High-order Nonlinear Systems Research Articles

Midpoint geometric integrators for inertial magnetization dynamics

We consider the numerical solution of the inertial version of Landau-Lifshitz-Gilbert equation (iLLG), which describes high-frequency nutation on top of magnetization precession due to angular momentum relaxation. The iLLG equation defines a higher-order nonlinear dynamical system with very different nature compared to the classical LLG equation, requiring twice as many degrees of freedom for space-time discretization. It exhibits essential conservation properties, namely magnetization amplitude preservation, magnetization projection conservation, and a balance equation for generalized free energy, leading to a Lyapunov structure (i.e. the free energy is a decreasing function of time) when the external magnetic field is constant in time. We propose two second-order numerical schemes for integrating the iLLG dynamics over time, both based on implicit midpoint rule. The first scheme unconditionally preserves all the conservation properties, making it the preferred choice for simulating inertial magnetization dynamics. However, it implies doubling the number of unknowns, necessitating significant changes in numerical micromagnetic codes and increasing computational costs especially for spatially inhomogeneous dynamics simulations. To address this issue, we present a second time-stepping method that retains the same computational cost as the implicit midpoint rule for classical LLG dynamics while unconditionally preserving magnetization amplitude and projection. Special quasi-Newton techniques are developed for solving the nonlinear system of equations required at each time step due to the implicit nature of both time-steppings. The numerical schemes are validated on analytical solution for macrospin terahertz frequency response and the effectiveness of the second scheme is demonstrated with full micromagnetic simulation of inertial spin waves propagation in a magnetic thin-film.

Neural-network distributed event-triggered consensus tracking control for high-order nonlinear strict-feedback multiagent systems

Neural-network distributed event-triggered consensus tracking control for high-order nonlinear strict-feedback multiagent systems

Non-predictor event-triggered controller for high-order feedforward nonlinear systems with unknown time-varying delays in the states and input

This paper studies the global regulation problem by a non-predictor event-triggered controller for high-order feedforward nonlinear systems with unknown time-varying delays in the states and input. We propose a non-predictor-based event-triggered controller with a dynamic gain-scaling factor, in which any information on the delays is not required in controller design. The dynamic gain-scaling factor is utilised to deal with high-order terms so that the considered class of systems are generalised over the previous results. The simulation results effectively demonstrate the validity of our proposed control method.

Sliding mode control with self-adaptive parameters of a 5-DOF hybrid robot.

Due to the advantages of high stiffness, high precision, high load capacity and large workspace, hybrid robots are applicable to drilling and milling of complicated components with large sizes, for instance car panels. However, the difficulty in establishing an exact dynamic model and external disturbances affect the high accuracy control directly, which will decrease the machining accuracy and thereby affect the machining quality and efficiency of the system. Sliding mode control is an effective approach for high-order nonlinear dynamic systems since that it is very insensitive to disturbances and parameter variations. However, chattering may exist in traditional sliding mode control with fixed parameters, which results from a constant approaching speed. Besides, the approaching speed will affect the chattering strength directly. To solve these problems, a modified sliding mode controller with self-adaptive parameters is proposed to enhance the trajectory-tracking performance of a 5-degree-of-freedom hybrid robot. Firstly, the kinematic model of the robot is established. Then adopting the principle of virtual work, a rigid dynamic model of the robot is built. Based on the built dynamic model, a modified sliding mode control method is developed, of which the approaching speed is dependent on the system state. Finally, the sliding mode controller with self-adaptive parameters is created for a hybrid robot. The proposed sliding mode controller can achieve a rapid approaching speed and suppress chattering simultaneously. Simulation results demonstrate that the proposed modified sliding mode controller can achieve a comparatively accurate and smooth trajectory, which owns good robustness to external disturbances.

Fixed-time fuzzy tracking control for high-order nonstrict feedback nonlinear systems with unknown virtual control gains and actuator faults

In this paper, fuzzy fault-tolerant tracking control is investigated for high-order nonstrict feedback nonlinear systems in fixed time interval. The gain fault and bias fault in actuator are considered for high-order nonstrict feedback nonlinear systems. Contrary to the existing results, an adaptive estimation tactic is proposed to estimate the coexisting uncertainties such that no priori knowledge is needed for the adaptive parameters, in spite of unknown virtual control gains, nonlinear uncertainties, time-varying disturbances and actuator faults. Based on this tactic, the unknown virtual control gains are slackened to completely unknown, which is more practical. Unlike the general fixed time control tactics, the singularity problem has been overthrew by using the inequality transformation strategy without destroying the control performance. The growth assumptions are removed and the complex nonstrict feedback structure is overcome with the support of fuzzy logic systems (FLS). Finally, two examples demonstrate the validity of the formulated method.

Prescribed-time stabilization and inverse optimal control of stochastic high-order nonlinear systems

Prescribed-time stabilization and inverse optimal control of stochastic high-order nonlinear systems

Optimized bipartite formation control for multiagent systems with obstacle and collision avoidance

This paper considers an optimal bipartite formation control problem for high-order nonlinear multiagent systems (MASs) with the consideration of obstacle/collision avoidance. Contrary to existing literature, the control strategy designed in this paper can render the agents in a bipartite formation to complete the obstacle/collision avoidance tasks without requiring the obstacles to be located on the coordinate axis. To save resources, an identifier-critic-actor-based optimized formation control scheme is designed for MASs. An obstacle/collision avoidance approach based on dynamical systems (DS) is designed for high-order nonlinear MASs. Different from the existing related results, the proposed DS-based obstacle/collision avoidance approach can avoid the phenomenon that the control quantities approach infinity near obstacles or other agents, and eliminate the dependence on global information. Finally, a simulation example is given to validate the proposed control method.

Neuro-adaptive non-singular terminal sliding mode control for distributed fixed-time synchronization of higher-order uncertain multi-agent nonlinear systems

This paper presents a novel design for a distributed fixed-time synchronization controller based on neuro-adaptive non-singular terminal sliding mode control for higher-order multi-agent nonlinear systems. In this study, a distributed control strategy is employed in which networked nonlinear systems, referred to as nodes, communicate through a predefined network topology. Within this framework, a leader-follower configuration is adopted, designating one node as the leader and the others as follower agents. Notably, the dynamics of the agents are assumed to be unknown, leading to the development of a generalized uncertain higher-order nonlinear dynamical system model that accounts for the disturbed dynamics of all agents, including the matched bounded uncertainty with an upper algebraic bound. The control design leverages radial basis function neural networks for approximation, effectively addressing unknown nonlinear terms, such as drift terms and input channels. Importantly, the proposed technique successfully mitigated matched-type uncertainty, resulting in rapid sliding-mode enforcement with reduced chattering and stress. This innovative approach establishes fixed-time synchronization by creating a sliding mode with respect to the sliding surface of networked synchronization mismatches. To underscore the effectiveness of this approach, a simulation example that vividly illustrates its captivating properties and contributions is presented.

Genetic algorithm-based secure cooperative control for high-order nonlinear multi-agent systems with unknown dynamics

AbstractResearch has recently grown on multi-agent systems (MAS) and their coordination and secure cooperative control, for example in the field of edge-cloud computing. MAS offers robustness and flexibility compared to centralized systems by distributing control across decentralized agents, allowing the system to adapt and scale without overhaul. The collective behavior emerging from agent interactions can solve complex tasks beyond individual capabilities. However, controlling high-order nonlinear MAS with unknown dynamics raises challenges. This paper proposes an enhanced genetic algorithm strategy to enhance secure cooperative control performance. An efficient encoding method, adaptive decoding schemes, and heuristic initialization are introduced. These innovations enable compelling exploration of the solution space and accelerate convergence. Individual enhancement via load balancing, communication avoidance, and iterative refinement intensifies local search. Simulations demonstrate superior performance over conventional algorithms for complex control problems with uncertainty. The proposed method promises robust, efficient, and consistent solutions by adapting to find optimal points and exploiting promising areas in the space. This has implications for securely controlling real-world MAS across domains like robotics, power systems, and autonomous vehicles.

Prescribed-time adaptive stabilization of high-order stochastic nonlinear systems with unmodeled dynamics and time-varying powers

<p>In this paper, the control problem of prescribed-time adaptive neural stabilization for a class of non-strict feedback stochastic high-order nonlinear systems with dynamic uncertainty and unknown time-varying powers is discussed. The parameter separation technique, dynamic surface control technique, and dynamic signals were used to eradicate the influences of unknown time-varying powers together with state and input unmodeled dynamics, and to mitigate the computational intricacy of the backstepping. In a non-strict feedback framework, the radial basis function neural networks (RBFNNs) and Young's inequality were deployed to reconstruct the continuous unknown nonlinear functions. Finally, by establishing a new criterion of stochastic prescribed-time stability and introducing a proper bounded control gain function, an adaptive neural prescribed-time state-feedback controller was designed, ensuring that all signals of the closed-loop system were semi-global practical prescribed-time stable in probability. A numerical example and a practical example successfully validated the productivity and superiority of the control scheme.</p>

Sampled-Data-Based Distributed Output Feedback Leader–Following Consensus for Time-Delay Multiagent Systems

This paper addresses the distributed output feedback leader-following consensus problem for high-order nonlinear multiagent systems (MASs) with time delays and disturbances under the directed network. Using sampled relative outputs to neighbors and the discrete control input, the continuous-discrete time compensator is constructed in each agent to compensate for the consensus errors, where the sampling time instants can be asynchronous and aperiodic without exceeding an explicit upper bound of sampling intervals. Based on the compensator, we propose a co-design algorithm for constructing the dynamic event-triggered protocol with a corresponding event-triggering mechanism which is a combination of discrete-time control input, continuous dynamic variables of each agent's own compensator, and a given threshold. The proposed methods can not only achieve consensus tracking under the effects of time delays in states and communications but also implement the discrete-time execution of measurement, communication, and control. Based on the novel lemmas, it is proved that the resulting closed-loop consensus error system is globally stable. Finally, a simulation is given to illustrate the effectiveness of proposed methods.

Game-Based Backstepping Design for Strict-Feedback Nonlinear Multi-Agent Systems Based on Reinforcement Learning.

In this article, the game-based backstepping control method is proposed for the high-order nonlinear multi-agent system with unknown dynamic and input saturation. Reinforcement learning (RL) is employed to get the saddle point solution of the tracking game between each agent and the reference signal for achieving robust control. Specifically, the approximate optimal solution of the established Hamilton-Jacobi-Isaacs (HJI) equation is obtained by policy iteration for each subsystem, and the single network adaptive critic (SNAC) architecture is used to reduce the computational burden. In addition, based on the separation operation of the error term from the derivative of the value function, we achieve the different proportions of the two agents in the game to realize the regulation of the final equilibrium point. Different from the general use of the neural network for system identification, the unknown nonlinear dynamic term is approximated based on the state difference obtained by the command filter. Furthermore, a sufficient condition is established to guarantee that the whole system and each subsystem included are uniformly ultimately bounded. Finally, simulation results are given to show the effectiveness of the proposed method.

Data-driven Predictive Control for a Class of Nonlinear Systems with Polynomial Terms

This article proposes a non-parametric representation for a class of high-order unknown nonlinear systems comprising polynomial functions. A data-driven approach is introduced that uses pure data for future simulation based on any given input set. We also consider a comprehensive class of nonlinear autoregressive exogenous (NARX) models which covers other existing representations as special cases. Then, a non-parametric representation of this class of NARX models are investigated by leveraging the idea of re-expressing the system in the context of a non-minimal state-space reformulation. A data-driven predictive control (DDPC) approach is as a result introduced that uses the fundamental lemma for future prediction during the open-loop optimization. The recursive feasibility analysis and the proof of stability are also given. Finally, the simulation results quantify the effectiveness of the proposed approach in different scenarios.

Finite-Time Output Feedback Stabilization for High-Order Stochastic Nonlinear Systems With Unknown Output Function

Finite-Time Output Feedback Stabilization for High-Order Stochastic Nonlinear Systems With Unknown Output Function

Data-Driven Modeling of Microgrid Transient Dynamics Through Modularized Sparse Identification

Modularized sparse identification (M-SINDy) is developed in this paper for effective data-driven modeling of the nonlinear transient dynamics of microgrid systems. The high penetration of power-electronic interfaces makes microgrids highly susceptible to disturbances, causing severe transients, especially in the islanded mode. The M-SINDy method realizes distributed discovery of nonlinear dynamics by partitioning a higher-order microgrid system into multiple subsystems and introducing pseudo-states to represent the impact of neighboring subsystems. This specific property of the proposed algorithm is found to be very useful while working with re-configurable and scalable microgrids. The governing equations of the subsystems are identified through regression by mapping the nonlinear system's data to a linear system in a large functional space. The effectiveness of the M-SINDy method is tested and validated through numerical examples and comparisons with other existing identification models on a typical islanded microgrid. The method can simultaneously compute the governing equations of different subsystems and is examined to be robust to measurement noises and partial observations. This paper highlights the advances of data science in providing a potent tool for modeling and analyzing higher-order nonlinear microgrid systems. Dynamic discovery of system transients from measurements can be beneficial for designing control strategies that improve the overall microgrid stability and reliability.

Tracking Control of High-Order Nonlinear Systems With Unknown Control Gains and Its Application: An Adaptive Fuzzy Control Method

Tracking Control of High-Order Nonlinear Systems With Unknown Control Gains and Its Application: An Adaptive Fuzzy Control Method

Recovering Robust Feedback Linearization With Generative Adversarial Networks for Uncertain High-Order Nonlinear Systems: A Path to Safe Learning and Practical Deployment

Recovering Robust Feedback Linearization With Generative Adversarial Networks for Uncertain High-Order Nonlinear Systems: A Path to Safe Learning and Practical Deployment

Adaptive Prescribed-Time Filtered Control Design for a Full-State Constrained Nonlinear System.

In this article, an adaptive prescribed-time neural controller is developed for the tracking problem of a class of high-order nonlinear systems with full-state constraints. First, a prescribed-time bounded stability criterion is designed. Then, to handle the "explosion of complexity" problem of the backstepping method, an adaptive prescribed-time filter is constructed, in which the filter error is prescribed-time stable. Compared with existing methods, the newly designed transformation approach can accommodate a broader range of state constraint types. Then, the unknown nonlinear function is handled by radial basis function neural networks (RBFNNs). The adaptive prescribed-time neural control scheme is developed based on above. It can guarantee that the closed-loop system achieves the prescribed-time stability, and all states do not transgress the constraints. To demonstrate the effectiveness of the control strategy, comparative simulations are provided at the end.

Dynamics of a Higher-Order Three-Dimensional Nonlinear System of Difference Equations

In this paper, we study the semi-cycle analysis of positive solutions and the asymptotic behavior of positive solutions of three-dimensional system of difference equations with a higher order under certain parametric conditions. Furthermore, we show the boundedness and persistence, the rate of convergence of the solutions and the global asymptotic stability of the unique equilibrium point of the proposed system under certain parametric conditions. Finally, for this system, we offer some numerical examples which support our analytical results.

Role of Lorentz force and nanoparticles morphology on the dynamics of ternary hybrid nanofluid flow subject to porous disks and gyrotactic microorganisms

This article explains the significance of Lorentz force and nanoparticle morphology on the dynamics of ternary hybrid nanofluid through porous disks. The gyrotactic microorganisms are investigated to avoid possible sedimentation of solid particles and maintain fluid stability. A 3-dimensional flow problem in the presence of two different types of tri-hybrids nanofluid nanomaterials (Metallic and Nonmetallic Oxides) is used here. By eliminating the pressure term, the governing partial differential equations are transformed into a high-order nonlinear system of differential equations. This system is subsequently utilized to construct the boundary layer model, and these equations are solved numerically using a shooting technique based on the Runge–Kutta method, with the assistance of MATLAB software. The comparison and validation results are in good agreement through a numerical approach. Different-shaped nanoparticles have a significant influence on motile microorganisms. Shear stress near porous surfaces was significantly reduced due to an increase in nanoparticle size. The addition of all types of nanoparticles improved the thermal performance. Many desirable results for engineering purposes are observed under suitable conditions of simultaneous effect of magnetohydrodynamics (MHD) with microorganisms.