Systems In Pure-feedback Form Research Articles

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.

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.

A novel nussbaum functions based adaptive event-triggered asymptotic tracking control of stochastic nonlinear systems with strong interconnections

In this work, the issue of event-triggered-based asymptotic tracking adaptive control of stochastic nonlinear systems in pure-feedback form with strong interconnections is considered. First, a new decentralized control scheme is developed by introducing the new types of Nussbaum functions, which enables the output of each subsystem to asymptotically track the desired reference signal. Second, the nonaffine structures and the unknown control gains existing in the nonlinear systems are a part of the considered system model, which makes it more complicated to design the decentralized controllers. Therefore, the complexity caused by the nonaffine structures is faciliated by mean value theorem and the unknown control gains are handled by a novel Nussbaum function in our proposed design scheme. Meanwhile, the unknown nonlinearities of the system are approximated by using intelligent control technology. Furthermore, an event-triggered method is introduced in the design process to save communication resources effectively. It is shown 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 effectivity of the presented scheme.

Finite-Time Adaptive Fuzzy Control for Unmodeled Dynamical Systems with Actuator Faults

This article concentrates upon the issue of finite-time tracking control for a category of nonlinear systems in pure-feedback form with actuator faults and unmodeled dynamics, where the loss of effectiveness and bias fault are considered. Meanwhile, the function approximation method utilizing fuzzy logic systems and dynamic surface control approach with first-order filter are implemented to model the unknown nonlinear terms induced from the proposed controller procedure and tackle the “explosion of complexity” issue of the classic backstepping method. The use of the maximal norm of the weight vector estimation method and adaptive approach reduces the computation load induced by fuzzy logic systems. Within the framework of backstepping control, a finite-time adaptive fuzzy fault-tolerant control protocol is derived to guarantee the boundedness of all signals and tracking error of the controlled system within a finite-time. Simulation studies are offered to show the validity of the derived theoretical results of the finite-time control protocol.

Dynamic Event-Triggered Communication-Based Adaptive Consensus Tracking of Uncertain Nonlinear Multiagent Systems in Pure-Feedback Form

This study is aimed at investigating a dynamic event-triggered communication-based adaptive distributed consensus control problem for a class of uncertain pure-feedback nonlinear multiagent systems with limited communication resources. The nonaffine nonlinear functions of multiagent systems are assumed to be unknown and heterogeneous, and intermittent inter-agent communication is considered to occur within a directed network. A novel adaptive distributed dynamic surface control strategy using neural networks is developed to manage non-differentiable virtual control laws associated with the intermittent communication between agents with uncertain nonaffine nonlinear parts. The key contribution of this research is the derivation of dynamic event-triggering conditions using distributed tracking errors to efficiently adjust inter-event times, while ensuring the consensus tracking performance and robustness against unexpected external disturbances. Compared with the existing static event-triggered communication approach, the proposed controller can alleviate the communication burden among agents. Using technical lemmas, it is shown that all signals of the considered system are semiglobally uniformly ultimately bounded, and Zeno behavior is strictly excluded. Comparative simulation results illustrate the effectiveness of the proposed dynamic event-triggered control approach.

Neural learning control for discrete-time nonlinear systems in pure-feedback form

Neural learning control for discrete-time nonlinear systems in pure-feedback form

Adaptive event-triggered tracking using nonlinear disturbance observer of arbitrarily switched uncertain nonlinear systems in pure-feedback form

An adaptive nonlinear disturbance observer (NDO) strategy is proposed for event-triggered tracking of switched uncertain pure-feedback nonlinear systems with mismatched external disturbances and arbitrary switching. Contrary to existing control results using NDOs for switched nonlinear systems, the main contribution of this study is the development of a common NDO-based event-triggered tracker with a triggering law to handle arbitrarily switched unknown nonaffine nonlinearities. Using the common Lyapunov function approach, a recursive NDO-based tracker design methodology is investigated to guarantee that all the closed-loop signals are uniformly ultimately bounded, and Zeno behavior is excluded in the resulting event-triggering mechanism. In each recursive step, the same adaptive estimate terms in the control laws and the NDO are derived via the function approximation technique to compensate for mismatched and switched unknown nonaffine nonlinearities. Finally, simulation examples are considered to verify the effectiveness of the proposed control technique.

Dynamic Extension for Adaptive Backstepping Control of Uncertain Pure-Feedback Systems

Abstract An adaptive backstepping algorithm is developed for a class of uncertain systems in pure-feedback form. The control is based on a dynamic state feedback that allows to compensate for parametric uncertainties which enter linearly into the system. As possible in the nominal case, a dynamic extension of just order one is required, in addition to the dynamics of the identifiers for the adaptation. The regularity of the control law only requires standard assumptions.

Neural Network-Based Adaptive Control for Pure-Feedback Stochastic Nonlinear Systems With Time-Varying Delays and Dead-Zone Input

For a class of stochastic nonlinear systems in pure-feedback form with dead-zone input and multiple time-varying delays, a novel neural network (NN)-based adaptive control approach is presented in this paper through the use of backstepping approach and dynamic surface technique. By choosing proper Lyapunov-Krasovskii functionals, utilizing the characteristic of hyperbolic tangent functions and adopting the function separation technique, difficulties of controller design that introduced by the time-varying delays can be dealt with properly. Moreover, all unknown nonlinear functions are lumped together and approximated by the NN. Additionally, any information over the boundedness of dead-zone parameters is not needed in the process of controller design. The control scheme proposed in this paper ensures the boundedness in probability of all signals in the closed-loop system, besides, excellent performance of arbitrarily small tracking error will be achieved by selecting control parameters appropriately. At last, two numerical simulation examples are provided to verify the validity of the designed algorithm.

Adaptive Fuzzy Fast Finite-Time Tracking Control for Nonlinear Systems in Pure-Feedback Form with Unknown Disturbance

In this paper, based on the fast finite-time stability theorem, an adaptive fuzzy control problem is considered for a class of nonlinear systems in pure-feedback form with unknown disturbance. In the controller design process, the mean value theorem is applied to address the nonaffine structure of the pure-feedback plant, the universal approximation capability of the fuzzy logic system (FLS) is utilized to compensate the unknown uncertainties, and the adaptive backstepping technique is used to design the controller model. Combined with the selection of the appropriate Lyapunov function at each step, a fuzzy-based adaptive tracking control scheme is proposed, which ensures that all signals in the closed-loop system are bounded and tracking error converges to a small neighborhood of the origin in fast finite-time. Finally, simulation results illustrate the validity of the proposed approach.

High Order Sliding Mode Backstepping Control for a Class of Unknown Pure Feedback Nonlinear Systems

This paper aims at addressing the problem of finite time exact tracking control for a class of unknown nonlinear systems in pure feedback form while guaranteeing the closed-loop stability. The uncertain nonlinear system considered in this paper is not only in completely non-affine form but also explicitly dependent on the time and therefore, can cover a general class of nonlinear systems. By incorporating high order sliding mode controller into backstepping design procedure, a new robust control scheme with novel integrators is proposed, which is able to steer the tracking error to zero. Moreover, the closed loop stability can be proved with the help of the constructed integrators in every design step. Two simulation examples are presented to illustrate the correctness and effectiveness of the proposed control scheme.

Observer-based adaptive neural control for switched stochastic pure-feedback systems with input saturation

The purpose of this paper is to investigate the problem of adaptive neural network (NN) output-feedback tracking control for input saturated switched stochastic nonlinear systems in pure-feedback form with unmeasured states. In order to facilitate the controller design process, a dead zone-based model of saturation is implemented and radial basis function NNs (RBFNNs) are employed to approximate unknown nonlinear functions and to construct an NN switched nonlinear observer to cope with difficulties raised by the presence of immeasurable state variables. Based on the adaptive backstepping technique and Lyapunov function method, an adaptive NN output feedback control scheme is developed. Furthermore, it is proved that the proposed controller can provide that, under arbitrary deterministic switching, all signals in the closed-loop system are semiglobally uniformly ultimately bounded in probability and the tracking error converges to a small neighborhood of the origin. Finally, simulation examples are presented to validate the effectiveness of the proposed adaptive NN control approach.

A novel alleviating fuzzy control algorithm for a class of nonlinear stochastic systems in pure-feedback form

In this paper, a novel alleviating computation adaptive fuzzy control scheme is presented for a class of uncertain stochastic nonlinear pure-feedback systems. Different from the existing results that are based on traditional back-stepping schemes as well as approximation technique of fuzzy logic systems (FLSs) for stochastic nonlinear systems, this new approach assumes that the norm of optimal approximation parameter vector of FLSs is bounded by unknown parameter. At each design step of this new approach, fewer bounded adaptive parameters need to be adjusted. Thus, this new approach can alleviate the online computation burden and improve the robust control performance. Meanwhile, combining Lyapunov theorem analysis, it is proven that all the signals in the closed-loop system are uniformly ultimately bounded (UUB) and the tracking error can converge to a small neighborhood of zero. The good performance of this approach is well demonstrated in a simulation example.

Decentralized finite-time neural control for time-varying state constrained nonlinear interconnected systems in pure-feedback form

This paper focuses on the problem of decentralized adaptive neural network finite-time control for pure-feedback nonlinear interconnected systems with input quantization and time-varying state constraints. Neural networks are used to model the unknown functions. To prevent the violation of state constraints, the time-varying barrier Lyapunov functions are employed in each step of the controller design. Meanwhile, combining with adaptive backstepping control technique, a decentralized adaptive neural network finite-time control strategy is raised. It is testified that the proposed control scheme can effectively ensure that all the closed-loop signals are semi-global practical finite-time stable via Lyapunov stability analysis and that the tracking errors converge to small bounded sets around the origin in finite time. Finally, some simulation results are used to verify the effectiveness of the proposed approach.

Asymptotic Tracking Control for a Class of Pure-Feedback Nonlinear Systems

This paper studies the adaptive asymptotic tracking problem for a class of unknown nonlinear systems in pure-feedback form. Different from the traditional literatures which only tackle the bounded tracking problem for pure-feedback systems, this paper investigates the asymptotic tracking problem by developing a novel controller design method. Moreover, the differentiable assumption on nonaffine functions is canceled, and only a mild semi-bounded assumption is required as the controllability condition. By utilizing Lyapunov theorem, it is proved that all the variables of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and the output tracking error can converge to zero asymptotically by choosing design parameters appropriately. Finally, a simulation result is presented to verify the effectiveness of the proposed control scheme.

Adaptive fuzzy dynamic surface control for uncertain nonlinear systems in pure-feedback form with input and state constraints using noisy measurements

ABSTRACTThis paper is concerned with the design of an adaptive fuzzy dynamic surface control for uncertain nonlinear pure-feedback systems with input and state constraints using a set of noisy measurements. The design approach is described as follows. The nonlinear uncertainties are approximated by using the fuzzy logic systems at the first stage, secondly the adaptive fuzzy dynamic surface control is introduced to remove the problem of the explosion of complexity for the derivation of the adaptive fuzzy backstepping control, thirdly a new saturation function for state constraints is proposed to design the controllers based on the Lyapunov function, fourthly the number of the adjustable parameters is reduced by using the simplified extended single input rule modules, and finally the weighted least squares estimator to take the estimates for the un-measurable states and the adjustable parameters is in a simplified structure designed. The proposed approach provides effective system performance in the simulation experiment.

Distributed Containment Control for Multi-agent Systems in Pure-feedback Form under Switching Topologies

The distributed containment control problem is investigated for nonlinear multi-agent systems in pure-feedback form subjected to switching directed communication topologies. Based on command filtered back-stepping technology and singular-perturbation theorem, a containment controller is addressed to guarantee that the followers’ outputs can converge to the convex hull spanned by multi-dynamic leaders, and the containment tracking errors between leaders and followers is semi-global practical exponential stable in the closed-loop system. A nonlinear anti-tangent filter is adopted to estimate the virtual control, avoiding the analytical deduction inherent in traditional back-stepping method and overcoming the ?circular construction problem? in non-affine pure-feedback systems. Differing from the existing back-stepping method, the proposed control scheme only requires leaders’ output signals and their first derivative signals, does not need the prior knowledge of their nth order derivative signals. The stability analysis is completed via the singular perturbation theory, revealing some novel features of the underlying back-stepping method. Finally, two simulation examples are provided to illustrate the effectiveness of the control scheme.

Distributed consensus tracking of a class of asynchronously switched nonlinear multi-agent systems

This paper addresses the distributed consensus tracking problem for a class of switched nonlinear multi-agent systems in pure-feedback form under directed communication networks. For a practical environment, switched non-affine nonlinearities for followers are unknown and their switching signals are assumed to be arbitrary and asynchronous. Compared with existing results in the literature, the main contribution of this paper is to provide a universal control strategy to deal with asynchronously switched nonlinear multi-agent systems in the consensus tracking field. By using the function approximation technique, an approximation-based novel recursive design approach for asynchronously switched followers is presented to design local common adaptive controllers without requiring the knowledge on the signs of control gain functions and on the leader’s velocity. From the common Lyapunov function method, it is shown that the consensus tracking errors are asymptotically bounded and converge to a neighborhood of the origin. A simulation example is included to demonstrate the effectiveness of the proposed methodology.

Adaptive practical finite-time stabilization for switched nonlinear systems in pure-feedback form

This paper investigates adaptive practical finite-time stabilization for a class of switched nonlinear systems in pure-feedback form. Under some appropriate assumptions, a controller and adaptive laws are designed by using adding a power integrator technique, and neural networks are employed to approximate unknown nonlinear functions. It is proved that all states of the closed-loop system converge to a small neighborhood of the origin in finite time. Finally, two simulations are provided to show the feasibility and validity of the proposed control scheme.

Adaptive fuzzy dynamic surface control for uncertain discrete-time nonlinear systems in pure-feedback form using a set of noisy measurements

This paper is concerned with the design of an adaptive fuzzy dynamic surface control for multi-input multi-output uncertain discrete-time nonlinear systems in pure-feedback form. The states of the systems are observed with independent measurement noises. The design approach of the proposed adaptive fuzzy dynamic surface control is described as follows. By applying the theory of the adaptive fuzzy dynamic surface control, the problem of the explosion of complexity due to the repeated differentials of nonlinear functions is removed so that the controller is simplified in a structure at the first stage; second, the number of the adjustable parameters is reduced by using the simplified extended single-input rule modules; and, finally, the simplified weighted least squares estimator is designed to take the estimates for the unmeasurable states and the adjustable parameters. The simulation experiment for a simple numerical system provides the effectiveness of the proposed approach.