Nonlinear Systems Research Articles

Adaptive neural network terminal sliding mode tracking control for uncertain nonlinear systems with time-varying state constraints

Adaptive neural network terminal sliding mode tracking control for uncertain nonlinear systems with time-varying state constraints

Data-driven learning and control of nonlinear system dynamics

Data-driven learning and control of nonlinear system dynamics

Adaptive tracking control of high-order nonlinear systems with unknown time-varying input delay and unmodeled dynamics

Adaptive tracking control of high-order nonlinear systems with unknown time-varying input delay and unmodeled dynamics

On examining the predictive capabilities of two variants of the PINN in validating localized wave solutions in the generalized nonlinear Schrödinger equation

We introduce a novel neural network structure called strongly constrained theory-guided neural network (SCTgNN), to investigate the behaviour of the localized solutions of the generalized nonlinear Schrödinger (NLS) equation. This equation comprises four physically significant nonlinear evolution equations, namely, the NLS, Hirota, Lakshmanan–Porsezian–Daniel and fifth-order NLS equations. The generalized NLS equation demonstrates nonlinear effects up to quintic order, indicating rich and complex dynamics in various fields of physics. By combining concepts from the physics-informed neural network and theory-guided neural network (TgNN) models, the SCTgNN aims to enhance our understanding of complex phenomena, particularly within nonlinear systems that defy conventional patterns. To begin, we employ the TgNN method to predict the behaviour of localized waves, including solitons, rogue waves and breathers, within the generalized NLS equation. We then use the SCTgNN to predict the aforementioned localized solutions and calculate the mean square errors in both the SCTgNN and TgNN in predicting these three localized solutions. Our findings reveal that both models excel in understanding complex behaviour and provide predictions across a wide variety of situations.

Dual-channel event-triggered prescribed performance adaptive fuzzy time-varying formation tracking control for nonlinear multi-agent systems

This paper is concerned with the problem of dual-channel event-triggered prescribed performance adaptive fuzzy time-varying formation tracking control for multi-agent systems subject to actuator saturation, in which state variables are unmeasurable and nonlinear functions are totally unknown. A fuzzy state observer is constructed to estimate unmeasurable states. Meanwhile, fuzzy logic systems are used to approximate unknown nonlinear functions. To effectively save the usage of communication resources, this paper designs both sensor output signal and control signal triggering mechanisms, respectively. Unfortunately, the output triggering can lead to a problem that virtual control laws are non-differentiable. To solve this problem, we first utilize observer output signals to construct virtual control laws to ensure the first-order differentiation of virtual control laws. Then, a dynamic filtering technology is introduced to avoid the repeated differentiation of virtual control laws. Furthermore, an improved first-order auxiliary system is designed to compensate for the impact of actuator saturation. It is shown that the designed controller can guarantee tracking errors steer to a preset accuracy within a prescribed settling time, and all signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, simulation results verify the effectiveness of the developed control scheme.

Fuzzy adaptive fixed-time control for output-constrained uncertain nonstrict-feedback time-delay systems

This paper deals with the problem of fuzzy adaptive fixed-time control for a class of uncertain nonlinear nonstrict feedback systems with time delays and output constraints. The negative effects of time delays on system performance and stability are overcome by introducing a new Barrier Lyapunov–Krasovskii (BLK) function and an innovative inequality. In addition, the singularity problem that arises in the process of deriving the control and adaptive laws, is solved by the proposed BLK function. The controller is designed in the backstepping framework which ensures that the system output does not violate predefined constraints. The proposed controller needs less information from the system and therefore has less implementation complexity than previous references, which leads to a more straightforward implementation. A fuzzy system approximation is utilized to overcome the uncertainties of the model. It is guaranteed that all closed-loop system signals converge to small neighborhoods around zero in a fixed time. Finally, an example is presented to verify that the proposed method achieves the control objectives.

Output fluctuation and overshoot restraining for a class of nonlinear discrete-time systems using a modified model-free adaptive control

Output fluctuation and overshoot restraining for a class of nonlinear discrete-time systems using a modified model-free adaptive control

Nonlinear evolution of disturbances in higher time-derivative theories

We investigate the evolution of localized initial value profiles when propagated in integrable versions of higher time-derivative theories. In contrast to the standard cases in nonlinear integrable systems, where these profiles evolve into a specific number of N-soliton solutions as dictated by the conservation laws, in the higher time-derivative theories the theoretical prediction is that the initial profiles can settle into either two-soliton solutions or into any number of N-soliton solutions. In the latter case this implies that the solutions exhibit oscillations that spread in time but remain finite. We confirm these analytical predictions by explicitly solving the associated Cauchy problem numerically with multiple initial profiles for various higher time-derivative versions of integrable modified Korteweg-de Vries equations. In the case with the theoretical possibility of a decay into two-soliton solutions, the emergence of underlying singularities may prevent the profiles from fully developing or may be accompanied by oscillatory, chargeless standing waves at the origin.

Extended Weyl-Wigner phase-space framework for nonlinear systems: Typical and modified prey-predator-like dynamics

Extended Weyl-Wigner phase-space framework for nonlinear systems: Typical and modified prey-predator-like dynamics

Predictive modeling of nonlinear system responses using the Residual Improvement Deep Learning Algorithm (RIDLA)

Predictive modeling of nonlinear system responses using the Residual Improvement Deep Learning Algorithm (RIDLA)

Data-Driven Learning Fuzzy Output-Feedback Control with Prescribed Performance for Nonlinear Systems

Data-Driven Learning Fuzzy Output-Feedback Control with Prescribed Performance for Nonlinear Systems

Event-triggered adaptive fault estimation and fault-tolerant control for strict-feedback nonlinear systems with full state constraints

Event-triggered adaptive fault estimation and fault-tolerant control for strict-feedback nonlinear systems with full state constraints

Adaptive fuzzy fixed-time control for uncertain switched nonlinear systems with non-symmetrical dead-zone

This paper addresses fuzzy adaptive fixed-time tracking control problem for uncertain switched nonlinear systems with non-symmetrical dead-zone, even if the tracking control problem for subsystems is not solvable. A fixed-time stability criterion for switched nonlinear systems using MLF(multiple Lyapunov functions) method is presented. Then, it is applied to fixed-time tracking control of uncertain strict-feedback switched nonlinear systems. The design methods of fuzzy adaptive feedback controllers and a state-dependent switching law are given to achieve the boundedness of all the signals of the resulting closed-loop system and the fixed-time output tracking control. Nonsymmetrical dead-zone model is used to estimate an adaptive factor through less parameters, which related to fixed-time tracking control for the uncertain switched nonlinear systems. Two examples are given to verify the effectiveness of the proposed design method.

Robust adaptive fixed‐time stabilization of disturbed planar high‐order nonlinear systems

Robust adaptive fixed‐time stabilization of disturbed planar high‐order nonlinear systems

Estimates of the accuracy of identification of a nonlinear dynamic system using step test signals

Machine learning (ML) has become widespread in everyday life. On its basis, programs with artificial intelligence work, on the basis of which many virtual assistants have evolved. ML plays an important role in various spheres of activity of many enterprises. ML helps to automate many processes, simplifying the functioning of the company. Named Entity Recognition (NER) models allow to automatically select and search for information according to certain criteria in mobile data extracted, for example, by the logistic method. Support for NER by Python models makes it possible to flexibly program specific requests that are generated in the forensic examination process. Open source creates a unique opportunity to continuously improve the model by training it on datasets. A powerful NER package is the spaCy framework, which helps to simplify data and extract detailed information from input data, train a model, perform model tuning, and more. spaCy is compatible with 64-bit CPython 3.7+ and runs on Unix/Linux, macOS/OS X and Windows. The latest spaCy releases are available over pip and conda.

Experimental Analysis of Dynamics of a Nonlinear Oscillatory System with Self-Synchronizing Vibration Exciters when Interacting with Bulk Material

Experimental Analysis of Dynamics of a Nonlinear Oscillatory System with Self-Synchronizing Vibration Exciters when Interacting with Bulk Material

Chaotic band-gap modulation mechanism for nonlinear vibration isolation systems based on time-delay feedback control

Chaotic band-gap modulation mechanism for nonlinear vibration isolation systems based on time-delay feedback control

Zero-sum games subject to uncertain stochastic noncausal systems considering polynomial control functions

An uncertain stochastic noncausal system (USNS) is an uncertain stochastic singular system that is expected to be regular but not impulse-free. This study investigates zero-sum games (ZSGs) under the constraint of nonlinear uncertain stochastic noncausal systems (USNSs) considering polynomial control functions. Firstly, a method is introduced to convert USNSs into subsystems, including forward uncertain stochastic difference equations as well as backward uncertain stochastic difference equations. Equilibrium equations are then derived to determine the saddle-point equilibrium solution of the zero-sum game (ZSG) for USNSs. Subsequently, a unified framework is developed to find the saddle-point equilibrium and equilibrium value of the ZSG. Additionally, a numerical example and an analysis of the treatment of industrial wastewater are provided to demonstrate the effectiveness of the proposed framework.

BLF-based neuroadaptive control for full state constrained nonlinear systems with input saturation: A feasibility-condition-free approach

BLF-based neuroadaptive control for full state constrained nonlinear systems with input saturation: A feasibility-condition-free approach

Predefined time fuzzy adaptive control for stochastic nonlinear systems with limited time interval output constraints

This article investigates the problem of fuzzy adaptive predefined time tracking control for stochastic nonlinear systems with limited time interval output constraints. Firstly, the considered output constraints occur within a finite time interval after the system starts running. By constructing shift functions and barrier Lyapunov functions (BLFs), the constrained system is converted into an unconstrained system, which solves the problem of function discontinuity resulting from output constraints within limited time intervals. Then, with the help of adaptive backstepping technique and predefined time control method, which reduces the parameters to be designed and removes the limitation of relatively large initial control input in existing approaches. The designed control technique ensures the boundedness of all variables of the stochastic system, the tracking error converges within a predetermined time, and the outputs do not exceed their constraint boundaries in a finite time interval. And this algorithm is applicable to both infinite time constraints and unconstrained outputs cases. Finally, the validity of this approach is demonstrated through simulation examples.