to be a class of positive L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> functions. Two numerical examples clearly verify the effectiveness of the proposed protocols.

Leader-following synchronization of complex dynamic networks via event-triggered impulsive control

This paper deals with the synchronization of complex dynamical networks. Based on the idea of event-trigger and impulsive control theory, an event-based impulsive control strategy is proposed to achieve synchronization of leader–follower coupled dynamical networks, where a class of forced impulse sequence is introduced to promote the synchronization. Moreover, the possible accumulations of event-times (i.e., Zeno behaviour) in control strategy can be excluded. Unlike classical event-triggered control that involve control inputs incessantly based on the sampled information in last event-triggered instant, the proposed control inputs are only carried out at some discrete event-triggered instants. In other words, it is not necessary to activate the sensor and control computation and/or communication between leader and followers when the controls do not need attention. The proposed event-triggered conditions in control strategy can be derived by solving linear matrix inequalities (LMIs). Finally, a chaotic neural network is discussed to illustrate the application of our proposed results.

Robust formation control under state constraints of multi-agent systems in clustered networks

This paper studies the formation control problem in clustered network systems composing of linear agents that are subjected to state constraints. In each cluster, there exists an agent called a leader who can communicate with other leaders outside of its cluster at some specific discrete instants. Moreover, the continuous-time communication structure in each cluster is represented by a fixed and undirected graph. A robust formation control protocol is proposed to deal with the hybrid communication described above and the constraints on states of agents. It is next shown that the hybrid robust formation control design for clustered multi-agent networks can be indirectly solved through the robust stabilization design of an equivalent system obtained by matrix theory and algebraic graph theory. Then, a robust controller is designed for the initial clustered network system in terms of linear matrix inequalities. Finally, a formation design for unmanned aerial vehicles is carried out and simulated to illustrate the effectiveness of the proposed hybrid formation control design method.

Set‐point output tracking problem for linear plants via periodic event‐triggered control

This study addresses event-triggered tracking control for linear systems with constant reference signals and disturbances. A remote observer-based proportional–integral controller, which communicates with the plant only at some discrete instants, is designed. The transmissions, involving both the sensor-to-controller and the controller-to-actuator channels, are scheduled by periodic event-triggered control. A new kind of summation-based triggering condition is proposed which can ensure that there exists a positive minimum inter-event time uniformly for a family of controllers parameterised by the verification periods. Then, it is proved that the proposed periodic event-triggered control can solve the set-point tracking problem asymptotically without the assumption that the reference signal is accessible to the sensor. Finally, simulation results are provided to illustrate the efficiency and feasibility of the obtained results.

Sampled-data scaled group consensus for second-order multi-agent systems with switching topologies and random link failures

This article studies the sampled-data scaled group consensus problem for second-order multi-agent systems with switching topologies and random link failures. It is assumed that each agent only interacts with its neighbors at discrete sampling instants rather than the complete continuous process. It is further assumed that the phenomenon of random link failures on the communication links is characterized by a Bernoulli stochastic variable. By supposing that each agent has a unique scale, a distributed control protocol that uses the sampled position information of the neighbors is designed. With the assistance of hybrid tools including graph theory and matrix theory, a sufficient condition based on the structures of topologies, the time-varying sampling periods, and the gain parameter, is established to ensure the asymptotic convergence of the agents under the action of sampled distributed protocol. Finally, some simulation instances are provided to verify our theoretical finding.

An Intelligent Monitoring System for Execution of Machine Engineering Processes

An integral part of the production system is monitoring technological process. This paper proposes assessment procedures for the characteristics of process operations, making it possible to track both the failure rate of each machine and the entire system at each stage of the technological process. A process simulation model is built, describing technological processes of various durations and sets of operations, which is based on Markov modeling, when the number of different system states is finite, and variations in the system states occur at different discrete instants of time. The initial formation of a set of contingency factors in the production system is based on the Delphi approach. Using the Pareto principle makes it possible to identify the most common factors of process failures. The neural network makes it possible to simulate various situations and evaluate the probability of process violation. The procedure for the formation of a matrix of transition probabilities is proposed for both the initial assessment of the process feasibility and matrices varying discretely in time, depending on the process operation state. Based on the proposed methods, an intelligent monitoring system for machine engineering process execution is developed.

Distributed Event-triggered Consensus Control for Heterogeneous Multi-agent Systems under Fixed and Switching Topologies

This paper investigates the distributed consensus problem for heterogeneous multi-agent systems via event-triggered scheme. To alleviate the communication burden, a distributed event-triggered consensus algorithm using an open-loop estimate and neighboring information is proposed. In the proposed event-triggered scheme, the control input of each agent is dependent on the estimate and information at discrete instants. Firstly, the novel event-triggered consensus algorithm is proposed for fixed topology, which involves the discrete communication between neighboring agents. Then, for the switching topology, the triggering condition is proposed by virtue of a topology-dependent dwell time approach. Further, the corresponding consensus procedures are given. Finally, the effectiveness of the proposed scheme is illustrated by numerical results.

Cooperative containment for second-order multi-agent systems with asynchronous setting and random link failures

The issue of cooperative containment control in second-order multi-agent systems with asynchronous setting and random link failures is examined in this paper. Asynchronous setting implies that each agent uses its neighbors’ information to update the state independently at certain discrete instants. The phenomenon of random link failure on each communication link is characterized by a Bernoulli stochastic variable. An asynchronous distributed protocol is designed by randomly measuring the position information of the previous one or two steps of the neighbors. Matrix theory and the composition of binary relation are explored to handle the containment control problem with both asynchronous setting and random link failures. Under a loose parameter selection strategy, a necessary and sufficient condition in terms of the topology structure can be established. A numerical example is finally provided to validate the theoretical result.

Integrating AGC to Generation Scheduling for Real-Time Operational Optimization

This work proposes a new real-time operational framework for electric grids. This framework is based on converting generation scheduling optimization, which is conventionally triggered only in discrete instants of time, into a closed-loop control-based problem that automatically adjusts the generator power outputs constantly as system conditions change. However, maintaining frequency deviations within acceptable levels solely by the control-based generation scheduler is not sufficient. Therefore, to ensure adequately fast action, automatic generation control (AGC) is still needed. This work aims to provide a novel integrative approach that combines AGC and control-based generation scheduling into one framework. Simulation results show the efficacy of the proposed integrative framework in achieving effective frequency regulation while operating the system optimally in real time.