Nonlinear Systems Research Articles

Stability Analysis of a Class of Nonlinear Fractional Differential Systems With Riemann-Liouville Derivative

This paper investigates the stability of n-dimensional nonlinear fractional differential systems with Riemann-Liouville derivative. By using the Mittag-Leffler function, Laplace transform and the Gronwall-Bellman lemma, one sufficient condition is attained for the asymptotical stability of a class of nonlinear fractional differential systems whose order lies in (0, 2). According to this theory, if the nonlinear term satisfies some conditions, then the stability condition for nonlinear fractional differential systems is the same as the ones for corresponding linear systems. Several examples are provided to illustrate the applications of our result.

Novel flexible fixed-time stability theorem and its application to sliding mode control nonlinear systems.

For the fixed-time nonlinear system control problem, a new fixed-time stability (FxTS) theorem and an integral sliding mode surface are proposed to balance the control speed and energy consumption. We discuss the existing fixed time inequalities and set up less conservative inequalities to study the FxTS theorem. The new inequality differs from other existing inequalities in that the parameter settings are more flexible. Under different parameter settings, the exact upper bound on settling time in four cases is discussed. Based on the stability theorem, a new integral sliding mode surface and sliding mode controller are proposed. The new control algorithm is successfully applied to the fixed-time control of chaotic four-dimensional Lorenz systems and permanent magnet synchronous motor systems. By comparing the numerical simulation results of this paper's method and traditional fixed-time sliding mode control (SMC), the flexibility and superiority of the theory proposed in this paper are demonstrated. Under the same parameter settings, compared to the traditional FxTS SMC, it reduces the convergence time by 18%, and the estimated upper bound of the fixed time reduction in waiting time is 41%. In addition, changing the variable parameters can improve the convergence velocity.

Distributed Fault Estimation for Nonlinear Systems With Sensor Saturation and Deception Attacks Using Stochastic Communication Protocols

Distributed Fault Estimation for Nonlinear Systems With Sensor Saturation and Deception Attacks Using Stochastic Communication Protocols

Data-Driven Adaptive Predictive Control Method With Autotuned Weighting Factor for Nonlinear Systems Using Triangular Dynamic Linearization

Data-Driven Adaptive Predictive Control Method With Autotuned Weighting Factor for Nonlinear Systems Using Triangular Dynamic Linearization

Robust adaptive learning control using spiking-based self-organizing emotional neural network for a class of nonlinear systems with uncertainties

For second-order general nonlinear systems with uncertainties, a control scheme combining fractional-order fast terminal sliding mode control (FOFTSMC) and self-organizing emotional neural network (SOENN) is proposed and designed. Firstly, a novel emotional neural network which can approximate the uncertainties in nonlinear systems is constructed and introduced. Meanwhile, in order to optimize the network structure and reduce the computing burden, a novel spiking-based self-organizing mechanism is added. Then the FOFTSMC is designed for second-order general nonlinear systems, and the stability and finite time convergence is proved by Lyapunov theory. Besides, the FOFTSMC and SOENN are combined to form the final control scheme, and adaptive laws of the parameters are also designed. Finally, inverted pendulum and active power filter (APF) are selected as the research objects to carry out a series of simulations and experiments to validate and highlight the effectiveness and superiority of the proposed control scheme.

H ∞ consensus control via intermittent communication for nonlinear multi-agent systems with unknown parameters and external disturbances

The consensus control problem is investigated for time-delayed nonlinear leader-following multi-agent systems, in which the unknown parameters and external disturbances are considered. Instead of using only one control method, a control scheme combining periodically intermittent control with H ∞ performance is employed. By manipulating the algebraic graph theory and constructing appropriate Lyapunov–Krasovskii functionals, sufficient solutions assuring the exponential H ∞ consensus of the considered systems are established in the form of linear matrix inequalities. The communication graph among the followers is directed, which removes the restrictions on undirected graph or balanced graph in the literature. Simulation analyses are finally presented to verify the theoretical results.

A new strategy optimisation method for underwater flapping foil propulsion based on Twin-Delayed Deep Deterministic and Gaussian process regression

In complex sea environments, underwater bionic flapping foils exhibit significant nonlinear characteristics across a high-dimensional parameter space. This study introduces a novel optimisation paradigm, G-TD3, integrating Twin-Delayed Deep Deterministic (TD3) reinforcement learning with Gaussian process regression (GPR). An automatic experimental device was developed, using which a series of flapping foil propulsion experiments were conducted, exploring both symmetric and asymmetric flutter modes. Utilizing GPR, we characterized the flapping foil's operational environment from experimental data. In addition, the TD3 algorithm was deployed to exploit this environment, enabling interactive learning in high-dimensional, continuous parameter spaces. Our integrated approach facilitates comprehensive exploration-exploitation dynamics. The optimized propulsion strategy, fine-tuned through maximizing acquisition rewards, demonstrates G-TD3's superiority over traditional brute-force methods, requiring less data for optimising both symmetric and asymmetric flutter strategies. This research provides a new optimisation method for nonlinear systems and offers valuable insights into the practical applications of bionic flapping foils.

Exponential output tracking via a saturated RLC for a class of nonlinear systems under PSD of periodic references

This paper considers the same class of zero-relative-degree nonlinear systems for which a saturated Repetitive Learning Control (RLC) has been recently shown to ensure exponential – and not just asymptotical – convergence to zero of both the output and the input tracking errors in the case of periodic output reference signals with a known single period. The explicit role of the nonlinear unstructured uncertainties is here investigated within the more general scenario in which the output reference signal is multi-periodic. Special emphasis is provided to the generation of the input reference whose effect has to be exponentially nullified by the RLC. In particular, the following question is answered. Restrict the design to the sub-class of periodic output reference signals that admit a Periodic Signal Decomposition (PSD) (namely, the ones that can be written as a finite sum of periodic functions) with pairwise-commensurable periods (so that the knowledge of the multiple periods characterizing the input reference is preserved once the common multiple among the single periods is additionally included). Then, which robustness and convergence properties can be still achieved by the same output-feedback (definitely saturated) RLC, once it is intuitively generalized to transiently include an additional bank of learning estimation schemes corresponding to the single periods? Interestingly, the theoretical tools of this paper can be also used to successfully address identifiability and convergence issues regarding the identification of periodic components of general multi-periodic signals.

Contribution of hall and ion slip effects with generalized mass and heat fluxes with entropy analysis on three-dimensional Prandtl model

A major challenging proffered study rely on the inquisitive optimization of entropy together with thermal as well as mass transportation towards the chemically reactive 3-D Prandtl liquid under consideration of applied magnetic field, variable thermal conductivity and also diffusivity, hall current together with ion slip features, viscous dissipation and heat generation. Moreover, in present research study, model such as Cattaneo Christov heat flux was implemented in order to explore the thermal relaxation characteristics. By employing correspondence transformations, the system of modeled equations modified into non-linear ODEs system. The Optimal Homotopy Analysis methodology (OHAM) was adopted to solve the proffered problem. The influential arising constraints demeanor within both velocities (horizontal as well as vertical), temperature and concentration profiles were discussed and also shown graphically. Moreover, outcomes of diverse parameters were also examined and presented graphically within the entropy formation rate and also Bejan number. The effects of implanted factors across the drag force, the rate of thermal as well as mass transportation are accessible in current study via tables and validate the obtained results. Both velocity profiles (horizontal as well as vertical) decreased for increment in Hartman number whilst opposite demeanor seen for other considered constraints. Temperature profile drops for Prandtl number and elastic constraints whereas enhanced for other influential considered parameters whilst concentration profile augmented with Prandtl number. Present problem novelty relies on the modeling of comprehensive system of equations which modified into nonlinear ODEs. In order to obtain the solution numerically, technique such as Optimal Homotopy was opted.

Neural networks-based framework for recognizing streaming patterns in magnetized Maxwell–Oldroyd-B blood blended with tetra-hybrid nanoparticles and microbes over stenosis in an elastic artery

The proposed study delves into investigating blood flow patterns and thermal and solutal transport in an artery affected by stenosis. Specifically, it explores the behavior of blood ingrained with tetra-hybrid nanoparticles and gyrotactic microbes under magnetic effects. To capture the non-Newtonian nature of blood in such complex scenarios, the Maxwell-Oldroyd-B (MO) fluid model is employed. The pertinent nonlinear partial differential equations system accounts for similarity transformations and boundary layer assertions. Numerical results are assessed using a potent shooting approach with a fourth-order Runge–Kutta (RK4) method implemented through MATLAB’s bvp4c commands. The computational outcomes are visualized via graphical representation and tabulated data for in-depth analysis and illustration. The research yields significant insights into various model parameters. For instance, the Lorentz force is observed to exert a drag effect, hindering blood flow velocity, while the opposite trend is observed for blood temperature. Additionally, higher Peclet numbers correlate with reduced mass concentration levels, while gyrotactic microbes’ density profile exhibits an upsurge with elevated Lewis numbers. Notably, the Nusselt number for Newtonian blood is lower than MO blood, shedding light on the impact of blood properties on heat transport. Furthermore, this study proposes a technique based on artificial neural networks (ANNs) for accurately predicting skin friction coefficient, Nusselt number, Sherwood number, and microbes’ density number. The proposed algorithm achieves remarkable accuracy rates of 99.65% on the testing dataset and 99.99% during cross-validation for predicting the skin friction coefficient. The novel findings generated by this model hold promising implications for the treatment and monitoring of arterial diseases, as well as the development of cutting-edge medical devices and technologies.

Investigation of a Non-linear Suspension System for Electric Multi-axle Military Truck Moving over Cross Country Terrains

Investigation of a Non-linear Suspension System for Electric Multi-axle Military Truck Moving over Cross Country Terrains

Finite-time adaptive NN dynamic surface control for nonstrict nonlinear FOSs subject to input dead-zone and full-states constraints

This article focuses on a kind of nonstrict nonlinear fractional-order systems (FOSs) suffering from state constraints and dead-zone input. Meanwhile, a finite-time adaptive dynamic surface control (DSC) approach based on backstepping technology and approximation principle of radial basis function neural network (RBFNN) is developed. To overcome the problem of inherent computational complexity, a fractional-order filter is applied to approach the virtual controller and its fractional-order derivative in each step of the backstepping procedure. The barrier Lyapunov function (BLF) is employed to handle the state constraints, and finite-time stability criteria on the basis of fractional-order Lyapunov method are introduced to prove the finite-time convergence of the tracking error into a small region around the origin. It is shown that all the solutions of the closed-loop system are bounded, while the state constraints are satisfied within a predetermined finite time. Finally, two examples are provided to demonstrate the effectiveness of the presented control scheme.

Probabilistic Estimation and Control of Dynamical Systems Using Particle Filter with Adaptive Backward Sampling

Estimating and controlling dynamical systems from observable time-series data are essential for understanding and manipulating nonlinear dynamics. This paper proposes a probabilistic framework for simultaneously estimating and controlling nonlinear dynamics under noisy observation conditions. Our proposed method utilizes the particle filter not only as a state estimator and a prior estimator for the dynamics but also as a controller. This approach allows us to handle the nonlinearity of the dynamics and uncertainty of the latent state. We apply two distinct dynamics to verify the effectiveness of our proposed framework: a chaotic system defined by the Lorenz equation and a nonlinear neuronal system defined by the Morris–Lecar neuron model. The results indicate that our proposed framework can simultaneously estimate and control complex nonlinear dynamical systems.

An Improved Wiener Path Integral Approach for Stochastic Response Estimation of Nonlinear Systems Under Non-White Excitation

Abstract An improved Wiener path integral (WPI) approach is developed for predicting the stochastic response probability density functions (PDFs) of nonlinear systems under non-white excitation. Specifically, the excitation process is modeled as the output of a filter whose input is Gaussian white noise, the joint response PDF of the nonlinear system is expressed as a functional integral of the stochastic action over the space of all possible trajectories between the initial and final states, and the second-order variation of the stochastic action is recast to a quadratic form and taken into account in the estimation of the joint response PDF. Compared to the standard WPI approach where the second-order variation of the stochastic action is regarded as a constant, the improved WPI approach developed herein considers the fluctuations of the second-order variation of the stochastic action in the computational domain, thus improving the accuracy of the stochastic response estimation. Two numerical examples are illustrated, and the nonstationary response PDFs estimated by the improved WPI approach agree well with the Monte Carlo simulation results.

Output feedback adaptive inverse optimal security control for stochastic nonlinear cyber-physical systems under sensor and actuator attacks

Output feedback adaptive inverse optimal security control for stochastic nonlinear cyber-physical systems under sensor and actuator attacks

Research and Simulation Analysis of Fuzzy Intelligent Control System Algorithm for a Servo Precision Press

With the rapid development of the manufacturing industry toward intelligence and flexibility, traditional mechanical presses are unable to meet the increased stamping requirements due to the difficulties in achieving variable speed control and changing slide motion trajectories. Servo presses, driven directly by servo motors, can realize the flexible control of press movement and have become the trend in the industry for future development. The independent research and development of servo press control systems has become a popular topic and challenge in the domestic press industry. This paper proposes a new type of press transmission mechanism suitable for high-precision stamping, analyzes the working principle of its transmission mechanism, and provides a detailed analysis and discussion on the main research methods of fuzzy intelligent control for servo presses, including fuzzy model and basic control algorithms, fuzzy modeling and control of nonlinear systems, fuzzy predictive control, and stability analysis of fuzzy control systems. Based on the principle of the control scheme, a closed-loop control system block diagram and mathematical model for servo high-precision presses are established. Taking the physical prototype parameters of the STSZG1-250 as an example, the control system is dynamically simulated and verified using Simulink modules. Finally, their role and effects in intelligent control, and prospects for the development of fuzzy intelligent control, are discussed.

Model Predictive Control based on Long-Term Memory neural network model inversion

Long Short-Term Memory (LSTM) neural networks are well suited for representing time series as, compared to other neural networks, their structure avoids vanishing or exploding gradients. LSTM has been embedded into Model Predictive Control algorithms in order to forecast the behavior of nonlinear systems. The new algorithm presented in the paper is of a different nature, as the LSTM network approximates the inverse of the system over a receding horizon and provides a sequence of future inputs as a function of a specified output trajectory. The main advantage of the method appears when the desired output trajectory is generated from a small set of parameters, for example, a convergence rate. The Model Predictive control optimizes its criterion with respect to this small set of variables, and the LSTM supplies the corresponding future control inputs. Eventually, the modeling error of the LSTM can be compensated by feeding the control sequence to the forward model and updating the controller according to the output deviation. The algorithm allows to design Model Predictive controllers for nonlinear systems in a generic way, using a very small number of decision variables even with a long receding horizon.

Dynamic formulation and inertia fast estimation of a 5-DOF hybrid robot

As the main driving mechanism of a hybrid robot, the parallel mechanism is a nonlinear time-varying system. The load inertia of its actuated joints changes with the configuration of the robot. Analyzing and fitting the inertia variation is of great significance to the design and control of hybrid robots. By taking a hybrid robot named TriMule as an example, the variation of load inertia of each actuated joint in the whole workspace is first revealed based on the dynamic analyses of the robot. Then two methods based on the circular and elliptical membership are proposed to calculate fitted inertia over the whole workspace using inertia information at a few configurations. Finally, the fitting methods of the two membership functions are compared and discussed. The results show that the maximum value and global mean value of the fitting error of the elliptical membership method are 39.18% (51.23%) and 65.79% (81.25%) for actuated joint-1 (joint-2 and joint-3) lower than those of circular membership method, which promise a better global fitting accuracy. The proposed method can be used to estimate the joint load inertia or other control variables affected by inertia in a quick manner, allowing the algorithm to be easily integrated into the robot control system.

Composite observer based finite time control for nonlinear systems subjecting to multiple disturbances

Composite observer based finite time control for nonlinear systems subjecting to multiple disturbances

Analysis of non-linear degradation over NOMA-GFDM communications systems

Generalized frequency division multiplexing (GFDM) and non-orthogonal multiple access (NOMA) schemes are currently regarded as promising techniques for meeting the requirements of sixth-generation (6G) communication systems. While significant attention has been devoted to studying these techniques, specific scenarios still need to be explored. Considering that one essential aspect of any communication system is the utilization of high-power amplifiers, which are typically modeled as non-linear systems, in this paper, we propose a novel methodology to analyze the bit error probability (BEP) of NOMA-GFDM systems operating on memoryless non-linear system. To account for the non-linear distortions induced by high-power amplifiers, a polynomial model is employed, and new theoretical expressions are developed to compute the BEP of the system. Specifically, exact BEP expressions for a two-user downlink NOMA-GFDM system are provided. The numerical results obtained demonstrate that non-linear distortion significantly degrades system performance.