Unknown Nonlinearities Research Articles

Fuzzy Adaptive Control for Vehicular Platoons With Constraints and Unknown Dead-Zone Input

In this paper, an adaptive fuzzy control problem is studied for a connected automated vehicles platoon subject to unknown dead-zone input and constraints. To better handle the unknown nonlinear dynamical functions and disturbances, the nonlinear dynamics model is transformed to a new model. Then, the fuzzy logic system (FLS) is used to identify the unknown nonlinear functions. A dead-zone inverse technique is introduced to eliminate the negative effects of the unknown dead-zone input nonlinearity. In the framework of backstepping, the tangent barrier Lyapunov function (BLF) is introduced in this paper, and a distributed adaptive fuzzy control scheme is designed so that the position, velocity and acceleration of the vehicle platoon do not violate the given constrained boundaries. Finally, based on the Lyapunov stability theory, it is noted that all signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood of the origin. The effectiveness of the proposed approach is validated by simulation results.

Predefined-Time Bounded Consensus of Multiagent Systems With Unknown Nonlinearity via Distributed Adaptive Fuzzy Control.

This article investigates uniformly predefined-time bounded consensus of leader-following multiagent systems (MASs) with unknown system nonlinearity and external disturbance via distributed adaptive fuzzy control. First, uniformly predefined-time-bounded stability is analyzed and a sufficient condition is derived for the system to achieve semiglobally (globally) uniformly predefined-time-bounded consensus. Therein, the settling time is independent of initial conditions and can be defined in advance. Then, for first-order MASs, distributed adaptive fuzzy controllers are designed by combining neighboring consensus errors to drive all following agents to globally track the leader's state within predefined time. For second-order MASs, by formulating filtered errors, the consensus errors between following agents and the leader are shown to be bounded if the filtered errors are bounded. Furthermore, with the distributed controllers designed based on filtered errors, second-order MASs achieve semiglobally uniformly predefined-time-bounded leader-following consensus. Finally, two numerical examples are simulated, including: 1) a first-order leader-following MAS and 2) a second-order Lagrangian system consisting of single-link manipulators, to demonstrate the performance of the proposed controllers.

Distributed Finite-Time Consensus Tracking Control for Nonlinear Multi-Agent Systems With FDI Attacks and Application to Single-Link Robots

This brief considers the distributed finite-time consensus tracking control problem for nonlinear multi-agent systems with false data injection (FDI) attacks. Firstly, since instability is inevitable when false datas are injected into the researched system, a security control algorithm combining the modified coordinate transformation and the dynamic surface control (DSC) method is developed to eliminate the negative impact of FDI attacks and reduce the burden caused by iterative computations of virtual controls. Besides, there are unknown nonlinearities in the dynamics of each agent, which can not be directly handled by the traditional control design. Thus, the neural-network-based approximation technique is introduced to compensate the unknown nonlinearities. In summary, a novel controller is constructed for each agent, which guarantees the consensus of the outputs of all agents can be achieved and that all the signals of the studied system are bounded within a finite-time period. To prove the correctness of the designed security control algorithm, a simulation example of the multi-agent system composed of multiple single-link robots is presented.

FTC Design for Switched Fractional-Order Nonlinear Systems: An Application in a Permanent Magnet Synchronous Motor System.

In this article, an adaptive fault-tolerant control (FTC) method and a fractional-order dynamic surface control (DSC) algorithm are jointly proposed to deal with the stabilization problem for a class of multiple-input-multiple-output (MIMO) switched fractional-order nonlinear systems with actuator faults and arbitrary switching. In each MIMO subsystem and each switched subsystem, the neural networks (NNs) are utilized to identify the complicated unknown nonlinearities. A fractional filter DSC technology is adopted to conquer the issue of "explosion of complexity," which may occur when some functions are repeatedly derived. The common Lyapunov function method is used to restrain arbitrary switching problems in the system, and the actuator compensation technique is introduced to tackle the failure faults and bias faults in the actuators. By combining the backstepping DSC design technique and fractional-order stability theory, a novel NN adaptive switching FTC algorithm is proposed. Under the operation of the proposed algorithm, the stability and control performance of the fractional-order systems can be guaranteed. Finally, a simulation example of a permanent magnet synchronous motor (PMSM) system reveals the feasibility and effectiveness of the developed scheme.

Fixed‐time event‐triggered consensus tracking control for uncertain nonlinear multiagent systems with dead‐zone constraint

AbstractThis research investigates the fixed‐time event‐triggered consensus tracking control for a class of uncertain nonlinear multiagent systems (MASs) under directed graphs. In MASs, frequent and continuous communication is difficult to achieve because the network bandwidth of the system is limited. In addition, unknown nonlinearities and dead‐zone input may exacerbate the communication burden of the system. It is challenging to guarantee the fixed‐time stability of the system when it suffers from these constraints. To overcome the above problems, based on the radial basis neural networks and backstepping technology, an event‐triggered mechanism is designed to reduce the frequency of control input updates and compensate for the dead‐zone input. On this basis, a novel consensus tracking control protocol is established based on the practically fixed‐time stability theorem. Technically, by using the protocol, the system is practically fixed‐time stable, even under the effect of those aforementioned constraints. Finally, some simulation examples validate the validity of the proposed protocol.

Neuroadaptive tracking control for uncertain pure‐feedback systems under dynamic constraints

AbstractThis paper presents a neuroadaptive tracking control method for a class of pure‐feedback nonlinear systems in the presence of dynamic constraints and unmodeled dynamics simultaneously. By introducing a nonlinear mapping (NM), the tracking control problem for constrained pure‐feedback system is recast into a regulation problem of the converted system without constraints. Such transformation allows the states to be confined within given regions directly, this is in contrast to the commonly used Barrier Lyapunov Function method that relies on the upper bound of the virtual control errors. To handle the unmodeled dynamics in the system, a dynamic compensation signal is introduced. It is shown that in the proposed scheme the neural networks (NN) not only act as a universal approximator to deal with unknown nonlinearity, but also function as a decoupler to cope with the coupling effects between state and the new variable arising from the introduction of the NM and the backstepping design. Simulation results also confirm the effectiveness of the proposed method.

Adaptive neural backstepping control of nonlinear fractional-order systems with input quantization

This article addresses the tracking control problem of uncertain fractional-order nonlinear systems in the presence of input quantization and external disturbance. An adaptive backstepping scheme is proposed by combining with radial basis function (RBF) neural networks (NNs), fractional-order disturbance observer (FODO), and backstepping method. The RBF NNs are used to approximate the unknown nonlinearities of fractional-order systems. The FODO is designed to compensate for disturbance and uncertain parameters. The hysteresis quantizer is used to avoid chattering that possibly appears in actual application. The stability of the proposed controller is proved by fractional-order Lyapunov method. In addition, all the signals in the closed-loop system are bounded. The effectiveness of the proposed method is confirmed by the simulation results.

Adaptive fuzzy finite-time tracking control of nonlinear systems with unmodeled dynamics

This paper considers an adaptive fuzzy finite-time tracking control issue for uncertain nonlinear systems in the presence of unmodeled dynamics via the backstepping technique. In the design procedure, the traditional dynamic signal structure is improved firstly such that it is suitable for the controller design within finite-time interval universally for the controlled systems and it can be utilized to dominate the unmodeled dynamics. The dynamic disturbances are compensated by nonlinear damping terms. The fuzzy logic systems (FLSs) are used to package the unknown nonlinearities. By constructing the appropriate Lyapunov functions in recursive step and employing the finite-time stability theorem, the developed FLS-based adaptive tracking control strategy within finite-time interval, which ensures the boundedness of all the closed-loop signals and the convergence of tracking error. In the end, simulation results are provided to test the availability of the developed strategy.

Adaptive neural network sliding mode control for reliable stabilization of uncertain Takagi–Sugeno fuzzy systems regulated by switching rules

The problem of adaptive sliding mode control for a class of continuous-time Takagi–Sugeno fuzzy systems regulated by the event of switching rules relying on neural network estimation method is put forward in this paper, where the plant suffers from state delay, internal structure uncertainty, and unknown nonlinearity. By proposing a switching surface in integral type, it obtains a sliding motion with desired property. In addition, to compensate the plant unknown nonlinearity and to meet the reaching condition, a radial basis function neural-network-based adaptive law is designed to ensure the existence of sliding motion in finite time. Furthermore, for the purpose of exponential stabilization of the sliding motion, a linear matrix inequality condition accompanied with switching signal characterized by an average dwell time is put forward. Finally, two numerical examples, one with all subsystems unstable and the other with stable subsystems and unstable systems, are shown to confirm the validity.

Nash Equilibrium Seeking for High-Order Multiagent Systems With Unknown Dynamics

In this article, we consider a Nash equilibrium seeking problem for a class of high-order multiagent systems with unknown dynamics. Different from existing results for single integrators, we aim to steer the outputs of this class of uncertain high-order agents to the Nash equilibrium of some noncooperative game in a distributed manner. To overcome the difficulties brought by the high-order structure, unknown nonlinearities, and the regulation requirement, we first introduce a virtual player for each agent and solve an auxiliary noncooperative game for them. Then, we develop a distributed adaptive protocol by embedding this auxiliary game dynamics into some proper tracking controller for the original agent to resolve this problem. We also discuss the parameter convergence issue under certain persistence of excitation conditions. The efficacy of our algorithms is verified by numerical examples.

Event-Triggered Output-Feedback Stabilization With Prescribed Convergence Rate

This article addresses event-triggered output-feedback stabilization with a prescribed convergence rate for uncertain nonlinear systems. Typically, the systems allow completely unknown nonlinearities, from which no any information is available for feedback. Nevertheless, an enhanced stabilization objective is pursued in this article to guarantee not only convergence, but particularly prescribed convergence rate. To this end, a distinct event-triggered output-feedback scheme is developed by integrating a powerful compensation technique with the event-triggering mechanism. Specifically, a set of delicate gains, motivated by the funnel control method, are introduced not only to handle the completely unknown nonlinearities and the execution error, but also to guarantee a prescribed rate. Particularly, a new event-triggering mechanism is given, where the threshold and suspension time are online adjusted with respect to the gains. As such, the threshold and suspension time could become adequately small as the gains increase, ensuring timely execution for the effectiveness of the compensation technique. It turns out that the designed event-triggered output-feedback controller guarantees the system states to globally converge to zero with the prescribed convergence rate.

Fast Finite-Time Tracking Consensus With Applications on Multiple Servo Motors

This article focuses on the fast finite-time tracking consensus for uncertain nonlinear multiagent systems. By gracefully combining the hierarchical decomposition, adding a barrier power integrator and disturbance compensation techniques, a new adaptive fast finite-time controller is proposed. Compared with the existing works, the proposed method has several distinguishing features: 1) It can achieve fast finite-time convergence with full state constraints; 2) it can deal with some fully unknown nonlinearities and state-dependent disturbance. Moreover, the nonlinearities can be related with the states of all the followers; 3) the input of the leader is not required to be zero, meaning a broad class of references signals can be generated; and 4) the controller is computationally simply and ready to be implemented. No fuzzy logic/neural networks are needed. Applications of the proposed method on multiple servo motors are also studied.

Emerging robust and data‐driven control methods for uncertain learning systems

Emerging robust and data‐driven control methods for uncertain learning systems

Adaptive fuzzy fixed‐time control for non‐triangular structural stochastic switching nonlinear systems

AbstractIn this article, the problem of adaptive fixed‐time tracking control is addressed for non‐triangular structural stochastic switching nonlinear systems. Fuzzy logic systems are used to compensate for unknown nonlinearities, and in the meantime, to avoid the algebraic loop problem, which exists in traditional backstepping controller design processes for non‐triangular structural nonlinear systems. The unknown control gain problem is addressed by the construction of proper Lyapunov function candidates. By employing Lyapunov stability theorem, all the closed‐loop signals can be ensured to be semi‐globally practical fixed‐time stable, the output signal can track the desired signal, and the tracking error can converge to a small zone around the origin. The effectiveness of the developed control approach is verified through simulation results.

Fixed-Time Fuzzy Adaptive Tracking Control for High-Order Systems with Unknown Nonlinearities and Control Directions

Fixed-Time Fuzzy Adaptive Tracking Control for High-Order Systems with Unknown Nonlinearities and Control Directions

A fixed-time distributed extended state observer for uncertain second-order nonlinear system

This paper investigates the fixed-time distributed estimation problem for a class of second-order nonlinear systems with uncertain input, unknown nonlinearity and matched perturbation. A fixed-time distributed extended state observer (FxTDESO) consisting of a group of local observer nodes under directed communication topology is proposed, and each node can reconstruct both the full state and unknown dynamics of the system. To achieve fixed-time stability, a Lyapunov function is elaborated, and based on this, sufficient conditions for the existence of the FxTDESO are established. Under time-invariant and time-varying disturbance, the observation errors can converge to the origin and a small region of the origin within a fixed time, respectively, where the upper bound of the settling time (UBST) is irrelevant to the initial conditions. Compared to the existing fixed-time distributed observers, the proposed observer can reconstruct both the unknown states and uncertain dynamics, and only the output of the leader and 1-dimensional output estimates from the neighboring nodes are needed in the observer design which effectively reduces the communication load. The paper also extends previous finite-time distributed extended state observer to the case of time-variant disturbance and eliminates the complex linear matrix equation assumption that guarantees the finite-time stability. Furthermore, the FxTDESO design for a class of high-order nonlinear systems is also discussed. Finally, simulation examples are conducted to demonstrate the effectiveness of the proposed observer.

Fuzzy L1 adaptive controller for chaos synchronization of uncertain fractional-order chaotic systems with input nonlinearities

This research work proposes a fuzzy fractional-order [Formula: see text] adaptive controller to deal with projective chaos synchronization problems for a general class of uncertain fractional-order chaotic systems subject to unknown input nonlinearities (dead-zone and sector nonlinearities). The suggested control architecture includes a fractional-order sliding surface, a fuzzy system, and an [Formula: see text] adaptive controller. The latter consists of a predictor, a control law, and its adaptive mechanism. The fuzzy system takes the role of an online estimator for system nonlinear uncertain functions which helps in the handling of the input nonlinearities. A designed low-pass filter is placed within the input channel of the [Formula: see text] adaptive controller to ensure that the control loop is decoupled from the estimation loop, which preserves response robustness along with improving transient performances. Finally, the closed-loop stability is rigorously proved, and the acquired results are demonstrated by two simulation examples as well as a comparative study.

Adaptive output feedback asymptotic tracking for uncertain nonlinear systems with dead-zone input

In this paper, the adaptive output feedback asymptotic tracking problem is investigated for nonlinear systems with dead-zone input and unknown nonlinearities, where only system output is available. First, an observer is constructed to estimate unavailable states. Then, by the observer and barrier Lyapunov function, an adaptive output feedback controller is designed, which compensates the influence of dead-zone input and unknown nonlinearities. Furthermore, based on the proposed controller and tuning function, the global boundedness of all signals in closed-loop system is achieved, and the tracking error can asymptotically converge to zero. Particularly, it should be noted that there is no need to calculate the derivatives of virtual control laws in controller design, thus reducing the computational complexity. Finally, two numerical examples are taken to verify the effectiveness of the designed controller.

Composite Observer-Based Optimal Attitude-Tracking Control With Reinforcement Learning for Hypersonic Vehicles.

This article proposes an observer-based reinforcement learning (RL) control approach to address the optimal attitude-tracking problem and application for hypersonic vehicles in the reentry phase. Due to the unknown uncertainty and nonlinearity caused by parameter perturbation and external disturbance, accurate model information of hypersonic vehicles in the reentry phase is generally unavailable. For this reason, a novel synchronous estimation is proposed to construct a composite observer for hypersonic vehicles, which consists of a neural-network (NN)-based Luenberger-type observer and a synchronous disturbance observer. This solves the identification problem of nonlinear dynamics in the reference control and realizes the estimation of the system state when unknown nonlinear dynamics and unknown disturbance exist at the same time. By synthesizing the information from the composite observer, an RL tracking controller is developed to solve the optimal attitude-tracking control problem. To improve the convergence performance of critic network weights, concurrent learning is employed to replace the traditional persistent excitation condition with a historical experience replay manner. In addition, this article proves that the weight estimation error is bounded when the learning rate satisfies the given sufficient condition. Finally, the numerical simulation demonstrates the effectiveness and superiority of the proposed approaches to attitude-tracking control systems for hypersonic vehicles.

Consensus Tracking for High-Order Uncertain Nonlinear MASs via Adaptive Backstepping Approach.

In this article, we focus on the problems of consensus control for nonlinear uncertain multiagent systems (MASs) with both unknown state delays and unknown external disturbances. First, a nonlinear function approximator is proposed for the system uncertainties deriving from unknown nonlinearity for each agent according to adaptive radial basis function neural networks (RBFNNs). By taking advantage of the Lyapunov-Krasovskii functionals (LKFs) approach, we develop a compensation control strategy to eliminate the effects of state delays. Considering the combination of adaptive RBFNNs, LKFs, and backstepping techniques, an adaptive output-feedback approach is raised to construct consensus tracking control protocols and adaptive laws. Then, the proposed consensus tracking scheme can steer the nonlinear MAS synchronizing to the predefined reference signal on account of the Lyapunov stability theory and inequality properties. Finally, simulation results are carried out to verify the validity of the presented theoretical approach.