High-order Systems Research Articles

Event-Triggered Mechanism-Based Discrete-Time Nash Equilibrium Seeking for Graphic Game With Outlier-Resistant ESO.

In this article, we consider a discrete-time Nash equilibrium (NE) seeking problem for graphic game subject to disturbances. For the first-order dynamics, the discrete-time outlier-resistant extended state observer (ESO)-based game strategy is proposed to enable the players to estimate the disturbances under effect of anomaly measurements and then compensate them. An event-triggered mechanism is applied between adjacent players to reduce the frequency of communication. The convergence of the outlier-resistant ESO and control strategy is presented. Moreover, the upper bound of ϵ -NE solution deviating from the unique point of nominal system is given analytically. Then, the addressed issues are extended to high-order game systems. The NE seeking-based control strategy for each player is designed such that the equilibrium point converges to the ϵ -NE which is also analytically calculated. Finally, in order to verify the effectiveness of the proposed game strategy, an example of satellite system is given.

Optimization Method for High-Order Wireless Power Transfer System Considering Gain Constraint and Components Stress

Optimization Method for High-Order Wireless Power Transfer System Considering Gain Constraint and Components Stress

Distributed Output-Feedback Asymptotic Consensus Tracking for High-Order Multiagent Systems With Quantized Input.

This article is devoted to distributed adaptive asymptotic consensus tracking control based on output feedback for the uncertain high-order multiagent systems with input quantization. Compared with the output-feedback canonical form, the system takes unmeasured states-dependent nonlinearities into account and also includes unknown parameters and quantized input. The improved K -filters with one dynamic gain are constructed to dispose the unmeasured states-dependent nonlinearities and estimate the unknown states. Then, the novel recursive control strategy with the aid of new first-order dynamic parameter filters is proposed, which is able to effectively counteract the filter errors and steer the consensus tracking errors to zero asymptotically with low design complexity. Moreover, the new funnel variable combined with prespecified time performance function is first introduced, which can predefine practical transition time and maximum overshoot of consensus error. Finally, simulation results are presented to illustrate the validity and superiority of the proposed scheme.

State Responses of Several Classes of Linear Systems Based on Fundamental Matrices.

State responses for several classes of linear systems are investigated in this article. The involved systems include state-delayed linear systems, and high-order linear systems. At first, the single-fundamental-matrix-based approach is extended to these systems, and their state responses are expressed by their fundamental matrices (FMs). In addition, the multiple-FMs-based approach is presented for these systems. Based on a group of FMs, the state responses for the considered time-invariant systems are derived. For the considered time-variant systems, their state responses are explicitly expressed by their transition matrices. As an application of the fundamental-matrix-based approach, a stabilizing control law is designed for a class of high-order fully actuated continuous-time linear systems with a single input-delay.

Distributed Optimal Time-Varying Resource Allocation for Networked High-Order Systems

Distributed Optimal Time-Varying Resource Allocation for Networked High-Order Systems

A novel tensor-based modal decomposition method for reduced order modeling and optimal sparse sensor placement

Data-driven modal decomposition methods have become fundamental algorithms in constructing reduced order models (ROMs), which serve as a critical tool in the digital twin modeling of large complex systems. Classical modal decomposition methods are particularly adept at handling matrix-form input data that contains columnized snapshots without retaining spatial structure and neighborhood information. Focusing on addressing this problem, this paper proposed a Tensor-Based Modal Decomposition (TBMD) method to deal with the high-order tensor-form input data. TBMD method is effective in finding the potential low-order manifolds of a given high-order dynamical system with low energy loss within fewer decomposited modes. Moreover, TBMD is extended to be used in the field of optimal sensor placement via the development of a tensor-based QR factorization method and a tensor-based compressive sensing algorithm. The tensor-based QR factorization method is able to consider the spatial structure and neighborhood information of the basis matrices data in tensor form. This is the first time that a compressive sensing model has been discussed and solved for the frontal slice-wise product of a tensor and a vector. Subsequently, comprehensive case studies are conducted based on the cylinder wake dataset, airfoil vortex dataset, sea surface temperature dataset, eigenfaces dataset and turbulent channel flow dataset. The experiment results show that TBMD can accurately capture lower-order manifolds, and the tensor-based QR factorization is effective in optimizing sensor placement with fewer sensors while maintaining high reconstruction accuracy. The proposed methods in this paper is promising to be utilized in the construction of large-scale complex system digital twins, in which TBMD can serve as a fundamental algorithm in constructing ROM.

Dual Channels Event-Triggered Asymptotic Consensus Control for Fractional-Order Nonlinear Multiagent Systems.

This article investigates the event-triggered leaderless consensus control problem for fractional-order multiagent systems (FOMASs), where both the agent-to-agent communication channel and the controller-to-actuator communication channel are based on the events. A filter is introduced to transform the original high-order system into a first-order one, greatly simplifying the complexity of controller design compared to the traditional backstepping. Further, the convergence of filtered output signals is proved to be consistent with that of the outputs of agents themselves. Superior to the traditional event-triggered scheme, two dynamic variables are designed for the triggering conditions of the communication among agents and the controller update, respectively. Via elaborately constructing the dynamic variables, zero-error leaderless consensus can be achieved instead of only ultimately uniformly bounded result. It is proved that the proposed control strategy can guarantee better control performance of leaderless consensus under limited communication resources, and Zeno behavior is excluded. Finally, two examples are provided to verify the effectiveness of our proposed control approach.

Adaptive fixed-time stabilization for high-order uncertain nonlinear systems with unknown measurement sensitivities

This paper investigates the adaptive fixed-time stabilization problem for a class of uncertain high-order nonlinear systems with unknown measurement sensitivities and unknown control magnitude. Compared to existing practical fixed-time control approaches, our control strategy is capable of driving all states of uncertain high-order systems to the origin within a fixed time, rather than just ensuring their boundedness. Additionally, this study relaxes the restrictions on the nonlinear functions of the system, while overcoming challenges such as unknown control magnitude and unknown measurement sensitivity without prior boundaries. To achieve the control objectives, our control strategy consists of two main steps. Firstly, we divide the initial value of the high-order system into two cases, and construct adaptive controllers separately for each case by adding a power integral technique and backstepping method. Subsequently, the reliance of the stability time of the closed-loop high-order system on the initial value is eliminated by designing an appropriate controller switching mechanism. Finally, we provide a simulation example to validate the effectiveness of our control strategy.

Computational insights into the structural, thermodynamic and transport properties of CaF2-MgF2 binary fluoride system at high temperatures

The structural, thermodynamic and transport properties of the CaF2-MgF2 molten salt system were investigated with ab initio molecular dynamics (AIMD), system-specific neural network interatomic potentials (NNIPs) and universal PreFerred Potentials (PFP). We trained an NNIP model using AIMD data as input and used this potential to efficiently simulate the interactions within a large supercell in a temperature range of 1273–1773 K. The Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code was employed to validate our trained NNIP model. The Matlantis software with universal PFP is also presented to prove its feasibility for MD calculations and can be considered as a useful alternative simulation tool for higher-order systems where existing potentials are not readily available. We calculated structural and thermodynamic properties including radial distribution function (RDF), angular distribution function (ADF), specific heat capacity, ionic self-diffusivity, and viscosity. Our results indicate that the system exhibited a high degree of structural disorder, with the Ca, Mg, and F ions forming a liquid solution. Using PFP, the positions of the first peak in RDFs for Ca-F and Mg-F pairs are only slightly left-shifted (<0.05 Å), and the estimated viscosity of the melt decreases from 4.613 mPa·s to 1.846 mPa·s with an increase in temperature from 1273 K to 1773 K, in agreement with the NNIP trained specifically for CaF2-MgF2. Our results provide valuable insights into the properties of the CaF2-MgF2 system at high temperatures and serve as predictive models for the development of new electrolytes that could be used for silicon epitaxy by adding silica.

Distributed adaptive tracking consensus control for a class of heterogeneous nonlinear multi-agent systems

The proposed approach differs from existing works in that it models the constraints of each follower as a nonlinear strict feedback system, rather than relying on a desired reference trajectory for accessible subsystems. To address the limitations caused by uncertain terms in systems, radial basis functions neural networks are utilized to compensate for these unknown nonlinear terms. This leads to a novel distributed adaptive consensus tracking control protocol for high-order nonlinear heterogeneous multi-agent systems, based on the backstepping technique. By introducing a non-zero parameter in the traditional radial basis functions neural network, a new universal approximation is constructed, which overcomes the limitation of the approximation’s finite domain. Additionally, the approximation precision can be adjusted online using provided laws, and the dimension explosion of virtual and real control gains can be avoided through the use of the designed control approach. Simulation results are provided to demonstrate the effectiveness of the proposed control scheme.

Formation control of high-order linear discrete-time multiple unmanned aerial vehicles systems in noisy environments

Formation control of high-order linear discrete-time multiple unmanned aerial vehicles (multi-UAVs) systems with multiplicative noises is studied in this article. Because of the existence of multiplicative noises, classical methods for discrete-time system control problems should be improved. Here, we develop a new discrete-time formation protocol for multi-UAVs systems. The stochastic Lyapunov stability theory and the positive definiteness theory of a generalized algebraic Riccati equation are then used to derive sufficient conditions for formation feasibility.

Neural networks-based composite learning control for robotic systems with predefined time error constraints

This paper investigates the neural networks-based control problem for robotic systems with error constraints. By embedding a new predefined time performance function into an asymmetric barrier function, a predefined time constraints method is proposed with the following features: (1) it is a general approach that can handle asymmetric error constraints and can be directly applied to the predefined performance control for other high-order nonlinear systems without any changing; (2) both settling time and convergent compact set can be preassigned by the user; (3) the results are global i.e., the robot can start arbitrarily within the physical domain. By extending the regression operators with online data memory, a prediction error is constructed, by using which, a new neural networks based composite learning law is constructed to handle unknown dynamics. Compared with the traditional method such as gradient descent algorithm, σ-modification and ϵ-modification which cannot guarantee the convergence of the neural networks weights or can only force the weights to stay around preselected values, the neural networks guarantees that the weights converge to the region around the true values, in particular under a weak interval excitation (IE) condition rather than the typically stringent persistent excitation (PE) condition. The benefits and effectiveness of the proposed control are theoretically authenticated and experimentally validated.

Barrier-function based adaptive trajectory tracking control for high-order nonlinear systems with collision avoidance

This paper considers the problem of trajectory tracking and collision avoidance for a class of high-order nonlinear strict feedback systems with unknown nonlinearities. The main issue is how to ensure collision avoidance and tracking performance simultaneously in the presence of unknown nonlinear functions. To address the issue, an integral-multiplicative barrier Lyapunov function (BLF) is integrated into the backstepping procedure to remove the dynamic mismatching issue of the existing SUM-type BLF. It has been proven that the proposed adaptive approach ensures both collision avoidance and tracking performance of high-order nonlinear systems in multi-obstacle environments, and all the signals in the closed-loop system are uniformly ultimately bounded (UUB). Simulation results confirm the effectiveness of the proposed method.

Synthesis of hardware and software for adaptive discrete high-order control systems based on a model of the desired transient process with a guaranteed degree of stability

In this work, analytical expressions for the connection between optimization criteria andsettings parameters of the adaptive PI-PID controller with variable parameters of the object andadaptive filter have been removed. A method for synthesizing a model of discrete controllersbased on given dynamic characteristics has been developed. A method has been developed forsynthesizing a model of a discrete PID controller based on given dynamic characteristics basedon the criterion of the transient process of a guaranteed level of stability. 3 figures, 0 tables, 32formulas, 19 bibliographic sources..Analytical expressions have been removed to link the optimization criteria andadjustment parameters of the adaptive PI-PID controller with the variable parameters of theobject and adaptive filter.A method for synthesizing a model of discrete controllers from specified dynamiccharacteristics has been developed. The average warehouse of output pulses at the output of anonlinear channel, which is formed at the output of such a regulator and is seen as an inertialinduced uninterrupted part, changes according to the law, which is designated as a reversetransmission the function of the lanyard of the new molded filter model at the collar of the non-linear element.A method has been developed for synthesizing a model of a discrete PID controller fromspecified dynamic characteristics based on the criterion of the required transient process of aguaranteed stability level.The modeling showed that while the parameters of the object and the adaptive filter willchange during the ASC operation, then, obviously, the optimal parameters for adjusting theadaptive PID controller will immediately change.

Tuning equations for sliding mode controllers: An optimal multi-objective approach for non-minimum phase systems

This article proposes an approach to create tuning equations based on optimal multi-objective design specifically for Sliding Mode controllers applied to non-minimum phase processes that can be approximated to a First-Order-Plus-Deadtime class of systems. This is achieved by taking into account various performance criteria, including tracking, controller action, and transient response. The proposed tuning equations aim to achieve a well-balanced trade-off among competing objectives. The paper presents a systematic framework for formulating the multi-objective optimization problem and derives analytical expressions for the tuning parameters based on the desired performance specifications. The effectiveness of the proposed method is demonstrated through simulations in three dynamic processes: a high-order linear system with dominant delay, a high-order plus inverse response system, and a nonlinear process with variable parameters and dominant deadtime. A comparative analysis with an existing SMC tuning technique shows superior performance results. This paper provides valuable information on the optimization procedure for obtaining analytical tuning equations for controllers, offering a promising avenue for improving the performance of control systems in practical applications.

A comparative study of predicting high entropy alloy phase fractions with traditional machine learning and deep neural networks

Predicting phase stability in high entropy alloys (HEAs), such as phase fractions as functions of composition and temperature, is essential for understanding alloy properties and screening desirable materials. Traditional methods like CALPHAD are computationally intensive for exploring high-dimensional compositional spaces. To address such a challenge, this study explored and compared the effectiveness of random forests (RF) and deep neural networks (DNN) for accelerating materials discovery by building surrogate models of phase stability prediction. For interpolation scenarios (testing on the same order of system as trained), RF models generally produce smaller errors than DNN models. However, for extrapolation scenarios (training on lower-order systems and testing on higher order systems), DNNs generalize more effectively than traditional ML models. DNN demonstrate the potential to predict topologically relevant phase composition when data were missing, making it a powerful predictive tool in materials discovery frameworks. The study uses a CALPHAD dataset of 480 million data points generated from a custom database, available for further model development and benchmarking. Experiments show that DNN models are data-efficient, achieving similar performance with a fraction of the dataset. This work highlights the potential of DNNs in materials discovery, providing a powerful tool for predicting phase stability in HEAs, particularly within the Cr-Hf-Mo-Nb-Ta-Ti-V-W-Zr composition space.

Nonsingular fixed-time K-filter output-feedback control for high-order nonlinear multi-agent systems

This paper investigates the problem of nonsingular fixed-time control for high-order nonlinear multi-agent systems with unmeasurable states and disturbances. To address the unmeasurable states, a K-filter is introduced to reconstruct the system with the input and output only and to facilitate the construction of the observer. To provide an approximation for the unknown nonlinear functions, the fuzzy logic system technique is applied. A novel tracking controller is proposed to ensure that all signals remain bounded for the closed-loop system and that the tracking error converges into a small and adjustable set within a fixed time by utilising the adaptive backstepping recursive technology and the adding power integrator technique. Meanwhile, the singular problems arising from the fixed-time stability criterion can be also avoided. Finally, a simulation experiment verifies the effectiveness of the designed control scheme.

Iterative learning resilient consensus of uncertain nonlinear multi-agent systems vulnerable to false data injection attacks

This work investigates the iterative learning resilient consensus of uncertain nonlinear high-order multi-agent systems (MASs) against false data injection (FDI) attacks. First, in order to reduce the impact of FDI attacks on the nonlinear MASs, a novel coordinate transformation technique is proposed, which is composed of the states after being attacked, and the Nussbaum gain technique is adopted to address the problem of unknown attack gains resulting from FDI attacks. Then, by employing compromised state variables, a fuzzy adaptive iterative learning resilient control method is presented based on the composite energy function, where unknown nonlinear functions are handled using fuzzy logic systems. The presented approach can guarantee that the outputs of all followers precisely track the leader in a limited time interval while ensuring that all closed-loop signals are bounded. Finally, a numerical simulation is provided to demonstrate the efficacy of the designed control strategy.

Dynamical topological quantum phase transitions in high-order topological systems

Dynamical topological quantum phase transitions in high-order topological systems

Output tracking of coupled stochastic strict-feedback higher-order nonlinear systems under pinning control

This paper focuses on the tracking problem for a class of coupled stochastic strict-feedback higher-order nonlinear systems under pinning control. Compared with existing stochastic nonlinear tracking designs, our approach stands out by simultaneously considering coupling and higher-order characteristics for the first time. By utilizing the backstepping technique and designing virtual controllers, we obtain actual controllers that ensure the closed-loop system has an almost surely unique solution and is bounded in probability. Additionally, the fourth-moment of the output tracking error can be rendered arbitrarily small in the long run. Notably, to address the cost implications of imposing a controller on each node, we employ a pinning control strategy to selectively control a portion of the nodes. Moreover, a global Lyapunov function is derived combining Lyapunov method with graph theory. Eventually, a numerical simulation is shown to verify the theoretical results.