Lower Triangular Nonlinear Systems Research Articles

Fixed-time stabilization for lower-triangular nonlinear systems under the p-normal form

This article investigates the fixed-time stabilization (FTS) problem for lower-triangular nonlinear systems under the [Formula: see text]-normal form. Under suitable assumptions condition of the system’s nonlinearities, a novel fixed-time partial-state feedback (PSF) control law is designed using backstepping design method and adding a power integrator (API) technique. With the help of one appropriate Lyapunov function, it is shown that the partial-state of the corresponding closed-loop system is fixed-time stable. Numerical simulation is given to illustrate the potency of the suggested continuous partial-sate feedback controller.

Robust cooperative output regulation for heterogeneous nonlinear multi-agent systems with an unknown exosystem subject to jointly connected switching networks

This paper investigates the robust cooperative output regulation problem for heterogeneous lower triangular nonlinear multi-agent systems with an unknown exosystem over jointly connected switching networks. The problem has been studied for the exactly known exosystem over switching networks. However, the existing result for the unknown exosystem is still limited to the static networks. To ensure that all followers acquire the reference trajectory generated by the unknown exosystem through the jointly connected switching networks, by combining a set of auxiliary filtering variables and fixed-time stability theory, an adaptive distributed observer is designed. On the basis of the adaptive distributed observer and the distributed internal model approach, we propose a distributed controller under several standard assumptions to solve the problem. Compared with the similar work subject to the static networks, the controller in this paper is applicable to the more general communication network while weakening the assumptions of the controlled system.

Output regulation problem with prescribed performance for nonlinear lower-triangular system

ABSTRACT This paper addresses the output regulation problem with prescribed performance for nonlinear lower-triangular systems. To achieve the transient prescribed performance, the output transformation technique and barrier Lyapunov function technique are introduced to solve the output regulation problem. The prescribed performance control scheme based on normal backstepping is constructed not only to restrict the output error of the closed-loop system keeping in a prescribed performance bound, but also to achieve that the output tracks a designed trajectory asymptotically. The effectiveness of the proposed method is illustrated by two simulation examples.

Stabilization of Triangular Nonlinear Systems With Multiplicative Stochastic State Sensing Noise

We present new state-feedback control designs for lower-triangular/upper-triangular nonlinear systems with multiplicative stochastic sensor uncertainty. For lower-triangular nonlinear systems with small sensor noise, we develop a novel control design where the control gains are suitably constructed to simultaneously dominate the nonlinear functions and sensor noise of sufficiently small multiplicative gain. For upper-triangular nonlinear systems, we propose a new low-gain domination design, the advantage of which is that it can effectively deal with the sensor noise with arbitrarily large intensities. These two designs can both ensure that closed-loop system has an almost surely unique global solution, the origin of the closed-loop system is mean-square stable, and the states can be regulated to zero almost surely. Finally, two simulation examples are given to illustrate the designs.

Leader–follower consensus for nonlinear multi-agent systems with unknown measurement sensitivities

In this paper, the leader–follower consensus problem is investigated for a class of lower-triangular nonlinear multi-agent systems with unknown measurement sensitivities. By developing a dual-domination gain method, a distributed compensator is proposed for each follower by utilising the output information of the follower and its neighbour agents. Based on the compensator, an output feedback control law is designed to achieve consensus. These two gains are used to deal with the unknown measurement noises and nonlinear terms, respectively. Then the consensus problem is transformed into a stability problem by introducing an appropriate state transformation. Based on the Lyapunov stability theory, it is proved that the states of the leader and followers can achieve consensus asymptotically. In the end, numerical simulations are provided to verify the correctness of the proposed consensus algorithm.

Global Regulation by Integral Feedback for Lower-Triangular Nonlinear Systems with Actuator Failures and Limited Delays

This paper studies the global asymptotic regulation problem for a class of lower-triangular nonlinear systems with actuator failures and limited delays. New integral controllers consisting of an integral dynamic are constructed to make all system states bounded and asymptotically convergent to zero. First, an integral dynamic is constructed and a novel state transformation is introduced, which ensures that the involved systems with actuator failures are converted into a class of auxiliary nonlinear systems without actuator failures. Second, by introducing the static high-gain technique, the problem of designing integral controllers for auxiliary nonlinear systems is converted into that of designing the gain parameter and determining the limit of the actuator delay. At last, with the help of the Lyapunov stability theorem, the gain parameter and the limit of the actuator delay are determined, and the stabilization of the auxiliary nonlinear systems yields the global asymptotic regulation of the involved systems. A physical system example is given to demonstrate the effectiveness of the proposed integral controllers.

Leader-following consensus for lower-triangular nonlinear multi-agent systems with unknown controller and measurement sensitivities

Leader-following consensus for lower-triangular nonlinear multi-agent systems with unknown controller and measurement sensitivities

Low-complexity observer–based output-feedback tracking control for a class of nonlinear lower-triangular systems

The tracking control problem for a group of nonlinear lower-triangular systems with multiple uncertainties is investigated in this work. Wherein, a novel performance constraint is first constructed to guarantee the fixed-time convergence of the output tracking error. Subsequently, a linear extended high-gain observer is employed to estimate the system uncertainties including the unmeasured states and the external disturbances. Based on the observer estimations, a novel output-feedback tracking control approach is formulated via using the backstepping technique, to ensure the boundedness of the closed-loop system. Compared with the existing works, the primary advantages of the proposed design are that (1) the problem of "explosion of terms" is avoided by eliminating the need for the derivative of the virtual control signals and (2) without the use of extra auxiliary techniques, the fixed-time convergence can be guaranteed, where the convergence time is independent of the system states and initial conditions. Then, the results about system stability are proved by the theoretical analysis. Moreover, an extension of the proposed approach to multi-input multi-output systems is deduced in this paper to further present its versatility. Finally, two groups of numerical examples are performed to validate the effectiveness of the proposed controller.

Adaptive Neural Control of Uncertain MIMO Nonlinear Pure-Feedback Systems via Quantized State Feedback

We present an adaptive quantized state feedback tracking methodology for a class of uncertain multiple-input multiple-output (MIMO) nonlinear block-triangular pure-feedback systems with state quantizers. Uniform quantizers are considered to quantize all measurable state variables for feedback. Compared with the existing tracking approaches of MIMO lower-triangular nonlinear systems, the main contributions of the proposed strategy are developing (1) a quantized-state-feedback-based adaptive tracker in the presence of nonaffine interaction of states and control variables of MIMO systems and (2) an analysis strategy for quantized feedback stability using adaptive compensation terms to derive bounded quantization errors. In addition, the stability of the closed-loop system with quantized state feedback is analyzed based on the Lyapunov stability theorem. Finally, simulation examples, including interconnected inverted pendulums, are presented to validate the effectiveness of the proposed control strategy.

Global Finite-Time Output-Feedback Stabilization of Nonlinear Systems Under Relaxed Conditions

This article presents a first constructive solution to the global finite-time output feedback stabilization of a large class of lower triangular nonlinear systems under relaxed conditions. The key idea is to introduce a switching strategy in the control design scheme. Unlike the previous literature, the nonlinearities of the systems are assumed to satisfy a general Hölder continuous condition, which include Lipschitz continuous nonlinearities as a special case. Global finite-time stability of the closed-loop observer-controller systems is proved by means of innovative Lyapunov-based analytical techniques. A benchmark practical example of controlling the single-link robotic manipulator coupled to a dc motor is adopted to illustrate the proposed method.

Reduced-Order Observer-Based Adaptive Fuzzy Tracking Control Scheme of Stochastic Switched Nonlinear Systems

In this article, an adaptive approximation-based output-feedback tracking control scheme is presented for a class of stochastic switched lower-triangular nonlinear systems with input saturation and unmeasurable state variables. First, to overcome the design obstacle caused by the nondifferential saturation nonlinearity, a carefully selected nonlinear function of the control input signal is applied to estimate the saturation function. Then, a reduced-order state observer is designed to model the unmeasured system states, which also means the error system can be established. Furthermore, the fuzzy-logic systems are utilized to approximate the unknown system nonlinearities in the adaptive backstepping-based controller design procedure. It is ensured that all the closed-loop system variables are bounded in probability and the error signal belongs to a compact set in the mean square sense. Finally, the effectiveness and the practicability of the proposed control scheme are shown by two examples.

Adaptive State-Quantized Control of Uncertain Lower-Triangular Nonlinear Systems with Input Delay

In this paper, we investigate the adaptive state-quantized control problem of uncertain lower-triangular systems with input delay. It is assumed that all state variables are quantized for the feedback control design. The error transformation method using an auxiliary time-varying signal is presented to deal with the compensation problem of input delay. Based on the error surfaces with the auxiliary variable, a neural-network-based adaptive state-quantized control scheme is constructed with the design of the input delay compensator. Different from existing results in the literature, the proposed method exhibits the following features: (i) compensating for the input delay effect by using quantized states; and (ii) establishing the stability of the adaptive quantized feedback control system in the presence of input delay. Furthermore, the boundedness of all the signals in the closed-loop and the convergence of the tracking error are analyzed. The effectiveness of the developed control strategy is demonstrated through the simulation on a hydraulic servo system.

Decentralized event-triggered adaptive control of a class of uncertain interconnected nonlinear systems using local state feedback corrupted by unknown injection data

This paper investigates a decentralized event-triggered adaptive control problem of uncertain interconnected lower-triangular nonlinear systems using corrupted local state feedback. The unknown injection data such as sensor faults or cyber attacks are assumed to be added to full state feedback measurements of each subsystem with unknown nonlinearities. Under this assumption, exactly measured local state variables are unknown during Lyapunov-stability-based recursive control design steps. The primary contributions of this study are (i) to develop a recursive adaptive control design strategy for achieving decentralization of unmatched interconnected nonlinearities using corrupted local state feedback information and (ii) to design a decentralized asynchronous event-triggering mechanism using the corrupted local state variables. To this end, local injection data compensators using neural networks and adaptive tuning laws are designed to compensate for unknown injection data and nonlinear interaction effects. It is shown that the proposed decentralized control system via the corrupted local state feedback ensures the practical stability of the total closed-loop system and the exclusion of Zeno behavior.

Backstepping Active Disturbance Rejection Control for Lower Triangular Nonlinear Systems With Mismatched Stochastic Disturbances

In this article, we apply the active disturbance rejection control (ADRC) to the output tracking of a class of lower triangular nonlinear systems subject to mismatched bounded stochastic disturbances of unknown statistic characteristics and nonvanishing at the origin. A major obstacle is that the paths of the stochastic disturbances are nowhere differentiable almost surely which causes that the stochastic disturbances cannot be refined into the control input channel by the usual way of state transformation. To overcome this obstacle, a set of second-order extended state observers is first designed to estimate, in real time, the disturbance in each channel, and then a backstepping ADRC based on feedforward compensation and a constructive backstepping procedure is developed, guaranteeing that the closed-loop output tracks a time-varying reference signal in practically mean square and the closed-loop states are practically bounded in probability first defined in this article. Finally, some numerical simulations are presented to validate the effectiveness of the proposed backstepping ADRC approach.

Neural-Network-Based Distributed Asynchronous Event-Triggered Consensus Tracking of a Class of Uncertain Nonlinear Multi-Agent Systems.

This article proposes a neural-network-based adaptive asynchronous event-triggered design strategy for the distributed consensus tracking of uncertain lower triangular nonlinear multi-agent systems under a directed network. Compared with the existing event-triggered recursive consensus tracking designs using multiple neural networks for each follower and continuous communications among followers, the primary contribution of this study is the development of an asynchronous event-triggered consensus tracking methodology based on a single-neural network for each follower under event-driven intermittent communications among followers. To this end, a distributed event-triggered estimator using neighbors' triggered output information is developed to estimate a leader signal. Subsequently, the estimated leader signal is used to design local trackers. Only a triggering law and a single-neural network are used to design the local tracking law of each follower, irrespective of unmatched unknown nonlinearities. The information of each follower and its neighbors is asynchronously and intermittently communicated through a directed network. Thus, the proposed asynchronous event-triggered tracking scheme can save communicational and computational resources. From the Lyapunov stability theorem, the stability of the entire closed-loop system is analyzed and the comparative simulation results demonstrate the effectiveness of the proposed control strategy.

A General Fixed-Time Observer for Lower-Triangular Nonlinear Systems

The design of global fixed-time observer for a category of lower-triangular nonlinear systems is reported in this brief. Under a wild condition that admits the Hölder continuous conditions as a special case, a constructive algorithm of global fixed-time observer design is proposed by virtue of non-recursive combining bi-limit homogeneous technique. Rigorous stability analysis as well as robustness with respect to exogenous disturbances is provided to show the proposed observer ensuring global fixed-time convergent performance of the estimation error dynamics. Simulation results of an example of MEMS mirror with the nonlinear viscous damping dissipative load are given to confirm the effectiveness of the proposed algorithm.

측정민감도와 비억제 성장율을 가지는 하삼각 비선형 시스템의 출력궤환 안정화

We propose an output feedback controller for lower triangular nonlinear systems which have the measurement sensitivity in the output function and the unbounded growth rate in the nonlinearities. To solve the regulation problem of the considered systems, the controller with a dynamic gain is newly designed by utilizing the range of the measurement sensitivity and the growth rate of the unbounded function. As a result, more generalized lower triangular nonlinear systems can be regulated by output feedback under the measurement sensitivity.

Neural-networks-based adaptive quantized feedback tracking of uncertain nonlinear strict-feedback systems with unknown time delays

We develop a quantized-feedback-based adaptive delay-independent control design for systems with unknown strict-feedback nonlinearities and time-varying delays. It is assumed that full state variables quantized by uniform quantizers are only available for the feedback control design. Compared with the previous adaptive control designs of lower-triangular nonlinear time-delay systems, the major contribution of this paper is to develop quantized-states-basedmemoryless adaptive control and stability analysis strategies to deal with unmatched and unknown time-delay nonlinearities. An adaptive neural network controller and its adaptive laws are designed via quantized state variables where neural networks are employed to compensate for unknown time-delay nonlinear effects. By deriving theoretical lemmas on the boundedness of quantization errors of the closed-loop signals, the stability of the resulting closed-loop system and the convergence of the tracking error are analyzed. Finally, simulation results are provided to validate the effectiveness of the theoretical result.

Decentralized adaptive quantized feedback tracking of a class of uncertain interconnected lower-triangular nonlinear systems

A decentralized adaptive quantized feedback tracking problem is addressed for uncertain interconnected nonlinear systems in a strict-feedback form. All local state variables for each subsystem are quantized by a hysteresis quantizer. Different from the existing results in the literature, the primary contribution of this study is to establish an adaptive control design and stability analysis strategy using the local quantized state variables in the decentralized tracking field. A novel recursive design approach is presented to deal with unmatched interconnections and nonlinearities in the quantized feedback control framework, without any restrictions on virtual control laws. The total closed-loop stability is analyzed by deriving some technical lemmas on the boundedness of quantization error signals.

Adaptive Fuzzy Control for Stochastic High-Order Nonlinear Systems With Output Constraints

This article investigates the adaptive fuzzy control design for p-norm stochastic high-order lower triangular nonlinear systems with output constraints and unknown nonlinearities. First of all, a tan-type barrier Lyapunov function (BLF) is constructed to deal with the output constraint issue. Subsequently, an adaptive fuzzy control algorithm is developed by combining the constructed BLF with adding a power integrator technique. Simultaneously, the Lyapunov analysis shows that the designed controller can guarantee the boundness of all the variables in the closed-loop system in probability without violating the given output constraint. Finally, some comparative simulation results are provided to demonstrate the effectiveness of the proposed method.