Pure-feedback Nonlinear Systems Research Articles

Neural network prescribed-time observer-based output-feedback control for uncertain pure-feedback nonlinear systems

To prevent the complicated backstepping design, as well as the coupled design of state observer/disturbance approximator and baseline controller that makes the parameter synthesis difficult, this article proposes a neural network (NN) prescribed-time observer-based output-feedback control approach for uncertain pure-feedback nonlinear systems. After reformulating the original system into a canonical form with matched lumped disturbance, an adaptive NN prescribed-time observer (NNPTO) is developed to quickly provide accurate estimates of unknown states and disturbance. Then the observer is integrated with designed non-backstepping state-feedback controller to construct an output-feedback control scheme. Three features distinguish our approach from existing non-backstepping methods: (1) the accurate estimation is realized in a finite time prescribed through a single parameter; (2) the design of the state observer/disturbance approximator and baseline controller is decoupled, which eases the synthesis process and makes lots of existing non-backstepping state-feedback controllers compatible with our output-feedback control approach; (3) The NNPTO has trivial oscillation and small observation peaking errors under large disturbance, which effectively improves the output tracking performance. Numerical examples and an application example of a rigid single-link manipulator system are presented to demonstrate the effectiveness and practicability of our approach.

An adaptive dynamic surface control strategy for suppressing pathological oscillations in a neural mass model

Pathological oscillations that have a frequency in the [Formula: see text] band are widely recognized to be involved in Parkinson’s disease. Now, we present an adaptive dynamic surface control strategy for suppressing pathological oscillations that exist in the Parkinsonian state. First, the interactions between the subthalamic nucleus and external globus pallidus are fully considered and establish a neural mass model of Parkinson’s disease. Next, by reasonable state transformation, suppressing pathological oscillations can be converted into a tracking control study of a pure-feedback nonlinear system. Moreover, the dynamic surface control technique adopted reduces the dimensionality of the neural network input and effectively eliminates the complexity explosion problem commonly associated with existing methods. By Lyapunov stability analysis, it can be obtained that all the signals of the resulting closed-loop system are bounded, and the tracking error converges to a small neighborhood of zero. Finally, the simulation results demonstrate the effectiveness of the designed control strategy. This work may provide an effective approach to closed-loop deep brain stimulation optimization for the alleviation of the Parkinsonian state.

Predefined-time adaptive fuzzy control of pure-feedback nonlinear systems under input and output quantization

Predefined-time adaptive fuzzy control of pure-feedback nonlinear systems under input and output quantization

Finite-time event-triggered output-feedback adaptive decentralized echo-state network fault-tolerant control for interconnected pure-feedback nonlinear systems with input saturation and external disturbances: A fuzzy control-error approach

In this paper, we introduce a decentralized Event-Triggered fault-tolerant echo-state network (ESN) direct adaptive controller for uncertain interconnected nonlinear systems in pure-feedback form. The proposed controller addresses input saturation, actuator faults, external disturbances, and unavailable states for measurement. Unlike the existing works in the literature that adapts the ESN weights using the tracking error, our method employs the control error that is estimated using a fuzzy inference system, to derive the adaptation laws. The complexity explosion typically seen with recursive back-stepping and Dynamic Surface Control (DSC) designs is completely avoided. Our control scheme addresses four types of state-dependent actuator faults: bias, drift, loss of accuracy, as well as loss of effectiveness. The ESNs approximate unknown ideal control laws, while robust terms are added to enhance the stability of the closed-loop system. Stability analysis ensures that tracking errors converge, in finite time, to a small compact set near the origin due to the strictly positive real (SPR) property. Simulation results of a quadrotor UAV and a mathematical system are presented. A comparative analysis is performed with another approach to emphasize the effectiveness of the proposed method.

Adaptive Barrier-Lyapunov-Functions Based Control Scheme of Nonlinear Pure-Feedback Systems with Full State Constraints and Asymptotic Tracking Performance

Adaptive Barrier-Lyapunov-Functions Based Control Scheme of Nonlinear Pure-Feedback Systems with Full State Constraints and Asymptotic Tracking Performance

Adaptive Projection and Fuzzy Tracking Design for Unknown Control Coefficients and References.

This article addresses the tracking control problem of nonlinear pure-feedback systems, where the control coefficients and the dynamics of the references are unknown. Fuzzy-logic systems (FLSs) are used to approximate the unknown control coefficients and at the same time the adaptive projection law is designed to allow each fuzzy approximation to cross zero, which yields that the proposed method avoids the assumption of using Nussbaum function, that is, the unknown control coefficients never cross zeros. Another adaptive law is designed to estimate the unknown reference and then it is intergraded into the saturated tracking control law to achieve the uniformly ultimately bounded (UUB) performance of the resulting closed-loop system. Simulations show the feasibility and effectiveness of the proposed scheme.

Backstepping-based adaptive fuzzy tracking control for pure-feedback nonlinear multi-agent systems

This work developed an adaptive fuzzy tracking control strategy for pure-feedback nonlinear multi-agent systems via backstepping. The relevant unknown functions are addressed by fuzzy logic systems (FLSs), which take into account entirely unknown nonlinearities. The non-affine pure-feedback form is dealt with a Butterworth low-pass filter (BLF), and the converted systems can be used to construct a controller. The implementation of the first-order sliding-mode differentiator overcomes the difficulty of calculation explosion. The backstepping method is applied to design the virtual controller step by step, and the actual controller is designed successfully. Furthermore, through Lyapunov stability theory, the stability of systems is ensured, and that the tracking error is kept to a minimum. Finally, the simulation result shows the validity of the designed control strategy.

Non-overshooting control of nonlinear pure-feedback systems

In this paper, the non-overshooting tracking control problem of nonlinear pure-feedback systems is studied. From the model, nonlinear pure-feedback systems are more general than nonlinear strict-feedback systems. In this way, the nonlinear pure-feedback system can express the physical system that the strict-feedback system cannot. Therefore, it is more meaningful to study the nonlinear pure-feedback system. At present, there are few reports on non-overshooting control of nonlinear systems. These documents are mainly aimed at nonlinear strict-feedback systems, and the obtained non-overshooting conditions are also conservative. Then, this paper aims at nonlinear pure-feedback systems, and obtains its non-overshooting conditions from another aspect. The specific narrative is as follows: the closed-loop system is structured by designing the auxiliary controller, and then the expressions of tracking error are derived. By analyzing these expressions, the conditions of non-overshooting tracking control of pure-feedback systems are obtained. Finally, the simulation results of three examples verify the effectiveness of this algorithm.

Finite-time adaptive prescribed performance DSC for pure feedback nonlinear systems with input quantization and unmodeled dynamics

<abstract><p>This paper presents a new prescribed performance-based finite-time adaptive tracking control scheme for a class of pure-feedback nonlinear systems with input quantization and dynamical uncertainties. To process the input signal, a new quantizer combining the advantages of a hysteresis quantizer and uniform quantizer has been used. Radial basis function neural networks have been utilized to approximate unknown nonlinear smooth functions. An auxiliary system has been employed to estimate unmodeled dynamics by producing a dynamic signal. By introducing a hyperbolic tangent function and performance function, the tracking error was made to fall within the prescribed time-varying constraints. Using modified dynamic surface control (DSC) technology and a finite-time control method, a novel finite-time controller has been designed, and the singularity problem of differentiating each virtual control scheme in the existing finite-time control scheme has been removed. Theoretical analysis shows that all signals in the closed-loop system are semi-globally practically finite-time stable, and that the tracking error converges to a prescribed time-varying region. Simulation results for two numerical examples have been provided to illustrate the validity of the proposed control method.</p></abstract>

Adaptive fault-tolerant tracking control for MIMO nonlinear systems with time-varying full state constraints

In this article, an adaptive fault-tolerant tracking control algorithm is developed for the multi-input-multi-output (MIMO) pure-feedback nonlinear systems with full state constraints. The state constraints are time-varying, hence greatly improve the applicability of the result but significantly increase the difficulties and complexities of control system design. To overcome the feasibility conditions in barrier Lyapunov function for handling time-varying constraints, a novel nonlinear mapping method for MIMO nonlinear systems is developed. Adaptive techniques and Neural Networks (NNs) are applied to estimate unknown uncertainties and disturbances, which the tracking control accuracy is improved. It is proved that the designed control algorithm can not only achieve the control objectives but also guarantee the boundedness of all signals. Finally, the effectiveness of the developed control algorithm is demonstrated via a simulation example.

Predefined-Time Output-Feedback Leader-Following Consensus of Pure-Feedback Multiagent Systems.

This article delves into the predefined-time output-feedback leader-following consensus problem of uncertain pure-feedback nonlinear multiagent systems for the first time. To streamline subsequent design, the original systems in pure-feedback form are first transformed into canonical systems. Following this, a distributed predefined-time extended state observer (ESO) and a local predefined-time ESO are developed to reconstruct the unknown states/lumped disturbance of the transformed leader system and follower systems, respectively. Based on the estimated states and utilizing a bounded regulation function, two nonsingular and nonconservative predefined-time control laws are formulated to achieve consensus tracking. The proposed method showcases the following advantages: 1) the actual convergence time rather than the upper bound of the convergence time (UBCT) of the tracking errors can be explicitly specified a priori regardless of the initial conditions in a bounded region, optimizing control energy usage and 2) the system overshoot could be effectively reduced by selecting appropriate parameters for the regulation function. Finally, numerical examples are conducted to verify the obtained results.

Fuzzy prescribed-time control for uncertain nonlinear pure feedback systems

Fuzzy prescribed-time control for uncertain nonlinear pure feedback systems

Adaptive Neural Network Control with Predefined-Time Convegence for PureFeedback Nonlinear Systems

Adaptive Neural Network Control with Predefined-Time Convegence for PureFeedback Nonlinear Systems

High-Order Fully Actuated System Approaches for a Class of Pseudo Pure-Feedback Nonlinear Systems

High-Order Fully Actuated System Approaches for a Class of Pseudo Pure-Feedback Nonlinear Systems

Adaptive Fixed-Time Performance Tracking Control for Unknown Nonlinear Pure-Feedback Systems Subject to Full-State Constraints and Actuator Faults

Adaptive Fixed-Time Performance Tracking Control for Unknown Nonlinear Pure-Feedback Systems Subject to Full-State Constraints and Actuator Faults

Event-Triggered Adaptive Bipartite Asymptotic Tracking Control Using Intelligent Technique for Stochastic Nonlinear Multiagent Systems

The problem of event-triggered based adaptive bipartite asymptotic tracking control for multi-agent stochastic pure-feedback nonlinear systems over sign digraph is considered. The agents classification optimization strategy (ACOS) is presented, which transforms a structurally unbalanced multi-agent topology graph into a structurally balanced multi-agent topology graph. Furthermore, how to deal with the nonaffine structure and unknown control gains for multi-agent stochastic pure-feedback nonlinear systems is a challenging issue for designing controllers. As a result, the mean value theorem is used to transfer the nonaffine systems into the affine systems, and the Nussbaum functions are used to eliminate the influence caused by the unknown control gains. In addition, the intelligent control technique is used to approximate the unknown nonlinearities, the event-triggered control strategy following the switching thresholds is introduced to save unnecessary communication resources, and the computation burden is eliminated by means of the dynamic surface technique. It is proved that all signals of the closed-loop systems are bounded in probability and the tracking errors asymptotically converge to zero in probability. Finally, the simulation results illustrate the validity of the proposed scheme. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Impact Statement</i> —In nature, there are a lot of interesting movements of multi-agents. In this paper, the multi-agent stochastic pure-feedback nonlinear systems over sign digraph is considered. How to handle the nonaffine structure and unknown control gains for the studied systems under interest is a difficult issue. Therefore, the mean value theorem and the Nussbaum functions are used to overcome the difficulty of designing controllers. The bipartition problem with the structurally unbalanced sign digraph is another design difficulty, then we propose the ACOS in the controller design process. In addition, the controllers designed in this paper, which are constructed by applying the backstepping method, event-triggered control strategy, and dynamic surface technique, can save the unnecessary communication resources and alleviate computation burden. Finally, the simulation results illustrate the validity of the proposed scheme.

Adaptive neural identification and non-singular control of pure-feedback nonlinear systems

This paper proposes a new constructive identification and adaptive control method for nonlinear pure-feedback systems, which remedies the ’explosion of complexity’ and potential control singularity encountered in the traditional adaptive backstepping controllers. First, to avoid using the backstepping recursive design, alternative state variables and the corresponding coordinate transformation are introduced to reformulate the pure-feedback system into an equivalent canonical model. Then, a high-order sliding mode (HOSM) observer is used to reconstruct the unknown states for this canonical model. To remedy the potential singularity in the control, the unknown system dynamics are lumped to derive an alternative identification structure and one-step control synthesis, where two radial basis function neural networks (RBFNN) are adopted to online estimate these lumped dynamics. In this framework, the online estimation of control gain is not in the denominator of controller, and thus the division by zero in the controllers is avoided. Finally, a new online learning algorithm is constructed to obtain the RBFNNs’ weights, ensuring the convergence to the neighborhood of true values and allowing accurate identification of unknown dynamics. Theoretical analysis elaborates that the convergence of both the tracking error and the estimation error is obtained simultaneously. Simulations and practical experiments on a hydraulic servo test-rig verify the effectiveness and utility of the suggested methods.

Global Predefined-Time Adaptive Neural Network Control for Disturbed Pure-Feedback Nonlinear Systems With Zero Tracking Error.

This article presents a global adaptive neural-network-based control algorithm for disturbed pure-feedback nonlinear systems to achieve zero tracking error in a predefined time. Different from the traditional works that only solve the semiglobal bounded tracking problem for pure-feedback systems, this work not only achieves that the tracking error globally converges to zero but also guarantees that the convergence time can be predefined according to the user specification. In order to get the desired predefined-time controller, first, a mild semibound assumption for nonaffine functions is skillfully proposed so that the design difficulty caused by the structure of pure feedback can be easily solved. Then, we apply the property of radial basis function (RBF) neural networks (NNs) and Young's inequality to derive the upper bound of the term that contains the unknown nonlinear function and external disturbances, and the designed adaptive parameters decide the derived upper and robust control gain. Finally, the predefined-time virtual control inputs are presented whose derivatives are further estimated by utilizing finite-time differentiators. It is strictly proved that the proposed novel predefined-time controller can guarantee that the tracking error globally converges to zero within predefined time and a practical example is shown to verify the effectiveness and practicability of the proposed predefined-time control method.

Neural Networks-Based Adaptive Dynamic Surface Control for Nonlinear Pure-Feedback Systems under Prescribed Performance and Zero Tracking Error

Neural Networks-Based Adaptive Dynamic Surface Control for Nonlinear Pure-Feedback Systems under Prescribed Performance and Zero Tracking Error

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