Error Dynamic System Research Articles

Control and Function Projective Synchronization of 3D Chaotic System

In this paper, we study a linear feedback control to dampen the chaotic behavior of a 3D dynamic system. Based on the Routh-Hurwitz criterion, the conditions are determined to achieve control. Furthermore, function projective synchronization (FPS) between two identical 3D chaotic systems is demonstrated. The proof of asymptotic stability of solutions for the error dynamical system depends on the negative eigenvalues of the system. Additionally, numerical simulations are utilized to demonstrate the impact and effectiveness of the proposed methods.

Distributed optimal consensus control for discrete-time multi-agent systems with composite switching topologies via an iterative Q-learning method

This paper aims to achieve distributed optimal consensus control for discrete-time multi-agent systems (MASs) under composite switching topologies through utilising the iterative Q-learning approach. First, the optimal consensus control strategy, independent of system dynamics information, is developed by using the designed iterative Q-learning approach to guarantee that all follower states can synchronise to the desired trajectory formulated by the leader. Compared with the invariable algebraic or edge-fixed topology structures, the designed Q-learning control algorithm in this paper is implemented based on the composite switching topologies consisting of periodic and stochastic mechanisms. Then, an error dynamic system is established, which transforms the optimal consensus control issue into an optimal regulation issue and removes the influence of the two types of switching topologies. To conquer the problems of lack of model information and the inaccessible analytical solution of Hamilton-Jacobi-Isaacs (HJI) equation, an iterative Q-learning approach is designed according to the reconstructed Q-function Bellman equation. Through further iterative learning, the optimal control strategy can be acquired so as to realise consensus control and ensure the stability of the closed-loop systems. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed distributed optimal control scheme.

Human-in-the-Loop Consensus Control for Multiagent Systems With External Disturbances.

In this article, the human-in-the-loop leader-follower consensus control problem is addressed for multiagent systems (MASs) with unknown external disturbances. A human operator is deployed to monitor the MASs' team by transmitting an execution signal to a nonautonomous leader in response to any hazard detected, with the control input of the leader unknown to all followers. For each follower, a full-order observer, in which the observer error dynamic system decouples the unknown disturbance input, is designed for asymptotic state estimation. Then, an interval observer is constructed for the consensus error dynamic system, where the unknown disturbances and control inputs of its neighbors and its disturbance are treated as unknown inputs (UIs). To process the UIs, a new asymptotic algebraic UI reconstruction (UIR) scheme is proposed based on the interval observer, and one of the significant features of the UIR is the capacity to decouple the control input of the follower. The subsequent human-in-the-loop asymptotic convergence consensus protocol is developed by applying an observer-based distributed control strategy. Finally, the proposed control scheme is validated through two simulation examples.

Distributed State Observer for Systems with Multiple Sensors under Time-Delay Information Exchange.

The issues of state estimations based on distributed observers for linear time-invariant (LTI) systems with multiple sensors are discussed in this paper. We deal with the scenario when the information exchange has known time delays, and aim at designing a distributed observer for each subsystem such that each distributed observer can estimate the system state asymptotically by rejecting the time delay. To begin with, by rewriting the target system in a connecting form, a subsystem which is affected by the time-delay states of other nodes is established. And then, for this subsystem, a distributed observer with time delay is constructed. Moreover, an equivalent state transformation is made for the observer error dynamic system based on the observable canonic decomposition theorem. Further, in order to ensure that the distributed observer error dynamic system is asymptotically stable even if there exists a time delay, a linear matrix inequality (LMI) which is relative to the Laplace matrix is elaborately set up, and a special Lyapunov function candidate based on the LMI is considered. Next, based on the Lyapunov function and Lyapunov stability theory, we prove that the error dynamic system of the distributed observer is asymptotically stable, and the observer gain is determined by a feasible solution of the LMI. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Geometric tracking control of a multi‐rotor UAV for partially known trajectories

AbstractThis article presents a trajectory‐tracking controller for multi‐rotor unmanned aerial vehicles (UAVs) in scenarios where only the desired position and heading are known without the higher‐order derivatives. The proposed solution modifies the state‐of‐the‐art geometric controller, effectively addressing challenges related to the non‐existence of the desired attitude and ensuring positive total thrust input for all time. We tackle the additional challenge of the non‐availability of the higher derivatives of the trajectory by introducing novel nonlinear filter structures. We formalize theoretically the effect of these filter structures on the system error dynamics. Subsequently, through a rigorous theoretical analysis, we demonstrate that the proposed controller leads to uniformly ultimately bounded system error dynamics. To demonstrate the controller's effectiveness and potential to enhance multi‐rotor performance and reliability in practical applications, we present a simulation study considering two examples with time‐varying trajectories.

Protocol-based state estimation of two-time-scale complex networks with nonhomogeneous sojourn probabilities

This paper is dedicated to researching the problem of the state estimation for two-time-scale complex networks (TTSCNs) subject to sojourn probabilities (SPs) under channel fadings and false data injection attacks (FDIAs). The network’s switching topology is governed by a novel switching law that incorporates time-varying SPs, with the variation of SPs being regulated through a persistent dwell-time (PDT) switching signal. Meanwhile, for the sake of achieving energy savings and mitigating data congestion, the dynamic probabilistic event-triggered weighted try-once-discard (DPEWTOD) policy is innovatively developed by integrating with the major merits of the dynamic probabilistic event-triggered mechanism (DPETM) and WTOD protocol (WTODP) based on hybrid compensation. Different from the traditional communication rules, this DPEWTOD concept not only captures stochastic behavior of the dynamic triggering threshold (DTT), but also enables a compensatory measurement that closely approximates the actual value. Subsequently, we construct time delay-, DTT-, and PDT-dependent Lyapunov functionals to analyze the stability of error dynamic systems in the presence of fading and malicious FDIAs. By employing a separation technique, our proposed solving algorithm transforms non-convex analysis conditions into tractable ones. Eventually, the rationality and effectiveness of the proposed method are demonstrated by an resistance–capacitance (RC) circuit example.

Active suspension hierarchical control with parameter uncertainty and external disturbance of electro-hydraulic actuators

In order to improve the ride comfort and handling stability of the electro-hydraulic active suspension system, a hierarchical control strategy is proposed. For the active suspension system with body mass uncertainty and safety constraints, an enhanced constraint adaptive backstepping controller is designed to generate the target force of body vertical motion. When dealing with constraints, nonlinear filters are introduced, backstepping technology and quadratic Lyapunov function are used to combine the control target and domain constraints, and the vertical displacement of the body and the suspension deflection control index are synthesized into a single controlled variable, so that the control variable converging to zero meets the suspension dynamic displacement limit. The ride comfort and safety of the active suspension system are improved. Secondly, stability analysis is conducted on the zero dynamic error system to ensure that all safety performance indicators are bounded. The effects of external disturbances, parameter uncertainties and modelling errors on the force tracking accuracy of asymmetric cylinder electrohydraulic systems are addressed. A backstepping dynamic surface control method based on a nonlinear perturbation observer is proposed, which estimates the composite perturbation terms such as modelling error and external perturbation, and uses the estimated value of the nonlinear observer to design a feedforward compensating control term to offset the effect of the composite perturbation on the system performance. In addition, the dynamic surface control method is used to calculate the derivative of the target force input, which avoids the derivative explosion phenomenon and reduces the computational complexity of the system. Simulation test results show that this method reduces the computational complexity of the system and improves the control performance. And under random and bumpy road conditions, the root-mean-square value of sprung mass acceleration performance index is reduced by 48.354 % and 72.677 % compared with passive suspension, which improves the ride comfort of the vehicle.

Distributed optimization for discrete time‐varying linear multi‐agent systems with event‐triggered communication

AbstractThis paper studies the distributed optimization problem (DOP) of discrete time‐varying linear multi‐agent systems (MASs), in which the global objective function is formed by a sum of local convex objective functions. Firstly, a DOP with discrete time‐varying MASs is considered, in which the time‐varying linear matrix satisfies a certain equality constraint. To solve this problem, a novel discrete‐time distributed optimization algorithm (DOA) with event‐triggered communication mechanism (ETCM) is proposed. Secondly, by constructing the error dynamical system and using a series of inequality techniques, some sufficient conditions for achieving consensus and obtaining the optimal solution are established. It is found that the considered MAS has generality and the proposed DOA has the advantage of reducing communication burden. Finally, a numerical simulation is presented to verify the validity of theoretical results.

Distributed interval estimation for sensor networks with energy-limited attacks and stochastic communication protocols

In this paper, the problem of the distributed interval estimation is investigated for wireless sensor networks under the energy-limited attack and the stochastic communication protocol (SCP). A model with randomness and restrictions is constructed to describe the energy-limited attack, which is considered to occur in two positions, one is the transmission process of sensors and local estimators (LEs), and another is the transmission process of LEs and their neighbor nodes. Furthermore, to mitigate the communication burden, the SCP is adopted to distribute network access rights to sensor nodes. All in all, the objective of this paper is to develop a distributed interval estimator (DIE) which can use local and neighbor information to generate an interval that covers all potential estimation states when SCP, bounded noises, and energy-limited attacks are all present at the same time. To achieve this, the positive system theory and the stability analysis theory are used to obtain some sufficient conditions for the error dynamic system to be positive system and stable, and the needed DIE gains are achieved by solving the linear matrix inequality. Finally, an example is presented to demonstrate the effectiveness and superiority of the offered method.

Design of event-triggered natural second-order observers for second-order vector systems

The problem of designing event-triggered natural second-order state observers for second-order vector systems subject to external disturbances is considered in this paper. In this work, state observer is constructed using discrete measurements at instants when an event-triggered condition is satisfied. Due to the errors that arise by using the event-triggered mechanism and the external disturbance, the method in this paper only robustly estimates the state position and the state velocity of the second-order vector observers instead of estimating them asymptotically. Instead of using the method based on a parameter-dependent Lyapunov function in investigating the stability of the dynamic error system of natural second-order observers, a convex optimization problem is established in this paper to give an event-triggered mechanism and minimized levels in evaluating the boundedness of the dynamic error system of the event-triggered natural second-order observers. An automobile suspension and two numerical examples demonstrate the effectiveness of the proposed method.

Discrete Impulsive Signal Observer for Fractional-Order Control Systems and Its Consumer Electronic Circuit Application

In the process of actual electronic equipment signal transmission, interference is inevitable. How to accurately estimate the device status to ensure valid signal travelling is very meaningful. This paper mainly investigates a new transmission signal estimation strategy for fractional order control systems with unknown inputs. Compared with integer order modeling, fractional order modeling can better describe and report the essential process of system signal transmission. By using the fractional order output derivative-based method and convex optimization technique, an effective discrete-time impulsive observer design algorithm is proposed to stabilize the error dynamic systems. Especially, the resulting criterion reflects well the relationship between the fractional order and the pulse signal, and then is applied on a fractional order electronic circuit. It implies that the given conclusions are of significance in signal estimation.

Exponential synchronisation for delayed Clifford-valued coupled switched neural networks via static event-triggering rule

In the paper, the exponential synchronisation for delayed Clifford-valued coupled switched neural networks via static event-triggering rule is studied. Firstly, the drive-response systems for delayed Clifford-valued coupled neural network models are established. So as to avoid the non-commutativity issue of Clifford number multiplication, the original n-dimensional Clifford-valued models are decomposed into 2 m n -dimensional real-valued models. On this basis, the error dynamics system is constructed, and then some new sufficient conditions are presented of the exponential synchronisation for the considered neural network models by using Lyapunov–Krasovskii (L-K) functional approach and the technique of linear matrix inequality. Finally, the effectiveness of the results are verified by numerical simulations.

Neuroadaptive Output-Feedback Tracking Control for Stochastic Nonlower Triangular Nonlinear Systems With Dead-Zone Input.

For stochastic nonlower triangular nonlinear systems subject to dead-zone input, a neuroadaptive tracking control frame is constructed by applying the dynamic surface technique with a state observer in this work. Its primary contribution lies in extending the stability criteria to encompass stochastic nonlinear systems characterized by nonlower triangular structures and unmeasured states. The control strategy is delineated as follows. First, the state observer is designed to address the issue of unmeasured states, thereby facilitating the generation of an error dynamics system for subsequent analysis. Second, within the backstepping design framework, a neural network-based tracking controller is devised using dynamic surface control technique and variable separation approaches, ensuring system performance despite the presence of unmeasured states. Finally, stability analysis is conducted to guarantee that all the system signals remain bounded. Simulation examples are presented to illustrate the validity and practicality of the framework.

Dynamic event-triggered asynchronous filtering of Markovian jump systems against cyber-attacks

The paper focuses on the asynchronous filter design based on hidden Markovian model for Markovian jump systems with time-delay and external disturbances. Cyber nonlinearities in the communication environment are also considered. To further reduce the network bandwidth usage, an internal dynamic variable is introduced based on the previously extensively studied (static) event-triggered method, which is called dynamic event-triggered approach. The hidden Markovian model is utilized to characterize the asynchronous phenomenon caused by clock signals out of sync between system and filter mode. Then, according to the augmented filtering error system dynamics, some less conservative sufficient conditions are proposed to guarantee the stochastic stability with H∞ performance. Consecutively, the filter parameter-solving problem is synthesized by a convex optimization problem. Finally, two numerical simulations are presented to demonstrate the effectiveness of the proposed approach.

Analysis of stability, energy consumption and [formula omitted] emissions in novel discrete-time car-following model with time delay under V2V environment

This article aims to explore the stability, energy consumption and CO2 emissions of a novel discrete car-following model with time delay. Under the assumption that the preceding two successive vehicles can realize the communication through V2V (Vehicle to Vehicle) communication environment. Moreover, the time-delayed average optimal velocity difference control scheme is also considered. Based on the proposed discrete car-following model, error dynamical system is formulated and asymptotic stability is developed. The sufficient condition for the time-delayed average optimal velocity difference control scheme of the discrete car-following model with time delay is obtained, the asymptotic stability is ensured. In addition, numerical simulations are constructed and further illustrated the cooperative driving by V2V communication can improve stability, reduce energy consumption and CO2 emissions of traffic system. Moreover, the time-delayed average optimal velocity control scheme is also conductive to improve stability, reduce energy consumption and CO2 emissions of traffic system.

An Interval Observer for a Class of Cyber–Physical Systems with Disturbance

This paper investigates the problem of interval estimation for cyber–physical systems with unknown disturbance. In order to realize the interval estimation of cyber–physical systems, two technical methods are adopted. The first one requires the observer dynamic error system to be non-negative, and the second one relaxes this limitation by coordinate transformation. The sufficient conditions are established using both Lyapunov stability and positive system theory. Furthermore, according to the Schur complement, the linear matrix inequality is solved to determine the observer gains. Finally, the effectiveness and feasibility of the designed interval observer are verified by one numerical simulation.

Tracking controller of extended chained nonholonomic systems with matched disturbance and input saturation

AbstractThis paper addresses the tracking control for an extended chained nonholonomic system under input saturation and matched disturbances. Specifically, the tracking error dynamic system is split into two subsystems in a cascade form. An integral sliding mode saturated controller is designed in combination with a finite‐time observer (FTDO) to ensure the finite‐time stability of the first subsystem, thereby simplifying the design of the second subsystem. A backstepping‐based adaptive saturated tracking control method is proposed for the second subsystem by incorporating the filter technology. The stability of the resulting closed‐loop system is demonstrated, and the tracking errors can be arbitrarily minimized through the appropriate design parameter selection. The effectiveness of the proposed scheme is validated through simulation and experimental results.

Does financial inclusion improve energy accessibility in Sub-Saharan Africa?

ABSTRACT We examine the nexus between financial inclusion and energy poverty. Analysing data for 27 energy-poor countries in the Sub-Saharan Africa region over 2004–2021, we employ sequential (two-stage), panel-corrected standard error (PCSE) and two-step dynamic system GMM (generalized method of moments) regression models, and control for endogeneity, CSD, slope heterogeneity as well as stationarity and cointegration patterns of the variables. Our empirical results show that financial inclusion significantly reduces energy poverty in the selected energy-poor countries. The study also finds a positive significant association between energy access and GDP per capita, while oil price and energy intensity are inversely associated with energy access. The results are robust to different control variables, estimation methods and subsamples. These findings have strong policy implications for energy-poor countries and point to the need for appropriate policies to promote financial inclusion for reducing energy poverty.

Event-Triggered Bipartite Time-Varying Formation Control for Multiagent Systems With Unknown Inputs.

This article addresses the issues of the bipartite time-varying formation (BTVF) control for multiagent systems (MASs) on signed digraphs. All the designs are performed under the assumptions that the leader and followers suffer from external disturbances, the control input signal of the leader is unreachable to any follower, and the state variables of the followers are unmeasurable. To begin with, an unknown input observer (UIO) is designed for each follower using a traditional interval observer to obtain the state estimates. To realize the BTVF tracking, a distributed consensus error dynamic system is constructed. Furthermore, a distributed unknown input reconstruction method is developed to estimate the multiple disturbances in the consensus error system. Then, an event-triggered BTVF control protocol is proposed which allows two antagonistic time-varying formations to be formed, while excluding Zeno behavior. A simulation of a group of wheeled robots is used to demonstrate the performance of the proposed methods.

Chance-Constrained State Estimation for Recursive Neural Networks Under Deception Attacks and Energy Constraints: The Finite-Horizon Case.

In this article, the chance-constrained state estimation problem is investigated for a class of time-varying neural networks subject to measurements degradation and randomly occurring deception attacks. A novel energy-constrained deception attack model is proposed, in which both the occurrence of the attack and the selection of released faked packet are random and the energy of the deception attack is introduced, calculated, and analyzed quantitatively. The main purpose of the addressed problem is to design an estimator such that the prefixed probabilistic constraints of the system error dynamics are satisfied and the performance is also ensured. Subsequently, the explicit expression of the estimator gains is derived by solving a minimization problem subjected to certain recursive inequality constraints. Finally, a numerical example and a practical three-tank system are utilized to demonstrate the correctness and effectiveness of the proposed estimation scheme.