Event-triggered asynchronous periodic distributed secondary control of microgrids under DoS attacks

A novel distributed secondary voltage and frequency control strategy is proposed with the Zeno-free event-triggered scheme for an island alternating current (AC) microgrid under Denial-of-Service (DoS) attacks. A DoS attack compensation mechanism and an event-triggered mechanism on the basis of the checking scheme are developed. Then, a secure event-checked based event-triggered secondary control method is explored to guarantee the tracking performance of the microgrid under DoS attacks. Further, some linear matrix inequalities (LMIs)-based sufficient conditions are derived to design the controller. What’s more, the proposed asynchronous periodic triggering method can efficiently save communication resources and further reduce the update number of the controller. Finally, the efficiency of this work is verified by an islanded AC microgrid with comparisons.     

Resilient sampled-data control design for singular networked systems with random missing data

This paper proposes an active resilient control strategy for singular networked control systems with external disturbances and missing data scenario based on sampled-data scheme. To characterize the missing data scenario, a stochastic variable satisfying Bernoulli distributed white sequence is introduced. Based on this scenario, in this paper, two different models are proposed. For both the models, by using Lyapunov–Krasovskii functional approach, which fully uses the available information about the actual sampling pattern, some sufficient conditions in terms of linear matrix inequalities (LMIs) are separately obtained to guarantee that the resulting closed-loop system is admissible and strictly dissipative with a prescribed performance index. In particular, Jensen’s and Wirtinger based integral inequalities are employed to simplify the integral terms which appeared in the derivation of stabilization results. Then, if the obtained LMIs are feasible, the corresponding parameters of the designed resilient sampled-data controller are determined. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed control design technique.     

Constrained load/frequency control problems in networked multi-area power systems

In this paper, we present a supervisory discrete-time predictive control strategy for load/frequency control problems in networked multi-area power systems subject to coordination constraints. Coordination between the control center and the spatially distributed areas is accomplished via data networks subject to communication latency modeled by time-varying time-delay. The aim here is finding supervising strategies able to reconfigure, whenever necessary in response to unexpected load changes and/or faults, the nominal set-points on frequency and generated power to the generators of each area so that viable evolutions would arise for the overall power system and a new sustainable equilibrium is reached. In order to demonstrate the effectiveness of the strategy, examples on a four-area power system are presented.     

Distributed state estimation and fault diagnosis using reduced sensitivity to neighbor estimates with application to building control

This paper proposes solutions that reduce the inaccuracy of distributed state estimation and consequent performance deterioration of distributed model predictive control caused by faults and inaccurate models. A distributed state estimation method for large-scale systems is introduced. A local state estimation approach considers the uncertainty of neighbor estimates, which can improve the state estimation accuracy, whereas it keeps a low network communication burden. The method also incorporates the uncertainty of model parameters which improves the performance when using simplified models. The proposed method is extended with multiple models and estimates the probability of nominal and fault behavior models, which creates a distributed fault detection and diagnosis method. An example with application to the building heating control demonstrates that the proposed algorithm provides accurate state estimates to a controller and detects local or global faults while using simplified models.     

Safety control using barrier certificates for multiagent systems with input saturation and formation constraints

Maintaining the given operational area is critical in guaranteeing the safety of nonlinear second-order multiple autonomous agents. The properties of multiagent systems and several physical constraints, including bounded modeling error and actuator saturation, dramatically affect the maneuverability of multiagent systems inside the specified operational area. Moreover, the existing safety control algorithms heavily rely on the boundaries of the operational area. To overcome this issue, by constructing a novel scalable control technique, the safety area for multiagent systems can be transformed into input-constrained control barriers along each coordinate of motion for agents. It is shown that the safety of each agent and the global asymptotic stability are guaranteed under the proposed distributed control algorithm. The asymmetrical closed-form scheme for the agent's safety rule is built by applying the adjustable low and high bounds of the control signals associated with the actual control inputs, which are repeatedly computed by using new local measurements as the agents move, and the saturated control inputs with asymmetrical constraints are ensured. The absolute values of the modeling errors and external disturbances can be tracked by the proposed safety controller. Super-twisting control (STC) is employed to address the formation constraint problem of multiagent systems, where the effect that arises from uncertain nonlinear complexity of the agents and external disturbances is eliminated. Moreover, finite-time convergence, a desirable robust behavior of multiagent systems, and the formation constraint are simultaneously achieved. Furthermore, the stability of the proposed integrated control strategy for multiagent systems is analyzed, which reveals that the proposed distributed safety control can seamlessly integrate with the robust control protocol with minimum modification under the directed information interaction topology. Safety formation control calibration and tuning are carried out, and comparative simulation results are provided to illustrate the effective performance of the obtained theoretical results.     

Resilient distributed MPC for systems under synchronous round-robin scheduling

This paper is concerned with the resilient dynamic output-feedback (DOF) distributed model predictive control (DMPC) problem for discrete-time polytopic uncertain systems under synchronous Round-Robin (RR) scheduling. In order to alleviate the computation burden and improve the system robustness against uncertainties, the global system is decomposed into several subsystems, where each subsystem under synchronous RR scheduling communicates with each other via a network. The RR scheduling is adopted to avoid data collisions, however the updating information at each time instant is unfortunately reduced, and the underlying RR scheduling of subsystems are deeply coupled. The main purpose of this paper is to design a set of resilient DOF-based DMPC controllers for systems under the consideration of polytopic uncertainties and synchronous RR scheduling, such that the desirable performance can be obtained at a low cost of computational time. A novel distributed performance index dependent of the synchronous RR scheduling is constructed, where the last iteration information from the neighbor subsystems is used to deal with various couplings. Then, by resorting to the distributed RR-dependent Lyapunov-like approach and inequality analysis technique, a certain upper bound of the objective is put forward to establish a solvable auxiliary optimization problem (AOP). Moreover, by using the Jacobi iteration algorithm to solve such a problem online, the distributed feedback gains are directly obtained to guarantee the convergence of system states. Finally, two examples including a distillation process example and a numerical example are employed to show the effectiveness of the proposed resilient DMPC strategy.     

Dynamic event-triggered output consensus of nonstrict-feedback MASs with predefined performance

This paper deals with the output consensus problem for uncertain nonstrict-feedback leader-follower multi-agent systems with predefined performance. A distributed event-triggered control strategy with dynamic threshold is proposed to update the actual control input and alleviate the computation burden of the communication procedure effectively. The unknown nonstrict-feedback structures are addressed by using the property of radial basis function neural networks. It is worth noting that in practical applications, the predefined performance often alternates between constrained and unconstrained cases in some extreme situations. To overcome this challenge, a novel coordinate transformation technique is incorporated to tackle both the two cases with and without performance constraint in a unified manner. As a result, the proposed event-triggered control approach ensures that the output consensus errors converge to zero asymptotically, and all the signals in the closed-loop system are bounded. Finally, the effectiveness of the proposed protocol is demonstrated by the simulation results.     

Population extremal optimization-based extended distributed model predictive load frequency control of multi-area interconnected power systems

How to design a set of optimal distributed load frequency controllers for a multi-area interconnected power system is an important but still challenging issue in the field of modern electric power systems. This paper presents an adaptive population extremal optimization-based extended distributed model predictive load frequency control method called PEO-EDMPC for a multi-area interconnected power system. The key idea behind the proposed method is formulating the dynamic load frequency control issue of each area power system as an extended distributed discrete-time state-space model based on an extended state vector, obtaining a distributed dynamic extended predictive model, and rolling optimization of real-time control output signal by adopting an adaptive population extremal optimization algorithm, where the fitness is evaluated by the weighted sum of square predicted errors and square future control values. The superiority of the proposed PEO-EDMPC method to a traditional distributed model predictive control method, a population extremal optimization-based distributed proportional-integral control algorithm and a traditional distributed integral control method is demonstrated by the simulation studies on two-area and three-area interconnected power systems in cases of normal, perturbed system parameters and dynamical load disturbances.     

Fixed-time leader-following consensus of multiple uncertain nonholonomic systems: An adaptive distributed observer approach

This paper discusses the fixed-time leader-following consensus problem for multiple uncertain nonholonomic systems, which are widely used in engineering models. According to our literature review, either the system is assumed to be known, or the uncertainty only contains state information, which does not meet the actual requirements. For this reason, this paper investigates more general nonholonomic systems with uncertainties driven by inputs and states. First, a fixed-time adaptive distributed observer is proposed to estimate the leader’s state and structural parameters, which ensures that the estimation errors converge to zero within a fixed time. Second, two regulator equations based on the idea of cooperative output regulation are constructed, and a novel observer-based distributed switching control law is proposed. This control law overcomes the nonholonomic constraints and appropriately relaxes the assumptions of uncertain functions in the existing references. Finally, the simulation results verify the effectiveness of the proposed control scheme.     

Optimal design for manipulation of random consensus over discrete information in networked systems

In distributed and cooperative systems, the network structure is determinant to the success of the strategy adopted to solve complex tasks. Those systems are primarily governed by consensus protocols whose convergence is intrinsically dependent on the network topology. Most of the consensus algorithms deal with continuous values and perform average-based strategies to reach cohesion over the exchanged information. However, many problems demand distributed consensus over countable values, that cannot be handled by traditional protocols. In such a context, this work presents an approach based on semidefinite programming to design the optimal weights of a network adjacency matrix, in order to control the convergence of a distributed random consensus protocol for variables at the discrete-space domain, based on the voter model. As a second contribution, this work uses Markov theory and the biological inspiration of epidemics to find out a dynamical spreading model that can predict the information diffusion over this discrete consensus protocol. Also, convergence properties and equilibrium points of the proposed model are presented regarding the network topology. Finally, extensive numerical simulations evaluate the effectiveness of the proposed consensus algorithm, its spreading model, and the approach for optimal weight design.     

A T-S fuzzy state observer-based model predictive reset control for a class of fuzzy nonlinear systems with event-triggered mechanism

In this study, the problem of observer-based control for a class of nonlinear systems using Takagi-Sugeno (T-S) fuzzy models is investigated. The observer-based model predictive event-triggered fuzzy reset controller is constructed by a T-S fuzzy state observer, an event-triggered fuzzy reset controller, and a model predictive mechanism. First, the proposed controller utilizes the T-S fuzzy model and is constructed based on state observations and discrete sampling output, which can greatly reduce the occupation of communication resources. Then, the model predictive strategy for reset law design is designed in this paper. With a reasonable reset of the controller state at certain instants, the performance of the reset control systems is improved. Finally, the validity of the proposed method is illustrated by simulation. The merits of the proposed controller in improving transient performance and reducing the communication occupation are demonstrated by comparing its results with the output feedback fuzzy controller and the first-order fuzzy reset controller.     

Corresponding drivability control and energy control strategy in uninterrupted multi-speed mining trucks

An hybrid uninterrupted multi-speed transmission (HUMST), based on the integration of a planetary gear set and a 3-speed automatic manual transmission (3-AMT), is developed to satisfy the specific performance indexes of mining trucks. The power-split device can alleviate and eliminate the inherent torque interruption of the 3-AMT during gear shift by implementing the designed cooperative shift control strategy which is optimized by quadratic performance index. In order to achieve fast torque coordination while guaranteeing the driving comfort performance, the torque profiles of the power split device and the traction motor are optimized by Linear-quadratic regulator (LQR) algorithm. Dynamic programming (DP) is implemented as a benchmark to demonstrate the maximum fuel efficiency of the proposed HUMST. Because of the high computational cost of optimal control strategies such as DP, an improved real-time control strategy (IRTCS) using modified Gaussian distribution function is proposed to significantly reduce the computing load. As efficiency-oriented energy control strategy would result in frequent gear shifts, to achieve a desirable tradeoff between the overall efficiency and the shift stability, multi-objective genetic algorithm (MGA) is integrated to optimize the overall performance. The detail mathematical and dynamic model shows that the proposed shifting strategy with LQR can effectively suppress shift jerk, and the proposed IRTCS with MGA can reduce shift frequency by 70.78% to improve the drivability, only sacrificing 4.86% of overall efficiency compared to that of DP.     

Connectivity-preserving approximation-free design for synchronized tracking of uncertain networked nonaffine nonlinear multi-agent systems

This paper presents a connectivity-preserving approximation-free design strategy for the distributed synchronized tracking of uncertain nonlinear multi-agent systems with limited communication ranges. All nonaffine nonlinearities in pure-feedback form are assumed to be unknown. The main contribution of this paper is to achieve approximation-free synchronized tracking while preserving the initial interaction patterns among agents. To this end, each synchronization error term is individually transformed to a nonlinear error function with a predefined time-varying function. The local tracking laws using only the relative output information among agents are designed via these nonlinear error terms. The connectivity preservation and preassigned tracking performance of the proposed synchronized tracking system are recursively analyzed in the Lyapunov sense, without employing any function approximators and potential functions. Finally, the effectiveness and robustness of the proposed strategy are demonstrated through simulation examples.     

Design of a model-free adaptive sliding mode control to synchronize chaotic fractional-order systems with input saturation: An application in secure communications

In this work, a model-free adaptive sliding mode control (ASMC) methodology is proposed for synchronization of chaotic fractional-order systems (FOSs) with input saturation. Based on the frequency distributed model and the non-integer version of the Lyapunov stability theorem, a model-free ASMC method is designed to overcome the chaotic behavior of the FOSs. The control inputs are free from the nonlinear-linear dynamical terms of the system because of utilizing the boundedness feature of the states of chaotic FOSs. Moreover, a new medical image encryption scheme is tentatively proposed according to our synchronization method, and its effectiveness is verified by numerical simulations. Furthermore, the performance and security analyses are given to confirm the superiority of the proposed encryption scheme, including statistical analysis, key space analysis, differential attack analysis, and time performance analysis.     

A fully distributed approach for consensus of multi-agent systems under multiple state-variables-dependent interaction topologies

In this paper, the consensus problem of multi-agent systems with general linear dynamics is studied. Motivated by the MIMO communication technique, a general framework is considered in which different state variables are exchanged in different independent interaction topologies. This novel framework could improve the control system design flexibility and potentially improve the system performance. Fully distributed consensus control laws are proposed and analyzed for the settings of fixed and switching multiple topologies. The control law can be applied using only local information. And the control gain can be designed depending on the dynamics of the individual agent. By transforming the overall multi-agent systems into cascade systems, necessary and sufficient conditions are provided to guarantee the consensus of the overall systems under fixed and switching state variable dependent topologies, respectively. Two simulation examples are provided to illustrate the effectiveness of the proposed theoretical results.     

Finite-horizon H∞-consensus control for multi-agent systems with random parameters: The local condition case

This paper is concerned with the distributed H_∞-consensus control problem over the finite horizon for a class of discrete time-varying multi-agent systems with random parameters. First, by utilizing the proposed information matrix, a new formula is established to calculate the weighted covariance matrix of random matrix. Next, by allowing every agent to track the average of the neighbor agents, a novel local H_∞-consensus performance constraint is presented to cater to the local performance analysis. Then, by means of the proposed definition of the stochastic vector dissipativity-like over the finite horizon, a set of sufficient conditions for every agent is obtained such that the controlled outputs of the closed-loop multi-agent systems satisfy the proposed H_∞-consensus performance constraint. As a result, the proposed consensus control algorithm can be executed on each agent in an indeed distributed manner. Finally, a simulation example is employed to verify the effectiveness of the proposed algorithm.     

Q-learning solution for optimal consensus control of discrete-time multiagent systems using reinforcement learning

This paper investigates a Q-learning scheme for the optimal consensus control of discrete-time multiagent systems. The Q-learning algorithm is conducted by reinforcement learning (RL) using system data instead of system dynamics information. In the multiagent systems, the agents are interacted with each other and at least one agent can communicate with the leader directly, which is described by an algebraic graph structure. The objective is to make all the agents achieve synchronization with leader and make the performance indices reach Nash equilibrium. On one hand, the solutions of the optimal consensus control for multiagent systems are acquired by solving the coupled Hamilton–Jacobi–Bellman (HJB) equation. However, it is difficult to get analytical solutions directly of the discrete-time HJB equation. On the other hand, accurate mathematical models of most systems in real world are hard to be obtained. To overcome these difficulties, Q-learning algorithm is developed using system data rather than the accurate system model. We formulate performance index and corresponding Bellman equation of each agent i. Then, the Q-function Bellman equation is acquired on the basis of Q-function. Policy iteration is adopted to calculate the optimal control iteratively, and least square (LS) method is employed to motivate the implementation process. Stability analysis of proposed Q-learning algorithm for multiagent systems by policy iteration is given. Two simulation examples are experimented to verify the effectiveness of the proposed scheme.     

Moments generating function of the harmonic mean of two non-identical gamma random variables and its applications in wireless communications

In this paper, a closed-form expression for the moments generating function of the half-harmonic mean of two independent, not necessarily identically distributed gamma random variables with arbitrary parameters is presented. This statistical result is useful to the performance analysis of dual-hop wireless communication systems with amplify-and-forward relays in a Nakagami-m fading environment. The proposed mathematical analysis is substantiated by various numerically evaluated and computer simulation results.     

Observer-based event-triggered sliding mode control for delayed systems with unknown disturbances

This paper develops the observer-based event-triggered sliding mode control strategy for delayed systems involving unknown disturbances. This strategy comprises a triggering rule which can effectively save resources and an observer-based control law which can drive the states of delayed systems into the practical sliding mode band in some finite time. Some sufficient conditions coupled with this control strategy are proposed to guarantee the robust performance of the delayed systems. Significant outcome of this strategy is that it can be applied to the case in which the disturbances are unmeasured or unknown. Finally, two numerical examples and its simulations are presented to show the performance of the systems and effectiveness of this control strategy.     

An improved passivity-based control strategy for providing an accurate coordination in a AC/DC hybrid microgrid

This paper proposes an improved passivity-based control (PBC) technique to provide accurate coordination between AC and DC sides of a grid-tied AC/DC hybrid microgrid. The proposed PBC is based on the passive properties of the system and the energy exchange between the subsystems. To this end, three mathematical formulations for the converters are driven in the first step. Then, using the formulations, the impedance injection is applied to shape the error dynamics of all DC/DC and DC/AC converters. The DC link-connected DC/AC converter is used to help the AC side for maintenance of the power quality factors such as, the grid frequency and voltage magnitude in the presence of any unbalanced power load sharing. The first contribution of the paper is the part of impedance injection to the DC/AC converter, which aims to provide more decoupling and faster convergence rate for both the steady states and the dynamical conditions. Secondly, a Lyapunov function is defined for converters’ error dynamics that provide more accurate statement of the proposed damping injections. Besides, as an attractive control feature, decoupling properties of the suggested method are investigated. Then, through achieving several curves, various operating conditions of DC/DC and DC/AC converters under varying the system errors and proposed damping injections are evaluated as well. For the purpose of validation, the system under study is simulated in the MATLAB/SIMULINK software package against a variety of system errors and converters’ operational conditions.