Simulation Examples Research Articles

Enhanced Looped Lyapunov Functional for Sampled-Data Control for T-S Fuzzy Systems with Time Delay

This paper addresses the problem of sampled-data control in T-S fuzzy systems with time delays. Initially, a negative-definite criterion is developed for the matrix containing membership functions with the help of the idea of a switching mechanism. Building upon this criterion, a membership-function-based looped Lyapunov functional is introduced. Furthermore, a sampling-time-dependent looped Lyapunov functional is constructed, incorporating crucial information about the sampling instance. Notably, this functional matrix is not constrained to satisfy positive-definiteness, and it varies with each sampling point. By utilizing the enhanced looped Lyapunov functional, less conservative stability conditions and a new controller criterion for the T-S fuzzy system with time delays are derived. This demonstrates that our proposed stability conditions allow for a larger sampling interval compared to existing work. Finally, the proposed method’s effectiveness is demonstrated through the validation of two simulation examples.

Simultaneous fault-tolerant consensus control and disturbance suppression for multi-agent systems with polynomial form fault under switching topology

For continuous-time linear leader-follower multi-agent systems with polynomial faults, the problem of fault-tolerant state consensus under switching topologies is studied. firstly, the average dwell time method is introduced, and observers are designed for different topologies to observe faults and disturbances. Secondly, according to the observed estimated value, the corresponding fault-tolerant control consensus protocol is proposed considering the switching situation of the communication topology. Finally, both theoretical analysis and simulation examples verify that the proposed design scheme can compensate faults and disturbance rejection.

Fuzzy adaptive asynchronous sampled-data consensus control for nonlinear multi-agent systems under DoS attacks

This article investigates the problem of fuzzy adaptive resilient asynchronous sampled-data consensus control (SDCC) for a class of uncertain nonlinear strict-feedback multi-agent systems (MASs) under denial-of-service (DoS) attacks and with a directed graph. Firstly, the upper bounds on the sampling intervals and a distributed sampled-data observer are proposed to estimate the leader's output and its high-order derivatives under DoS attacks. Then, the sufficient conditions to ensure the asymptotic convergence of the designed distributed sampled-data observer are established. Based on the distributed sampled-data observer and backstepping control design technique, a distributed fuzzy adaptive resilient control algorithm is developed. It is proved that the proposed control scheme can guarantee that the controlled MASs are stable, and the consensus errors converge to a small neighbourhood of zero. Finally, a simulation example on heterogeneous vehicular platoons verifies the feasibility of the proposed control scheme.

Sampled‐Data Based Second‐Order Discrete‐Time Sliding Mode Control via Output Feedback

ABSTRACTThis article proposes a second‐order discrete‐time sliding mode controller (DSMC) by only using sampled‐data information of the system output. On one hand, different from the continuous‐time sliding mode control, the finite‐time stability of the closed‐loop system under DSMC is usually not kept due to the limited sampling frequency. On the other hand, in the output feedback framework, the second‐order sliding mode observer cannot independently estimate the internal state of the system if there exist unknown mismatched term and unknown time‐varying coefficient of the control input. To solve the above problems, a joint design strategy of second‐order discrete‐time sliding mode observer and sliding mode controller based on the “non‐separation principle” is proposed. The stability and robustness of the closed‐loop system is analyzed based on the Lyapunov design method. Finally, simulation example verifies the correctness of the theory.

Tobit Kalman fusion filtering under dynamic event-triggering protocol with token bucket specification

This paper addresses the multi-sensor fusion filtering problem for a class of linear discrete time-varying systems with censored measurement, described by the Tobit model, and scheduled by dynamic event-triggering protocols with token bucket specification. A dynamic event-triggering mechanism is first used to determine whether to transmit measurements under the token bucket specification, allowing transmission only if there are sufficient tokens and if the event-triggering condition is satisfied. Next, two indicator variables are denoted to represent the combined impact of the dynamic event-triggering protocol and the token bucket specification. A local Tobit Kalman filtering algorithm is then designed for each node by minimizing the trace of the filtering error covariance matrix under censoring and information transmission protocols' influence. Subsequently, all local estimates from each node are transmitted to the fusion center, where global estimates are generated using a federal fusion rule. The global estimates with suitable weights are sent back to every node for predictions at subsequent time instants. Finally, an illustrative simulation example is used to evaluate performance of this fused filtering scheme proposed in this paper.

Adaptive Predefined‐Time Fuzzy Control for Nonlinear Systems Subject to Unknown Control Direction and Mismatched Disturbances Based on Command Filter Technique

ABSTRACTThis article proposes an adaptive predefined‐time event triggered fuzzy tracking control strategy for strict‐feedback nonlinear systems with unknown control direction and mismatched disturbances by applying command filters. The Nussbaum‐type function is employed to tackle the unknown control direction problem, and the fuzzy logic systems (FLSs) are applied to model the nonlinear functions. And then, command filters are adopted to deal with the problems of complexity explosion, and the event‐triggered technique is exploited to conserve communication resources. With the help of backstepping mechanism and predefined‐time stability theory, the constructed adaptive control scheme is proposed to ensure all signals in the closed‐loop system are bounded and that the tracking error converges to a residual set. Finally, a simulation example proves the validity of presented control mechanism.

Generalized Mean Square Exponential Stability for Stochastic Functional Differential Equations

This work focuses on a class of stochastic functional differential equations and neutral stochastic differential functional equations. By using a new approach, some sufficient conditions are obtained to guarantee the generalized mean square exponential stability for the equation under consideration. Certain existing results are refined and extended. Lastly, the validity of the main results is confirmed through several simulation examples.

SAM: A Modern System Code for Advanced Non-LWR Safety Analysis

The System Analysis Module (SAM), developed at Argonne National Laboratory and by collaborators at other organizations, is for advanced non–light water reactor safety analysis. SAM aims to provide fast-running, modest-fidelity, whole-plant transient analysis capabilities that are essential for fast-turnaround design scoping and engineering analyses of advanced reactor concepts. To facilitate code development, SAM utilizes the MOOSE object-oriented application framework, its underlying finite element library, and linear and nonlinear solvers to leverage modern advanced software environments and numerical methods. SAM aims to solve tightly coupled physical phenomena, including fission reaction, heat transfer, fluid dynamics, and thermal-mechanical responses in advanced reactor structures, systems, and components with high accuracy and efficiency. This paper gives an overview of the SAM code development, including goals and functional requirements, physical models, current capabilities, verification and validation, software quality assurance, and examples of simulations for advanced nuclear reactor applications.

Event-Triggered Fuzzy Adaptive Predefined-Time Control for Fractional-Order Nonlinear Systems with Time-Varying Deferred Constraints and Its Application

This paper focuses on the fuzzy adaptive predefined-time control for fractional-order nonlinear systems with time-varying deferred constraints. First, a modified dynamic surface control technique is introduced to address the problem of computational complexity exposed in the backstepping framework, and the interval type-2 fuzzy logic systems are applied to model the unknown nonlinearities of the systems. Next, a shifting function and the barrier Lyapunov function with variational barrier bounds are formulated to deal with the constraints issue. Particularly, the constraint conditions can be satisfied within a predetermined time, even if they are transgressed initially. Furthermore, a switching threshold event-triggered controller is devised to balance the control energy and communication resources. With the help of the predefined-time stability criterion, it is proven that the presented predefined-time event-triggered controller can ensure that all the signals involved in the closed-loop system are bounded and the tracking error fluctuates to a small neighborhood of the origin in a predefined-time interval. Finally, two simulation examples are provided to confirm the effectiveness of the put-forward control algorithm.

Stability of stochastic difference equations with multiplicative and additive fading noise

In this paper, the effects of multiplicative and additive fading stochastic perturbations on the solutions of stochastic difference equations are studied, in which the strength of fading stochastic perturbations is square summable. Different from the existing research, this paper mainly studies the influence of two kinds of stochastic perturbations on the stability of the system, and applies the Lyapunov functional method, the asymptotic mean square trivial sufficiency conditions are obtained for the solutions of stochastic difference equations which based on the influence of multiplicative and additive fading noises. At the same time, the conditions of stochastic perturbation fading rate are obtained. Finally, the above conditions are verified by numerical simulation examples, and the results of numerical simulation show that: (1) the additive perturbations have less influence on the system than the multiplicative perturbations; (2) the fading stochastic perturbations can make the system reach a stable state in a faster time.

Adaptive Free‐Will Arbitrary Time Tracking of a Class of Uncertain SISO Nonlinear Systems

ABSTRACTThis paper investigates the free‐will arbitrary time (FWAT) tracking problem for a class of single‐input single‐output (SISO) strict‐feedback nonlinear systems without/with parametric uncertainties. First, we design an FWAT backstepping tracking controller for strict‐feedback nonlinear systems without uncertainties in a recursive manner. It is shown that the proposed virtual controllers and their derivatives are continuously differentiable for the backstepping design, and the tracking error converges to zero within the pre‐specified settling time independent of design parameters and initial conditions and remains at zero after the pre‐specified settling time. Second, we address the adaptive FWAT tracking problem of SISO strict‐feedback nonlinear systems with parametric uncertainties in the practical stability sense. The continuously differentiable and nonsingular time‐varying adjustment functions for practical FWAT tracking are developed to transform error variables for the recursive backstepping design. Then, the adaptive FWAT backstepping tracking design and stability analysis strategy are established to ensure practical FWAT convergence within the pre‐specified settling time independent of design parameters and initial conditions. The designed adaptive virtual and actual controllers are continuous for all . Furthermore, a practical adaptive prescribed‐time tracking scheme is provided using the proposed practical adaptive FWAT tracking scheme. Finally, the effectiveness of the theoretical approaches is confirmed through a simulation example and an experimental result.

Geometry, Topology and p-Adic Numbers in Geospatial Data Modelling, Management and Processing: Review and Future Approaches

Abstract. Geometry and topology are both central concepts in geospatial data modelling and management. While geometry is the central concept for computational geometry applications, e.g. to intersect surfaces and solids in 3D space, topology is helpful for many application classes starting from city modelling to subsurface modelling and indoor navigation. Furthermore, p-adic numbers are useful for describing hierarchical processes on topological models. In this paper we first shortly review geometry- and topology-based approaches used for geospatial applications. We then describe our approach on turning geometry “upside down” focusing on topology during the whole process of distributed geospatial computing, data modelling, data management, and simulation. Furthermore, the way to use p-adic numbers for the description of hierarchical processes on topological models is shown for the example of simulation and the idea of p-adic analysis in distributed simulations is presented in the context of topological city and building models. The approach opens new insights such as topological relationships, components, and efficiently studying of the approximate behaviour of processes in the built environment using distributed computational systems. Finally, exemplary applications are presented to underline the importance of this new approach.

Stubborn State and Disturbance Observer Co‐Design for Nonlinear Descriptor Systems With δQC$$ \delta \mathrm{QC} $$ via a Dynamic Event‐Triggered Mechanism

ABSTRACTThis article studies the state and disturbance simultaneous estimation problem for a class of nonlinear descriptor systems with using a dynamic event‐triggered mechanism. refers to incremental quadratic constraints, which can provide a unified description of many types of common nonlinear functions. To reduce the negative impact of measurement outliers on the identification estimation, a stubborn state and disturbance observer co‐design scheme is proposed for the first time by embedding dynamic saturation output estimation errors. Meanwhile, a dynamic event‐triggered mechanism is introduced to avoid the need for continuously available output information, which can reduce the pressure on communication resources. By constructing a Lyapunov function, existence conditions of the stubborn state and disturbance observer are obtained in the form of a convex optimization problem so that the error estimation maintains an acceptable estimation performance. Finally, simulation examples illustrate the universality and stubbornness of the proposed observer.

Event‐Triggered Secure Control of Positive Networked Control Systems Under Multi‐Channels Attacks

ABSTRACTThis paper focuses on the secure control of positive networked control systems under multi‐channel attacks characterized by a Bernoulli distribution. Specifically, the sensor‐to‐controller channel suffers from false data injection (FDI) attacks, whereas the controller‐to‐actuator channel suffers from denial of service (DoS) attacks. The objective is to design a static output feedback controller that guarantees the positivity and stochastic stability of the closed‐loop system in the presence of DoS and FDI attacks. To conserve communication resources, we employ an event‐triggered scheme to reduce the frequency of information transmission. Due to the positivity of the system, the proposed event‐triggering mechanism employs the 1‐norm form instead of the 2‐norm form, which allows that the controller parameter is determined via linear programming rather than LMI technique. Finally, two simulation examples are provided to verify the effectiveness of our methods.

Finite-time output feedback control for a class of stochastic low-order nonlinear systems with output function

This paper studies the problem of finite-time output feedback stabilisation for a class of stochastic low-order nonlinear systems with output function. Under the assumption that output function is continuous, by generalising the adding a power integrator technique, constructing a new implementable reduced-order observer and using the stochastic finite-time stability criterion, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee finite-time stability in probability of the closed-loop system. A simulation example is provided to verify the effectiveness of the proposed design method.

Consensus for discrete-time second-order multi-agent systems in the presence of noises and semi-Markovian switching topologies

In this paper, we focus on the control problem of mean square consensus for second-order continuous-time multi-agent systems with multiplicative noises under Markovian switching topologies. A new Lyapunov function based on the Laplacian matrix of the corresponding union topology of all possible topologies is designed for the stochastic stability analysis of consensus. Applying matrix theory and stochastic stability for stochastic differential equations, we can analyze the consensus problem of the considered systems with the designed Lyapunov function. In addition, we present the sufficient conditions of the mean square consensus exponentially for the considered stochastic systems. Finally, we give an simulation example to numerically validate our theoretical results.

A novel hybrid PD-FEM-FVM approach for simulating hydraulic fracture propagation in saturated porous media

To enhance the computational efficiency of fluid–solid coupling in peridynamics (PD), a hybrid modeling approach based on the classical Biot theory is proposed for simulating hydraulic crack propagation in saturated porous media. The deformation and damage of solids are described by the coupling of the finite element method (FEM) and PD. Based on Darcy’s law, the finite volume method (FVM) is used to describe fluid seepage and calculate pore water pressure. The mutual transfer of fluid pressure and solid deformation is realized through the transition layer between the solid layer and the fluid layer. Firstly, the effectiveness of the proposed method is verified by a porous media seepage simulation example. Secondly, the ability and efficiency of this method to simulate crack propagation in saturated porous media are verified by several examples of hydraulic fracturing of rock with a single pre-existing crack. Finally, the synchronous hydraulic fracturing process of rock with double cracks is simulated. The ability of this method to simulate the simultaneous propagation of multiple fractures in the rock under fluid–solid coupling is further illustrated. The aforementioned studies demonstrate that the novel hybrid PD-FEM-FVM approach not only ensures computational accuracy and effectiveness but also significantly enhances computational efficiency.

Sampled‐data‐driven event‐triggered secure control of uncertain nonlinear cyber‐physical systems against multiple attacks

AbstractIn this paper, the sampled‐data‐driven event‐triggered secure control is discussed for a class of uncertain nonlinear cyber‐physical systems under multiple attacks containing deception attacks and replay attacks. Compared with exisiting research, the studied systems take into account the uncertainty and coupling that may occur in practical situations. Notably, deception attacks impede the application of a gain design approach in control design. To address this issue, an artful state transformation is presented to convert the considered system into an auxiliary system. Based on this, a novel sampled‐data‐driven attack compensation scheme is devised via the gain design approach, and an event‐triggered mechanism is further introduced into the scheme to cancel needless control updates, which successfully ensures state convergence meanwhile resisting the impact of multiple attacks. Particularly, the designed control scheme not only utilizes data efficiently but also avoids Zeno behaviour automatically by judging triggering conditions in sampled points. Finally, the validity of the results is verified through two simulation examples.

Multiplayer hierarchical decision‐making for discrete‐time nonlinear networks of service via value iteration adaptive dynamic programming

AbstractIn this article, the multiplayer hierarchical decision‐making problem for discrete‐time nonlinear networks of service is studied from the perspective of Nash–Stackelberg–Nash games. A novel two‐level value iteration adaptive dynamic programming algorithm is developed to solve the coupled nonlinear Hamilton–Jacobi–Bellman equations associated with the game problem, which neither requires the system drift dynamics to be known as a priori nor requests the initial strategies to be admissible. Moreover, both the value function sequences and the strategy sequences generated by the algorithm converge to their theoretical optimality. An implementation framework for the algorithm is constructed by leveraging the regularized least‐squares method, and a convergence criterion that guarantees the admissibility of the approximated strategies is also proposed. The effectiveness of the proposed algorithm and implementation framework are finally demonstrated through two numerical simulation examples.

State Estimation for Measurement-Saturated Memristive Neural Networks with Missing Measurements and Mixed Time Delays Subject to Cyber-Attacks: A Non-Fragile Set-Membership Filtering Framework

This paper is concerned with the state estimation problem based on non-fragile set-membership filtering for a class of measurement-saturated memristive neural networks (MNNs) with unknown but bounded (UBB) noises, mixed time delays and missing measurements (MMs), subject to cyber-attacks under the framework of weighted try-once-discard protocol (WTOD protocol). Considering bandwidth-limited open networks, this paper proposes an improved set-membership filtering based on WTOD protocol to partially solve the problem that multiple sensor-related problems and multiple network-induced phenomena influence the state estimation performance of MNNs. Moreover, this paper also discusses the gain perturbations of the estimator and proposes an improved non-fragile estimation framework based on set-membership filtering, which enhances the robustness of the estimation approach. The proposed estimation framework can effectively estimate the state of MNNs with UBB noises, estimator gain perturbations, mixed time-delays, cyber-attacks, measurement saturations and MMs. This paper first utilizes mathematical induction to provide the sufficient conditions for the existence of the desired estimator, and obtains the estimator gain by solving a set of linear matrix inequalities. Then, a recursive optimization algorithm is utilized to achieve optimal estimation performance. The effectiveness of the theoretical results is verified by comparative numerical simulation examples.