Nonlinear Systems Research Articles

Fuzzy Adaptive Approaches for Robust Containment Control in Nonlinear Multi-Agent Systems under False Data Injection Attacks

This study addresses the problem of fractional-order nonlinear containment control of heterogeneous multi-agent systems within a leader–follower framework, focusing on the impact of False Data Injection (FDI) attacks. By employing adaptive mechanisms and fuzzy logic, the suggested method enhances system resilience, ensuring reliable coordination and stability even in the presence of deceptive disturbances. To deal with these uncertainties, our controller makes use of interval type-II (IT2) fuzzy sets, and we create matrix equalities and inequalities to account for the asymmetry of Laplace matrices. Also, we use the Lyapunov functions for the stability analysis of our system. Lastly, we explain the numerical simulations for the effectiveness of our theoretical results, and these simulated examples are used to verify the effectiveness of our approach and designed model.

An output-feedback stabilisation scheme with exponential convergence for nonlinear systems with unknown polynomial-of-output growth rate

ABSTRACT This paper seeks adaptive output-feedback control which enables exponential stabilisation for nonlinear systems with unknown polynomial-of-output growth rate and dynamic uncertainties. The existence of uncertainties naturally requires the introduction of adaptive compensation mechanisms, while, convergence rate, as an important performance specification, is usually hard to attain in the context of adaptive control. For this, we are compelled to pursue a comprehensive and competent adaptive compensation mechanism which possesses dual capabilities of compensating uncertainties and affording convergence rate. Crucially, a subtle dynamic gain is designed with its dynamic updating law incorporating exponential-type time-varying information. Notably, the gain would not only deal with the unknown polynomial-of-output growth rate but particularly ensure exponential convergence with the convergence rate online adjusting in conformity to the dynamic uncertainties. Correspondingly, an adaptive output-feedback controller is constructed based on a dynamic-gain observer, which can render exponential convergence for system and observer states.

Dual-channel event-triggered model-free adaptive iterative learning control under DoS attacks

This paper investigates a dual-channel event-triggered model-free adaptive iterative learning control problem for unknown nonlinear systems under periodic denial-of-service (DoS) attacks. Firstly, periodic DoS attacks on the measured output of the system are modelled using the Bernoulli distribution. Then, to minimise the utilisation of system bandwidth resources, a dual-channel event-triggered mechanism is designed for the sensor-to-controller and controller-to-actuator channels. Subsequently, a dual-channel event-triggered model-free adaptive iterative learning control algorithm is introduced. The convergence of the tracking error is proven in terms of mathematical expectation using Lyapunov stability theory. Finally, the effectiveness of the proposed algorithm is verified through two simulation cases.

Optimal switching of MPC cost function for changing active constraints

Model predictive control (MPC) allows for dealing with multivariable interactions, known future changes and dynamic satisfaction of constraints. Standard MPC has a cost function that aims at keeping selected controlled variables at constant setpoints. This work considers systems where the steady-state optimal active constraints change during operation. This situation is not handled optimally by standard MPC which uses fixed controlled variables for the unconstrained degrees of freedom. We propose a simple framework that detects the constraint changes and updates the controlled variables accordingly. The unconstrained controlled variables are chosen to be the reduced cost gradients, which when controlled to zero minimizes the steady-state economic cost. In this paper, the nullspace method for self-optimizing control is used to estimate the cost gradient using a static combination of the measurements. This estimated gradient is also used for detecting the current set of active constraints, which in particular allows for giving up constraints that were previously active. The proposed framework, here referred to as “region-based MPC”, is shown to be optimal for linear constrained systems with a quadratic economic cost function, and it allows for good economic performance in nonlinear systems in a neighborhood of the considered design points.

Velocity observer design for a class of uncertain nonlinear mechanical systems: a self-adaptive fuzzy logic-based approach

Velocity observer design for a class of uncertain nonlinear mechanical systems: a self-adaptive fuzzy logic-based approach

Application of Supplementary Inerter-Based Damping Devices Alongside Unbonded Fiber-Reinforced Elastomeric Isolators

Earthquakes have always been a menace to the lives and properties of human beings since the beginning of modern times. Several methods have been proposed since to mitigate the various types of seismic hazards, base isolation being one of them. The base-isolated structures being very effective for general far-fault earthquakes, are, however susceptible to high responses under near-fault ground motions; thus, several inerter-based supplementary damping devices have been proposed in this study to be applied alongside a highly nonlinear and effective unbonded fiber-reinforced elastomeric isolators (UFEI) system. The dampers are optimally designed and comparatively investigated with the isolation system for mitigation of a wide range of ground motions to the benchmark structure. Furthermore, two parametric studies were also carried out, which investigated the effect of the inertance-mass ratio and floor connectivity of the grounded damper on various responses of the isolator-damper-structure system. The parametric results are further used to suggest the best configuration and inertance-mass ratios for various dampers for effective seismic mitigation of the aforementioned base-isolated structure. The results show an effective reduction in seismic responses with the use of optimal inerter-based dampers in UFEI-isolated structures.

Adaptive fixed-time difference synchronization for different classes of chaotic dynamical systems

This article examines adaptive fixed-time difference synchronization for various classes of chaotic dynamical systems. The adaptive fixed-time control technique has been used in this article to investigate the difference synchronization for the Sprott chaotic system, both with and without delay. The fixed settling time (T) has been estimated successfully. It is also shown that the trajectories of error states approach to the origin within a fixed time (T). The theoretical analysis is validated by simulating Sprott chaotic systems both with and without delay. On the other hand, various nonlinear chaotic systems are explored for difference synchronization in discrete chaotic systems. Several chaotic maps, including Tinkerbell, Henon, and Hitzl-Zele, have been used to achieve synchronization in these discrete systems. The numerical results are presented graphically, verifying the theoretical outcomes of difference synchronization for various classes of chaotic dynamical systems.

Stochastic configuring networks based adaptive sliding mode control strategy to improving stability of SG-VSG paralleled microgrid

This article proposes an adaptive sliding mode control (SMC) strategy based on stochastic configuring networks (SCNs) to improve the stability of synchronous generator (SG) and virtual synchronous generator (VSG) paralleled microgrid and enhance the dynamic performance. First, derives an equivalent swing equation what coupling of inherent inertia/damping of SG and virtual inertia/damping of VSG, the parameters design problem is established to a stabilization problem of second-order uncertain nonlinear system with bounded uncertainties. Second, an adaptive sliding mode control based on variable-speed reaching law is designed to maintain the second-order nonlinear system stable, and the switch function of adaptive reaching law is improved to reduce system chattering. Then, the stochastic configuring networks is introduced to approximate the nonlinear term, and the approximation ability of SCNs is improved by designing the configuration range of input parameters of hidden layer nodes. The stability of proposed control strategy is proved by Lyapunov theory. Finally, the feasibility and effectiveness of the proposed control strategy are verified by the designed simulations and experiments.

Practically fast finite-time stability of stochastic constrained nonlinear systems with actuator dead zone

This article addresses the challenge of achieving practically fast finite-time stabilization for stochastic constrained nonlinear systems, which are subject to both quantization effects and actuator dead zones. To tackle these issues, adaptive parameterization and partial control strategies are introduced with the aim of efficiently approximating and counteracting nonlinear disturbances. This approach ensures the robust stabilization of the controlled system within a finite time frame, despite the presence of uncertainties. Additionally, a novel barrier function is propose that mitigates the constraints usually imposed by boundary functions, while also leveraging a fuzzy logic system to manage nonlinear terms adeptly. Building on these innovations, we formulate a new theorem dedicated to practically fast finite-time control mechanisms for stochastic nonlinear systems. The efficacy of our theoretical developments is substantiated through an illustrative example involving a current-controlled DC motor system, demonstrating the practical applicability and robustness of the proposed control scheme.

Discussion on the accuracy of methods for determining interface force between numerical and physical substructures in shaking table-based real-time hybrid simulation

Real-time hybrid simulation (RTHS) is a developing experimental technology that combines the advantages of numerical simulation and physical test. In RTHS, the interface force is a key physical quantity coupling the dynamic response of physical substructure and numerical substructure. An inaccurate force determination method can distort RTHS results and may cause incorrect estimations of the dynamic performance of structures. This article aims to systematically discuss the impact of possible error in determining the interface force during shaking table-based RTHS. The errors caused by two typical force determination methods, (1) using force sensors and (2) using strain gauges, are comprehensively investigated. These two force determination methods are typically used for (1) performance evaluation of nonlinear damping systems and (2) investigation of soil–structure interaction effects. Virtual hybrid simulation numerical models (in which both physical and numerical substructures are simulated numerically) representing the interface force determination processes are established. The impacts of error on the RTHS results are evaluate quantitatively. The reported findings can assist in developing a deeper understanding of the causes of errors during RTHS and enhance the experimental designs. This, in turn, leads to more accurate and reliable results in RTHS testing.

Finite time prescribed performance control for stochastic systems with asymmetric error constraint and actuator faults

This paper investigates the problem of finite time prescribed performance control (PPC) for a number of nonlinear stochastic systems with asymmetric error constraint, unknown control directions, and actuator faults. Firstly, instead of introducing the performance constraint function in the Lyapunov function, a new asymmetric error conversion function (AECF) is presented, which can successfully constrain the tracking errors into the specified asymmetric boundaries and eliminate the feasibility condition of requiring tracking errors to be bounded. Then, in iterative process, the unknown intermediate virtual controller is approximated by the fuzzy logic system (FLS), which makes each actual virtual controller to be reduced to only one item. Furthermore, the investigated finite time PPC strategy can fully compensate the faults impact on the systems and have only one adaptive parameter. In the end, the efficacy of investigated strategy is verified by inverted pendulum systems with stochastic disturbances.

A new solution to force analysis including Coulomb friction in mechanism joints

The objective of this paper is to propose a novel approximate solution for determining the reactions of joints in mechanical systems, which involves the influence of Coulomb friction. It is widely acknowledged that if Coulomb friction is used in determining an exact solution to the equilibrium equations for a mechanism, then it will involve nonlinear systems of equations. With the abundance of computer tools now available, tasks of this kind, especially numerical computations, are not particularly challenging. However, new analytically tractable approximate methods are still valuable as a straightforward way of solving the problem. Several studies have been carried out in this field to find a simple solution. In this paper, a new approach based on friction circle concept and Babylonian algorithm is developed for various mechanisms, which is exceptionally well-suited for calculating and streamlining the solution process for mechanical systems by eliminating the necessity for iterative steps at each stage of the force analysis.

Multivariate ocean waves dynamics in North Sea and Norwegian Sea by Gaidai reliability method

Current study presents state-of-the-art approach for evaluating spatiotemporal multivariate environmental risks, especially suitable for complex environmental systems that have been either numerically simulated or physically observed. Advocated methodology provides accurate hazard risk forecasts, based on real-time in situ environmental data. Design of offshore structures requires multivariate risk assessment – offshore and naval operations require both short- and long-term risk and reliability analyses. Contemporary risk evaluation techniques often struggle with raw timeseries multivariate data due to intrinsic multidimensionality and nonlinear interconnections among critical system’s dimensions/components. In the current study effectiveness of the Gaidai multivariate risk evaluation method is illustrated by utilizing significant wave heights dataset, measured within two offshore zones: Heidrun and Troll Norwegian oil fields. Analyzing offshore waves being particularly challenging due to their complexity, high nonlinearity, multidimensionality, yet dynamic inter-correlations. Global warming being among several significant factors, affecting ocean and sea wave heights. For naval, offshore and marine structures operating in harsh weather conditions, robust multivariate environmental risk evaluation methods being crucial for both design and safe operations. Current study aims to validate and benchmark state-of-the-art methodology, enabling extraction. Advocated approach allows for efficient yet accurate assessment of global damages, failures or hazard risks for a wide range of complex nonlinear multivariate environmental and energy systems. Primary advantage of presented multivariate reliability methodology lies within its ability to treat complex systems with practically unlimited number of dimensions, while existing reliability methods being mostly limited to univariate and bivariate analyses.

Exact cosmological solutions for a Chaplygin Gas in anisotropic petrov type D spacetimes in Eddington-inspired-Born-Infeld gravity: Dark Energy model

We consider a Petrov Type D physical metric g, an auxiliary metric q and a Chaplygin Gas of pressure P in Eddington-inspired-Born-Infeld theory. From the Eddington-inspired-Born-Infeld-Chaplygin Gas equations, we first derive a system of second order nonlinear ordinary differential equations. Then, by a suitable change of variables, we arrive at a system of first order linear ordinary differential equations for the non-vanishing components of the pressure P, the physical metric g and the auxiliary metric q. Thanks to the superposition method, we collect an analytical solution for the nonlinear system obtained, which allows to retrieve new exact cosmological solutions for the model considered. By studying the Kretschmann invariant, we see that a singularity exists at the origin of the cosmic time. By the Kruskal-like coordinates, we conclude that this solution is the counterpart of the Friedman-Lemaître-Robertson-Walker spacetime in the Eddington-inspired-Born-Infeld theory. The Hubble and deceleration parameters in both directions of the physical metric g and the auxiliary metric q, as well as their behaviours over time, are also studied. The thermodynamic behaviour of the Chaplygin Gas model is investigated and, as a result, we show that the third-law of thermodynamics is verified. This means that the value of the entropy of the Chaplygin Gas in the perfect crystal state is zero at a temperature of zero Kelvin, which yields a determined value of the entropy and not an additive constant. Finally, we show that the solutions change asymptotically to the isotropic regime of expansion of Dark Energy. With this, we infer that the Chaplygin Gas can show a unified picture of Dark Energy and Dark Matter cooling during the expansion of the Universe.

Multi-variable constrained control for uncertain high-order strict-feedback fully actuated nonlinear systems

This study focuses on multi-variable constrained control for uncertain high-order strict-feedback (HOSF) fully actuated nonlinear systems using the high-order fully actuated (HOFA) system approach. By employing the practical prescribed time control (PPTC) method, the system states’ convergence time and accuracy are ensured without requiring constrained initial conditions. Subsequently, the considered constrained nonlinear systems are transformed into unconstrained ones through coordinate transformation. The integration of command filtered control and radical basis function (RBF) neural network into the HOFA system approach control design allows for the approximation of unknown nonlinear functions and reduces computational complexity. Under the presented control strategy, the complexity of the system’s control design can be further reduced, simultaneously enhancing the performance of the system. Furthermore, the designed controller guarantees that all system signals remain bounded and the prescribed constraints for all system states are satisfied. Finally, simulation results demonstrate the effectiveness of the proposed strategy.

Joint Bayesian estimation of process and measurement noise statistics in nonlinear Kalman filtering

Bayesian filtering aims at sequentially estimating the states and parameters in nonlinear dynamical systems, and finds applications in a variety of engineering fields. Extended and unscented Kalman filter are popular choices for this purpose as they typically achieve a good trade-off between computational complexity and accuracy, while still quantifying posterior uncertainty. However, the accuracy of the identified states and parameters, both in terms of their posterior mean and variance, is heavily influenced by the assumed statistics of both the process and measurement noise terms. Therefore, learning the noise characteristics becomes an essential aspect of Bayesian filtering, but is non-trivial especially in cases where process and measurement noise statistics are jointly non-identifiable. This article proposes a methodology that decomposes measurement and process noise learning in a fully Bayesian setting. For measurement noise estimation, we improve upon a Bayesian method that leverages conjugacy of the inverse-Wishart distribution with respect to the Gaussian likelihood model. For process noise estimation, Bayesian model averaging is coupled with a mutation scheme to compare the performance of competing models while exploring high-probability regions in the space of the unknown process noise variance. The algorithm is first tested on simple numerical models for both state estimation and parameter learning, highlighting the superior accuracy of the proposed measurement noise correction and the benefits of decoupling process and measurement noise learning in non-identifiable settings. Then we demonstrate the usefulness of this algorithm in more challenging problems, namely identification of a multi-degree-of-freedom system under unmeasured excitation, and modeling of the highly nonlinear response of a full-scale bridge pier using experimental data.

K-filter-based distributed adaptive bipartite tracking for nonlinear multi-agent systems with unknown control direction

This paper investigates K-filter-based distributed adaptive output-feedback bipartite tracking problem for multi-agent systems with unknown control direction. The agents are partitioned into two groups, where agents belonging to the same group are cooperative while agents belonging to the distinct group are competitive. Firstly, the unmeasurable state variables of the system under unknown control direction are estimated through K-filters. Then, a neighbourhood error is introduced to transform a structurally balanced network into a cooperative network. Based on K-filters, neighbourhood error, Nussbaum-type functions and dynamic surface control, a distributed adaptive output-feedback control protocol is designed to achieve the bipartite tracking. It is shown that all signals in the resulting closed-loop systems are semi-global bounded and the output of each agent can track the reference signal provided that the network is structurally balanced and contains a directed spanning tree. Finally, a numerical example is given to verify the effectiveness of the proposed method.

On the local quadratic stability of T–S fuzzy systems in the vicinity of the origin

The main goal of this paper is to introduce new local stability conditions for continuous-time Takagi-Sugeno (T-S) fuzzy systems. These stability conditions are based on linear matrix inequalities (LMIs) in combination with quadratic Lyapunov functions. Moreover, they integrate information on the membership functions at the origin and effectively leverage the linear structure of the underlying nonlinear system in the vicinity of the origin. As a result, the proposed conditions are proved to be less conservative compared to existing methods using fuzzy Lyapunov functions. Moreover, we establish that the proposed methods offer necessary and sufficient conditions for the local exponential stability of T-S fuzzy systems. Discussions on the inherent limitations associated with fuzzy Lyapunov approaches are also given. To illustrate the theoretical results, we provide comprehensive examples that demonstrate the core concepts and validate the efficacy of the proposed conditions.

Oscillation-free implicit pressure explicit concentration discontinuous Galerkin methods for compressible miscible displacements with applications in viscous fingering

The system of compressible miscible displacements is widely adopted to model surfactant flooding in enhanced oil recovery techniques, where a low-viscosity fluid is injected underground to replace the high-viscosity oil. When the mobility ratio of the injected fluid to oil is high, the waterflood front tends to be unstable and exhibits a finger-like growth pattern, known as viscous fingering. Due to its unstable nature, the viscous fingering phenomenon is sensitive to mesh orientation and numerical discretization. Therefore, high-order numerical methods are preferable to reduce numerical artifacts and mesh dependence. In this paper, we propose a high-order discontinuous Galerkin method for the coupled nonlinear system of compressible miscible displacements to simulate the viscous fingering fluid instability in porous media. We adopt the IMplicit Pressure Explicit Concentration time marching approach based on implicit-explicit Runge-Kutta methods to achieve high-order temporal accuracy. Additionally, we introduce an oscillation-free damping term to control the spurious oscillations encountered in the waterflood front due to the large gradient of saturation. We have conducted ample numerical tests in two space dimensions to demonstrate the effectiveness and robustness of the proposed schemes in recovering viscous fingering.

Event-triggered adaptive bounded control of high-order uncertain switched nonlinear systems with full-state time-varying constraints

ABSTRACT In this article, an adaptive event-triggered bounded control strategy is proposed for a class of high-order uncertain switched nonlinear systems with full-state time-varying constraints under average dwell time switching rule. In order to achieve the boundedness of the control signal, the projection operator is introduced. At the same time, the high-order log-type time-varying barrier Lyapunov function method is chosen to ensure that the desired output and states of the systems do not violate the relevant constraints. In addition, the improved event-triggered control strategy effectively reduces the transmission burden and saves the resource cost. The stability analysis shows that the proposed scheme achieves the ultimate boundedness of all signals in the closed-loop systems and the states of the systems do not violate the corresponding constraints. It should be noted that the proposed controller has a known bound and this bound can be ensured by the rectification of the feedback control gain. Finally, the simulation results verify the effectiveness of the control method.