High-order Nonlinear Systems Research Articles

Adaptive Fixed-Time Control for State-Constrained High-Order Uncertain Nonlinear Cyber-Physical Systems Under Malicious Attacks

A novel fixed-time adaptive fuzzy tracking control strategy is developed to resolve the fixed-time tracking control issue for a category of state-constrained high-order uncertain nonlinear cyber-physical systems (CPSs), which suffer from malicious attacks launched in controller-actuator (C-A) channel. The proposed control strategy is independent of the exact system model and can accommodate external disturbances and malicious attacks. Meanwhile, distinguished from the existing control methods for state-constrained uncertain CPSs under malicious attacks which can only ensure the system performance when time leans towards infinity or in finite time, the presented control strategy can guarantee the system performance in fixed time. It has been substantiated that the developed control strategy can make sure that the output tracking error converges to a predefined small neighborhood of the origin, and all signals of the resulting closed-loop system satisfy the corresponding time-varying state constraints during the total operation. In particular, the settling time and tracking precision are known and can be preconfigured by selecting the design parameters appropriately. More significantly, all the initial states of the system are independent of the developed fixed-time adaptive fuzzy tracking control law and can be arbitrarily chosen in the constrained region specified by the corresponding time-varying state constraints conditions. Ultimately, a representative simulation is supplied to illustrate the effectiveness and superiority of the proposed control scheme.

Adaptive guaranteed cost control for nonlinear systems with unknown parameters and time delays based on fully actuated system approaches

This paper investigates the adaptive guaranteed cost stabilization (AGCS) problems for two classes of high-order nonlinear systems with unknown parameters (vector) and time delays. Firstly, based on the high-order fully actuated (HOFA) system approaches, the Lyapunov–Krasovskii functional (LKF) and the guaranteed cost control (GCC), a new AGCS strategy is proposed for HOFA nonlinear system with unknown parameter vector and time delays. Then, based on the above result, another AGCS controller for a class of strict-feedback systems (SFSs) with unknown parameters and time delays is obtained. Two designed controllers ensure that all of the states of two closed-loop systems are global boundedness, and preset arbitrarily the upper bound of cost functions (UBCFs) characterizing the output performance. More importantly, the UBCFs are independent of system initial values, unknown parameters (vector), and even time delays, which is difficult to achieve by using existing control methods. To do this, this paper introduces a local smooth nonlinear function (LSNF), and gives its corresponding lemma, which provide an important mathematical tool. Finally, three simulation examples, including an application in the electromechanical system, are given to prove the effectiveness and the practicability of our proposed control method.

Prescribed-Time Control for Stochastic High-Order Nonlinear Systems With Parameter Uncertainty

This brief focuses on the problem of prescribed-time mean-square control for uncertain stochastic high-order (p-normal) nonlinear systems. Compared to existing results, a more general model is considered. First, a prescribed-time mean-square stable controller is constructed with the assistance of the power integrator technique, the time-varying prescribed-time function and a non-scaling framework. Then, based on the stability theorem of stochastic systems and the useful proposition of the selected Lyapunov function, the prescribed-time mean-square stability of all signals is analyzed. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed control strategy.

Transient Stability Analysis for a Multi-VSC Parallel System Based on the CFND Method

Because of the control complexity of voltage source converters (VSCs), transient stability analysis of multi-VSC parallel systems is challenging, and there are still no effective methods to solve this problem. Inspired by the decoupling principle and combined with the normal form method, an innovative coupling-factor-based nonlinear decoupling (CFND) method is proposed. According to the coupling factors that can be used to evaluate the nonlinear coupling degree among different state variables, the CFND method approximately transforms a high-order nonlinear multi-VSC parallel system into multiple decoupled low-order modes. Thus, the transient stability of the original high-order multi-VSC system can be reflected indirectly by the mature inversing trajectory method and the phase plane method. The CFND method has universality, flexibility, and insensitivity to system order, and no need to construct corresponding Lyapunov functions for different nonlinear systems, breaking through the inherent limitations of traditional analysis methods. Furthermore, this paper derives a reduced-order large-signal model and the corresponding truncated model for a single VSC grid-connected system. The effectiveness of the reduced-order model is verified through simulation waveforms and ROAs partitioning. Subsequently, a generalized model of the multi-VSC grid-connected system is developed. Finally, taking the grid-connected system with three VSCs as an example, the proposed CFND method is used to analyze typical operation cases, and the conclusions of transient stability analysis are verified using the hardware-in-loop (HIL) experiments.

Fuzzy adaptive resilient control against unknown false data injection attacks for high-order nonlinear systems with actuator failures

An adaptive resilient control technique for high-order nonlinear systems with actuator failures is presented in this work. The unknown false data injection (FDI) attacks make all controlled system states unavailable. To counteract this negative impact of FDI attacks, a new coordinate transformation is constructed during the procedure of recursive design. Moreover, the effect of the actuator faults is completely eliminated by skillfully designing the controller and the adaptive laws. On the basis of the backstepping technology and the Nussbaum gain technique, an adaptive resilient control strategy is presented by using compromised state variables, which ensures all the signals of the closed-loop system is bounded when the sensor is attacked. Compared with the existing results, the proposed control approach not only solves the resilient control problem of high-order nonlinear systems whose powers are positive odd numbers, but also eliminates the assumption that the attack weights are positive. In the end, a simulation result is presented to verify the feasibility of the designed scheme.

Low-complexity prescribed performance tracking control for uncertain high-order nonlinear systems considering input quantization

Low-complexity prescribed performance tracking control for uncertain high-order nonlinear systems considering input quantization

Global Consensus Tracking Control for High-Order Nonlinear Multiagent Systems With Prescribed Performance.

In this article, we investigate the prescribed performance tracking control problem for high-order nonlinear multiagent systems (MASs) under directed communication topology and unknown control directions. Different from most existing prescribed performance consensus control methods where certain initial conditions are needed to be satisfied, here the restriction related to the initial conditions is removed and global tracking result irrespective of initial condition is established. Furthermore, output consensus tracking is achieved asymptotically with arbitrarily prescribed transient performance in spite of the directed topology and unknown control directions. Our development benefits from the performance function and prescribed-time observer. Both theoretical analysis and numerical simulation confirm the validity of the developed control scheme.

Neural network-based output tracking control of high-order nonlinear systems with DoS attacks and perturbations

This paper focuses on the output feedback tracking control of a high-order nonlinear system with denial-of-service (DoS) attacks and exogenous disturbances. A radial basis function neural network (RBFNN)-based state observer is employed to estimate the system states. A new nonlinear filter with adaptive regulation is developed to eliminate the impacts of perturbed factors such as RBFNN approximation errors and disturbances. Constituting with filtering operation and backstepping control technique, a RBFNN-based security controller is constructed to suppress the influences of perturbations and DoS attacks based on the observation signals. The uniformly ultimately bounded output tracking result is established by using the security control signals via Lyapunov criterion in the cases of DoS attacks, nonlinearities, and disturbances. Comparative results are provided to validate the efficiency of the developed RBFNN-based observation and security control strategies of a nonlinear system.

Computer simulation of tracking in high-order nonlinear systems with time delay

In this paper, we study the problem of global practical tracking of a class of high-order nonlinear systems with feedback. A feature of the system under consideration is that the degree of limitation of the upper boundary of the nonlinearity is taken on a continuous interval. We develop a tunable and delayindependent tracking controller that dominates the effect of delay time non-linearity by generating a Lyapunov function, respectively, using a generalized method of adding a signum function and a power integrator. The resulting controller ensures global boundedness of all states of the studied closed system and a sufficiently small control error over a finite time. In addition, in this work, priority was given to computer simulation of previously achieved results.

Adaptive Cooperative Secure Control of Networked Multiple Unmanned Systems under FDI Attacks

With the expanding applications of multiple unmanned systems in various fields, more and more research attention has been paid to their security. The aim is to enhance the anti-interference ability, ensure their reliability and stability, and better serve human society. This article conducts adaptive cooperative secure tracking consensus of networked multiple unmanned systems subjected to false data injection attacks. From a practical perspective, each unmanned system is modeled using high-order unknown nonlinear discrete-time systems. To reduce the communication bandwidth between agents, a quantizer-based codec mechanism is constructed. This quantizer uses a uniform logarithmic quantizer, combining the advantages of both quantizers. Because the transmission information attached with the false data can affect the accuracy of the decoder, a new adaptive law is added to the decoder to overcome this difficulty. A distributed controller is devised in the backstepping framework. Rigorous mathematical analysis shows that our proposed control algorithms ensure that all signals of the resultant systems remain bounded. Finally, simulation examples reveal the practical utility of the theoretical analysis.

Adaptive guaranteed cost tracking control for high-order nonlinear systems based on fully actuated system approaches

This paper considers the adaptive guaranteed cost tracking (AGCT) control problems for two classes of high-order nonlinear systems with unknown parameters. A new local smooth nonlinear function (LSNF) is introduced first, which provides an important mathematical tool for our controller design. Then, based on the LSNF and the high-order fully actuated (HOFA) system approaches, the AGCT controller is designed for HOFA system with unknown parameter, which guarantees that all of the states of the closed-loop HOFA system are globally bounded, and the tracking error is asymptotically convergent. Moreover, the upper bound of cost function (UBCF) characterizing the tracking performance can be arbitrarily preseted, and is completely independent of the system initial value and the unknown parameter, which significantly improves the tracking performance, and is difficult to achieve by using existing guaranteed cost control (GCC). Furthermore, an extra result, the AGCT controller for a class of strict-feedback systems with high-order form and unknown parameters, is obtained in this paper, which also guarantees that the system tracking error is globally asymptotically convergent with the arbitrarily preseted UBCF characterizing the tracking performance. Three simulation examples, including an inverted pendulum, are presented to show the effect and the superiority of the proposed method.

Adaptive stabilisation of output-constrained high-order nonlinear systems with high-order and low-order nonlinearities

This paper investigates the adaptive stabilisation of output-constrained high-order nonlinear systems with more general high-order and low-order nonlinearities. By skilfully introducing nonlinear mappings, a key coordinate transformation, integral Lyapunov functions and the sign function into the adding a power integrator technique, and combining a novel analysis method, a continuous adaptive state-feedback controller is constructed. When the initial value of system states lies in the constrained set, it is rigorously proved that all the closed-loop signals are uniformly bounded, the asymmetric output constraint isn't transgressed, and the equilibrium point of the closed-loop system is uniformly asymptotically stable. A simulation example shows the effectiveness of this control scheme.

Neuro-Based Consensus Seeking for Nonlinear Uncertainty Multi-Agent Systems Constrained by Dead-Zone Input

The topic about consensus target track seeking for high-order nonlinear multi-agent systems (MASs) with unmodeled dynamics, dynamic disturbances, and dead-zone input is considered in the paper. Using the strong nonlinear map characteristic of radial basis function neural networks (RBFNNs), the complex functions arising from recursive procedure are simplified. Also, inspired by input-to-state practical stability (ISpS), the authors construct a dynamical signal in order to counteract the impact of unmodeled dynamics and dynamic disturbances. The bounded inequality expression has been applied to tackle the unknown input of dead zone. Based on this, consensus control protocol suitable for nonlinear constraints has been constructed by using the recursive backstepping technique and adaptive neural network method. Theoretical analysis indicates not only the uniform boundary of all signals in the closed-loop under the neuro-based consensus controller, but uniform ultimate convergence of consensus tracking errors. The final simulations also confirmed the correctness of the theoretical analysis.

Global Tracking Control for High-Order Odd-Rational-Powers Systems with Unknown Nonlinearities and Powers

The global control problem of high-order nonlinear systems with unknown odd rational powers and nonlinearities has been solved in this paper for the first time. Barrier functions were introduced into the controller to set the controller free from rational powers, which solved the problem caused by unknown odd rational powers. In utilizing barrier functions and their inverse functions, two transformations were constructed for the state and tracking errors, which resulted in the global tracking controller for the high-order odd-rational-powers nonlinear systems with unknown system nonlinearities. No knowledge of system nonlinearities and odd rational powers is required to construct the controller in this paper, and only control gains are assumed to be positive to guarantee the controllability of the system, which implies that the proposed method is model-free and has much more relaxed conditions than all the existing methods for high-order nonlinear systems. The global boundedness of all closed-loop signals was proved based on the Lyapunov stability theorem. Finally, simulation results were given to demonstrate the effectiveness of the proposed method.

Fuzzy Adaptive Asymptotic Control for a Class of Large-Scale High-Order Unknown Nonlinear Systems

This paper studies the asymptotic control problem of a class of large-scale high-order nonlinear systems (LSHONSs), and an asymptotic fuzzy adaptive dynamic surface controller is developed. Unknown nonlinear terms are learned online by fuzzy logic systems (FLSs) such that the accurate nonlinear model is released in the controller design procedure, where the parameters of FLSs are updated by developing adaptive laws. To compensate for the “boundary error” caused by the dynamic surface control method where a linear filter is added in the backstepping procedure to handle the “explosion of complexity” problem, a nonlinear filter is proposed to eliminate the boundary layer error. Some simulations are given to demonstrate the effectiveness of the proposed algorithm.

Optimization controller synthesis using adaptive robust control Lyapunov and barrier functions for high-order nonlinear system

Optimization controller synthesis using adaptive robust control Lyapunov and barrier functions for high-order nonlinear system

Adaptive Fuzzy Fixed-Time Control for High-Order Nonlinear Systems With Sensor and Actuator Faults

The adaptive fuzzy fixed-time fault-tolerant tracking control problem for high-order nonlinear systems (HONS) with sensor and actuator faults is considered in this paper. The fuzzy logic systems is introduced to approximate the unknown nonlinear functions of the HONS. In addition, on the basis of backstepping technology and fixed-time theory, an adaptive fuzzy fixed-time fault-tolerant controller is developed to ensure all signals of the closed-loop HONS to be bounded. Eventually, the numerical example can be shown to prove rationality of developed method.

A novel adaptive neural network-based time-delayed estimation control for nonlinear systems subject to disturbances and unknown dynamics

This paper presents an adaptive backstepping-based model-free control (BSMFC) for general high-order nonlinear systems (HNSs) subject to disturbances and unstructured uncertainties to enhance the system tracking performance. The proposed methodology is constructed based on the backstepping control (BSC) with radial basis function neural network (RBFNN) -based time-delayed estimation (TDE) to overcome the obstacle of unknown system dynamics. Additionally, a command-filtered (CF) approach is involved to address the complexity explosion of the BSC design. As the errors arising from approximation, new control laws are established to reduce the effects in this regard. The stability of the closed-loop system is guaranteed through the Lyapunov theorem and the superiority of the proposed methodology is confirmed through a comparative simulation with other model-free approaches.

A new strongly predefined time sliding mode controller for a class of cascade high-order nonlinear systems

A new strongly predefined time sliding mode controller for a class of cascade high-order nonlinear systems

Fixed-time safe tracking control of uncertain high-order nonlinear pure-feedback systems via unified transformation functions

Fixed-time safe tracking control of uncertain high-order nonlinear pure-feedback systems via unified transformation functions