Stability Of Nonlinear Systems Research Articles

Hermitian Solutions of the Quaternion Algebraic Riccati Equations through Zeroing Neural Networks with Application to Quadrotor Control

The stability of nonlinear systems in the control domain has been extensively studied using different versions of the algebraic Riccati equation (ARE). This leads to the focus of this work: the search for the time-varying quaternion ARE (TQARE) Hermitian solution. The zeroing neural network (ZNN) method, which has shown significant success at solving time-varying problems, is used to do this. We present a novel ZNN model called ’ZQ-ARE’ that effectively solves the TQARE by finding only Hermitian solutions. The model works quite effectively, as demonstrated by one application to quadrotor control and three simulation tests. Specifically, in three simulation tests, the ZQ-ARE model finds the TQARE Hermitian solution under various initial conditions, and we also demonstrate that the convergence rate of the solution can be adjusted. Furthermore, we show that adapting the ZQ-ARE solution to the state-dependent Riccati equation (SDRE) technique stabilizes a quadrotor’s flight control system faster than the traditional differential-algebraic Riccati equation solution.

Anti-windup scheme-based control for fractional-order systems subject to actuator and sensor saturation

This paper addresses the problem of dissipative-based stabilization for fractional-order nonlinear control systems with uncertainties, time-delay, external disturbances, actuator faults, actuator and sensor saturations. Specifically, a non-fragile reliable dynamic output feedback controller is designed for the purpose of stabilization of the addressed system. Due to the effect of saturation phenomena occurring in both the actuator and sensor, the anti-windup loops framed with the help of the observer design are incorporated into the controller design. Some sufficient conditions are formulated in terms of linear matrix inequalities by choosing a suitable Lyapunov function thereby assuring the dissipative-based stabilization. The derived results are thus validated by two numerical examples including the practical model of two-stage chemical reactor.

Output feedback and adaptive output feedback control design for input-affine nonlinear systems based on Riemannian metrics

This paper deals with output feedback and adaptive output feedback control design for input-affine nonlinear systems on the basis of Riemannian metrics. Firstly, an observer for the considered class of nonlinear systems is proposed. Then, it is shown that by combining the introduced observer with state-feedback controllers in a suitable way, output tracking can be achieved. Moreover, the obtained results are extended to be used for adaptive output feedback stabilization of uncertain nonlinear systems. The introduced adaptive controller is more general than the existing adaptive output feedback ones because it does not assume any constraint on the structure of the system and the parametric uncertainty. Simulation results are presented to verify the effectiveness of the proposed control methods.

Theoretical and In Situ High Speed Measurement Study on Friction-Induced Vibration in Water Lubricated Rubber Bearing-Shaft System

A water-lubricated rubber stern bearing causes frictional vibration and noise under extreme conditions, severely threatening the survivability and concealment performance of underwater vehicles. To investigate the mechanism of friction-induced vibration and noise, a four-degree-of-freedom nonlinear dynamic model that included bearing support vibration, frictional bearing vibration and torsional shaft vibration was proposed. The velocity-dependent Stribeck friction model described the dynamic friction characteristics between the rubber bearing and stern shaft. Nonlinear system stability was examined using the Lyapunov indirect method and the transient dynamic responses determined by the Runge-Kutta method. Meanwhile, a high-speed in situ measurement experimental study was adopted to explore the mechanism of frictional and torsional vibrations in a water-lubricated bearing-shaft system. Results showed that nonlinear friction excitation was the fatal cause of friction-induced vibration in bearing-shaft system. Under different friction excitations, the coupling vibrations formed between the bearing and bearing support were different, resulting in two main modes of friction-induced vibration: “Chatter” and “Squeal.” The frictional vibration of the bearing and torsional vibration of the stern shaft were tightly coupled. These trends and results might provide a theoretical basis for further research on frictional vibration and wear control in water-lubricated rubber bearing-shaft systems.

Stability for nonlinear delay systems: Self-triggered impulsive control

This paper studies the stability problem of nonlinear delay systems in the framework of self-triggered impulsive control (STIC), where a class of self-triggered mechanisms is designed based on comparison approach. Different from the traditional event-triggered impulsive control (ETIC), in this paper the next impulse instant can be predicted at the previous impulse instant, and there is no need for state monitoring between two adjacent impulse instants. Under the proposed STIC strategy, some sufficient conditions for non-Zeno behavior and asymptotical stability of nonlinear delay systems are presented, respectively. Finally, two numerical examples are carried out to illustrate the effectiveness of the theoretical results.

Stability Analysis for Model-Based Event-Triggered Nonlinear Control Systems Under DoS Attacks

In this paper, we study the stability of a novel nonlinear event-triggered control system under denial-of-service (DoS) attacks based on an ISS-Lyapunov function analysis. A new dual-mode model-based event-triggering strategy is proposed which works based on consistency between the approximate and exact discretization of the nonlinear plant. We combine an event-triggered module with a controller based on the state prediction, together with a packetized transmission at the controller-to-actuator channel to provide the desired stability properties under DoS attacks. We also provide proof of Zeno-free behavior for the event-based system. Our proposed method provides a maximum percentage of time that the system can tolerate attacks without performance degradation. Finally, a numerical example is used to illustrate the effectiveness of the proposed approach.

Robust Stabilization of Time-Varying Nonlinear Systems With Time-Varying Delays: A Fully Actuated System Approach.

A general time-varying nonlinear uncertain system with time-varying delays is proposed, which is composed of two subsystems: one is an uncertain fully actuated subsystem representing the controllable part in the system, the other is an isolated globally uniformly asymptotically (GUA) stable autonomous subsystem which represents the uncontrollable part in the system. Both the single-order fully actuated system (FAS) and the multiorder FAS representations of the controllable subsystem are introduced. The problem of robust stabilization of such a compound system with full-state feedback can be converted into an input-to-state GUA stabilization problem of the fully actuated subsystem, which is solved for both types of single- and multiorder FASs with very general assumptions on the uncertain perturbed functions. Under certain conditions, the solution reduces to that for robust stabilization with partial-state feedback, and naturally reduce to that for robust stabilization of FASs. Two illustrative examples demonstrate both the effect and the application procedure of the proposed robust stabilization approach.

Finite-Time Stability of Nonlinear Systems With Delayed Impulses

Finite-Time Stability of Nonlinear Systems With Delayed Impulses

Hyperbolic function-based fixed/preassigned-time stability of nonlinear systems and synchronization of delayed fuzzy Cohen–Grossberg neural networks

In this article, the fixed-time (FIT) and preassigned-time (PRT) stability of nonlinear models and the FIT/PRT synchronization of discontinuous delayed fuzzy Cohen–Grossberg neural networks (DFCGNNs) are explored, respectively. Firstly, by means of hyperbolic-cosine function and Gudermannian function, a novel FIT stability theorem is established by utilizing Lyapunov method. Then, based on the developed stability theorem, several new discontinuous control schemes with hyperbolic-cosine function are developed to discuss the FIT synchronization of DFCGNNs. Furthermore, the PRT synchronization is also explored by slightly modifying FIT control schemes, where the synchronization time is predetermined. Eventually, two numerical examples are provided to validate the theoretical research.

Generalized Lyapunov stability theory of continuous-time and discrete-time nonlinear distributed-order systems and its application to boundedness and attractiveness for networks models

The Lyapunov direct method is a powerful tool for analyzing the stability of nonlinear dynamical systems. However, most existing research has primarily focused on asymptotic stability, neglecting the crucial aspect of boundedness. In light of this, this paper aims to address the issues concerning the generalized Lyapunov stability theory of distributed-order systems and its application to ensure uniform boundedness and global attractiveness for distributed-order Hopfield neural networks (DOHNNs) with time-varying external input. To achieve this, several essential inequalities that form the foundation of our main work are proposed. Subsequently, two stability criteria in the form of generalized distributed-order Lyapunov theorem are derived by employing Laplace transform techniques. Meanwhile, building upon the proposed inequalities and Lyapunov theorem, sufficient conditions that guarantee the uniform boundedness and global attractiveness of DOHNNs with time-varying external input are established. By the way, all our proposed conclusions are presented in both continuous-time and discrete-time cases to present the distinction and relationship between these two cases. Finally, various simulation examples are designed meticulously to validate the correctness of our proposed theorems and the effectiveness to real-world applicability of our approach.

Output-Feedback Control of Interconnected Nonlinear Systems With Both State and Input Delays Based on Truncated Prediction

In this paper, we investigate decentralized output-feedback control of interconnected nonlinear systems with both state and input delays. Unlike existing related works, in this paper, both the state delays and the input delay of each subsystem are unknown and different from each other. In order to achieve global asymptotic stability of the interconnected nonlinear system based on output feedback, we construct a finite-dimensional observer based on the output information to asymptotically estimate the state information. Simultaneously, based on a truncated prediction of the system state over the delay period, a novel decentralized observer-based output-feedback controller is proposed for each subsystem. Then, under the framework of Lyapunov-Krasovskii functional, a set of conditions for the global asymptotic stability of the closed-loop system is determined. Finally, a simulation example is given to verify the effectiveness of the proposed control scheme.

Finite- and Fixed-Time Nonovershooting Stabilizers and Safety Filters by Homogeneous Feedback

Non-overshooting stabilization is a form of safe control where the setpoint chosen by the user is at the boundary of the safe set. In this paper we develop homogeneous feedback laws for fixed-time nonovershooting stabilization for nonlinear systems that are input-output linearizable with a full relative degree, i.e., for systems that are diffeomorphically equivalent to the chain of integrators. These homogeneous feedback laws can also assume the secondary role of ‘fixed-time safety filters’ (FxTSf filters) which keep the system within the closed safe set for all time but, in the case where the user's nominal control commands approach to the unsafe set, allow the system to reach the boundary of the safe set no later than a desired time that is independent of nominal control and independent of the value of the state at the time the nominal control begins to be overridden.

Practical Finite-Time Stability of Nonlinear Systems With Delayed Impulsive Control

Practical Finite-Time Stability of Nonlinear Systems With Delayed Impulsive Control

Semi-global robust stabilisation of disturbed nonlinear systems with state-dependent uncertainties: a DOBC approach

The robust stabilisation for a general class of disturbed nonlinear systems subject to state-dependent uncertainties is addressed in this paper. Different from most existing results, the lumped uncertainty, including external disturbances and model uncertainties, is relaxed to be bounded by some nonlinear functions rather than constants in this paper. Based upon the classical design procedure of disturbance observer-based control (DOBC), a new continuous saturation-based dynamic controller is proposed to estimate the lumped uncertainty. By the delicate design of several compact sets, the qualitative robust stability of the closed-loop system is guaranteed in the sense that all the signals of the closed-loop system can converge to an arbitrarily small compact set in a finite time. Furthermore, when the external disturbances are constants, the semi-global asymptotic stability can also be guaranteed by the proposed controller. Finally, the relationship between system uncertainties and observer gain is shown by a numerical simulation example.

Fixed‐time adaptive neural tracking control for nonlinear multiagent systems with communication link faults

AbstractThis paper addresses the fixed‐time adaptive neural distributed control problem of uncertain nonlinear multiagent systems (MASs) with unknown communication link faults. To handle the unknown terms caused by communication link faults and the unknown functions in each agent, a radial basis function neural network (RBF NN) is employed. In contrast to existing methods that focus solely on practical finite‐/ fixed‐time stability of nonlinear systems, the control scheme developed in this paper goes beyond by not only mitigating the effects of unknown communication link faults in nonlinear MASs but also addressing the singularity problem of fixed‐time controllers. These advancements are realized through the design of new power exponent functions and the introduction of new lemmas. This way, the tracking error of MASs converges to a preset range within a fixed time and achieves better control performance. Finally, the feasibility of the proposed scheme is verified through two simulations.

New results on finite‐time stability and H∞control for nonlinear Hamiltonian systems

AbstractIn this paper, we investigate the finite‐time stability (FTS) and control of nonlinear Hamiltonian systems with time‐varying state delays and output delays subject to input saturation. By introducing a new class of Lyapunov–Krasovskii (L‐K) functionals and the assumption about the Hamiltonian function, we present a delay‐dependent FTS criterion. Then, a finite‐time feedback control is designed for the nonlinear Hamiltonian systems. Finally, the validity of the proposed results is demonstrated by a numerical example.

Global stability of discrete-time non-linear systems with descriptor standard and fractional positive linear parts and scalar feedbacks

Global stability of discrete-time non-linear systems with descriptor standard and fractional positive linear parts and scalar feedbacks

Stability of nonlinear impulsive systems with non-uniformly distributed packet loss

This study focuses mainly on the stability of a class of nonlinear systems with impulsive disturbance. In particular, we consider the possible non-uniformly distributed packet loss phenomenon in the controller-to-actuator channel. This packet loss is described by a characterization scenario in the average sense, known as the average packet loss interval (APLI). In this scenario, an average allocation strategy between the number of impulsive sampling intervals and the length of packet loss intervals is established. This implies that the limitations on the proportion or the upper bound of packet loss intervals can be relaxed. A sampled-data control is put forward based on impulsive disturbance, which not only brings better control performance but also reduces conservatism. In view of the Halanay inequality, the number of subsystem switchings caused by packet loss is allowed to be arbitrary. Based on the elastic constraint relationships established between system parameters and APLI, a series of conditions guaranteeing the globally uniformly exponential stability (GUES) are provided. Further, the admissible packet loss intervals can be estimated on an average basis by solving an algebraic inequality. Finally, a numerical example is discussed to demonstrate the validity of our study.

Finite-time robust adaptive simultaneous stabilisation of nonlinear time-delay systems with actuator saturation

This paper focuses on finite-time robust adaptive simultaneous stabilisation for nonlinear time-delay systems, taking into account actuator saturation and unknown parameters. Firstly, by employing adaptive control strategies and finite-time stability theory, a finite-time adaptive simultaneous stabilisation scheme for the nonlinear time-delay systems is developed. Secondly, utilising the orthogonal decomposition method, a finite-time robust adaptive simultaneous stabilisation scheme for nonlinear time-delay systems with external disturbances is proposed. Finally, simulations demonstrate the effectiveness of the provided control scheme.

Stability and multi-frequency dynamic characteristics of nonlinear grid-connected pumped storage-wind power interconnection system

Stability and multi-frequency dynamic characteristics of nonlinear grid-connected pumped storage-wind power interconnection system