Unknown Nonlinear Terms Research Articles

Adaptive fuzzy backstepping control of flexible marine riser with uncertain parameters and input saturation constraint

To suppress the vibration of a flexible riser system with input saturation and uncertain parameters under the influence of unknown external disturbances, an adaptive fuzzy backstepping boundary control algorithm was designed. First, the backstepping method and Lyapunov function are used to analyze the subsystem and design the virtual control law. On this basis, the adaptive fuzzy system was designed to approximate the unknown nonlinear term in the design process, and the smooth hyperbolic tangent function and the auxiliary system based on Nussbaum function were introduced to limit control input. The stability and uniform boundedness of the closed-loop control system are proved by the Lyapunov stability theory without simplifying or discretizing the infinite dimensional dynamic model. Finally, the effectiveness of the proposed control algorithm is verified by comparing the control effect with proportional–integral–derivative control and the previous adaptive backstepping control by MATLAB simulation. The simulation results show that the proposed control algorithm can overcome the uncertainty of system parameters and effectively suppress the riser vibration under input constraints, and its control effect is better than proportional–integral–derivative control and adaptive backstepping control.

Composite learning sliding mode control of uncertain nonlinear systems with prescribed performance

This paper explores the prescribed performance tracking control problem of nonlinear systems with triangular structure. To obtain the desired transient performance and precise estimations of uncertain terms, the techniques of neural network control, sliding mode control and composite learning control are incorporated into the proposed control method. The presented control strategy can ensure the tracking error converges to a prescribed small residual set. Compared with the persistent excitation condition required in the conventional adaptive control, the interval excitation condition needed in the proposed control approach is weak, which guarantees that the radial basis function neural networks approximate the unknown nonlinear terms more accurately. Finally, two simulation examples are exploited to manifest the effectiveness of the proposed approach.

Path following Control of an Underactuated Catamaran for Recovery Maneuvers

This paper focuses on the autonomous recovery maneuvers of an unknown underactuated practical catamaran, which returns to its initial position corresponding to the man overboard (MOB) by simply adjusting the rate of turn. This paper investigates the completion of model-based path following control for not only the traditional Williamson turn, but also complex recovery routes under time-varying disturbances. The main difficulty of model-based path following control for predicting the hydrodynamic derivatives of a practical catamaran was solved by the approximated calculation of a diagonal matrix. The second key problem of differential calculation for an underactuated model in the case of complex reference trajectories under severe disturbances was investigated. Even though this paper employs a diagonal matrix with unknown nonlinear terms, the experimental test using a small craft with payloads by remote control demonstrated the sway force per yaw moment in turning cases. Adaptive backstepping mechanisms with unknown parameters were proven by the Lyapunov theory as well as the passive-boundedness of the sway dynamics, guaranteeing the stability of sway motion in the case of unavailable sway control. The effectiveness of the algorithms of the guiding concept and error dynamics is demonstrated by the numerical simulations.

Discrete‐time extended state observer‐based model‐free adaptive sliding mode control with prescribed performance

AbstractTo tackle the trajectory tracking problem and achieve high control accuracy in many actual nonlinear systems with unknown disturbance, a novel discrete‐time extended state observer‐ (DESO) based model‐free adaptive sliding mode control strategy with prescribed tracking performance is studied, which only relies on the input/output data of the system rather than explicit model information. Firstly, a compact‐form dynamic linearization method is used to reconstruct the discrete‐time nonlinear process, where the time‐varying parameter linearly connected with the control input is obtained by an adaptive method and the unknown nonlinear term is estimated by a DESO. Then, by considering the prescribed performance and using an unconstrained vector transformed from the constrained tracking error, one model‐free sliding mode controller is designed. In addition, a rigorous stability analysis is presented to show the boundedness of the sliding mode function and the prescribed transient‐state and steady‐state performance of the output tracking error. Finally, the simulations with comparing results verify the effectiveness and superiority of the developed control scheme.

Adaptive Fuzzy Observer-Based Fault Estimation for a Class of Nonlinear Stochastic Hybrid Systems

This article studies the fault estimation problem for a class of continuous-time nonlinear Markovian jump systems with unmeasured states, unknown bounded sensor faults, and unknown nonlinearities simultaneously. In this article, a new adaptive fuzzy observer design scheme is developed, where the completely unknown nonlinear terms are approximated by adaptive fuzzy logic systems. By means of a novel online adaptive mechanism, the asymptotic stability of the error dynamic system is guaranteed despite of sensor faults and unknown nonlinear terms. Moreover, the sliding surface switching problem in the traditional sliding mode observer techniques can be avoided for Markovian jump systems. Finally, two practical examples are given to demonstrate the effectiveness of the proposed approach.

Finite-time tracking control for nonstrict-feedback nonlinear systems with unknown time delays and input saturation

In this article, the problem of adaptive finite-time control is studied for a category of nonstrict-feedback nonlinear time-delay systems with input saturation and full state constraints. The fuzzy logic systems are applied to model the unknown nonlinear terms in the systems. Then, a novel tan-type barrier Lyapunov function is adopted to overcome the problem of full state constraints. By utilizing the finite-time control theory and the backstepping technique, a finite-time fuzzy adaptive controller is designed. The controller can guarantee that the tracking error is adjusted around zero with a small neighborhood in a finite time and all the signals in the closed-loop system are bounded. Finally, two simulation examples are included to verify the validity and feasibility of the control scheme.

Design of an adaptive controller to capture maximum power from a variable speed wind turbine system without any prior knowledge of system parameters

Even though some wind turbine manufacturers are no longer active, and are not willing to disclose their intellectual property, their turbines are still in operation. Since the exact values of wind turbine parameters like the aerodynamic model, drive-train model and generator parameters are not always accessible, the design of a controller which does not require prior knowledge of the system parameters can be very useful and effective. As a result, this paper proposes a disturbance observer-based controller to harvest the maximum power from a wind turbine system with fully unknown parameters. To reduce control efforts, a disturbance observer is designed to estimate unknown nonlinear terms caused by unknown model parameters in the presence of unknown control coefficient that uses only the tracking error to estimate nonlinear disturbance. Compared with previously published works, in this paper, both aerodynamic model and drive-train model parameters are assumed to be fully unknown. Closed-loop stability of the proposed controller is analyzed by the Lyapunov stability theorem. To demonstrate the performance of the proposed controller, it is compared with some existing controllers. Comparative simulation results show its effectiveness. Furthermore, although the proposed controller does not require system parameters and includes fewer tuning parameters, it shows the same tracking performance as the other three controllers. The numerical comparative results are listed in a table, which shows that Mean Square Error (MSE) of the proposed controller is 75% less than minimum MSE of the other three controllers of previous works, while its control effort is 1.7% higher than the minimum control effort of the other three.

Adaptive neural network control for a class of interconnected pure-feedback time-delay nonlinear systems with full-state constraints and unknown measurement sensitivities

This paper investigates the problem of the adaptive neural network control design for full state constrained interconnected pure-feedback time-delay systems with unknown measurement sensitivity. Based on the dynamic surface design approach, constrained transform functions are used to deal with the asymmetric state constraints, which can remove the feasibility conditions. The problem of unknown measurement sensitivity is considered in interconnected systems, and the inaccurate information of states and output brings more difficulties and challenges to this design. Through transforming the nonlinearities caused by unknown measurement sensitivity into bounded nonlinear functions, radial basis function neural network can be utilized to approximate the unknown nonlinear terms. And the proposed control strategy can ensure all signals of the system are semi-globally ultimately uniformly bounded and the asymmetric state constraints are strictly maintained. Finally, simulation examples are given to show the effectiveness of the proposed method.

BLS-based adaptive fault tolerant control for a class of space unmanned systems with time-varying state constraints and input nonlinearities

In this paper, a Broad Learning System (BLS) based adaptive full state constrained controller is investigated for a class of Space Unmanned Systems (SUSs) subjected to the actuator faults and input nonlinearities. In order to guarantee the time-varying state constraints and reduce the control complexity simultaneously, two nonlinear error transformations are utilized in this work. By estimating the lower boundary of the nonlinear actuator effectiveness, the instable dynamic caused by the actuator faults and input nonlinearities can be overcome. With the aid of the universal approximation ability of the BLS, the unknown nonlinear terms existing in the SUS attitude dynamic model can be handled. Furthermore, benefiting from the nodes dynamic adjusting mechanism of BLS, the control response speed and accuracy can be improved. The simulation results are presented to demonstrate the effectiveness and advantages of the proposed BLS-based adaptive full state constrained control method.

Rejection and Attenuation of Multiple Disturbances for a Class of Uncertain Systems

A novel anti-disturbance strategy for a class of uncertain systems is investigated. Besides the unknown frequency sinusoidal, the controlled plant is subjected to bounded noise and unknown nonlinear term simultaneously. Through the construction of auxiliary observer, the sinusoidal is represented in a parametric uncertainty form. Only one unknown scalar needs estimating to construct compensation signal, meanwhile the unwanted nonlinear operation between frequency and equivalent disturbance can be removed. By integrating a feedback control law, all the unexpected dynamics can be rejected and attenuated respectively, where the conditions on the stability and optimal performance are also provided. Finally, a computer simulation example is presented to illustrate the effectiveness and the applicability of the suggested method.

A Signal Compensation-Based Robust Swing-Up and Balance Control Method for the Pendubot

This article proposes a novel robust swing-up and balance control method using data-driven compensation signals for the Pendubot system, which is underactuated and subject to dynamic friction, backlash, and modeling uncertainty. The method involves three major developments. First, the uncertainty of the system is described by a previous sampled unknown nonlinear term and its changing rate. Compensation signals are then designed to eliminate the influence of the previous sampled unknown nonlinear term and its changing rate on the outputs of the controlled plant. Second, based on the Lyapunov stability theory, a robust swing-up control method is proposed. Third, in order to eliminate the limit cycle phenomenon caused by the uncertainty near the unstable equilibrium point, a proportional-derivative balance controller based on compensation signals is proposed. The stability and tracking error analysis show that the compensation signals can effectively eliminate the influence of dynamic friction, backlash, and modeling uncertainty on the system. Experimental results verify the effectiveness of the proposed method by showing significant improvements in production rate, accuracy, and cost.

Sampled-Data Adaptive Fuzzy Control of Switched Large-Scale Nonlinear Delay Systems

A decentralized adaptive fuzzy sampled-data control problem for switched large-scale nonlinear systems with time-varying delays is considered in this article. Fuzzy logic systems are applied to handle unknown nonlinear terms. A novel fuzzy adaptive law is proposed utilizing only the information of the system states at sampling instants. Moreover, a proper CLF and a new decentralized adaptive sampled-data control law are constructed to ensure that all states of the CLS are bounded. The developed strategy’s effectiveness is verified with two examples.

Fuzzy adaptive finite-time consensus tracking control for nonlinear multi-agent systems

This paper focuses on the finite-time consensus tracking control problem of nonlinear multi-agent systems. Dynamics of each agent has completely unknown nonlinear terms that cannot be directly used for control design. Therefore, fuzzy logic systems are employed to approximate these nonlinear functions. Furthermore, a finite-time fuzzy adaptive consensus tracking protocol is proposed for a class of nonlinear multi-agent systems by using integral-type Lyapunov functions. The developed adaptive backstepping design scheme successfully avoids the singularity problem of the derivatives of virtual control signals. It is shown that with the presented control protocol, the consensus tracking errors converge to a small neighbourhood of the origin in finite time, and the other signals of multi-agent systems are bounded. Finally, a numerical example is used to verify the effectiveness of the proposed control protocol.

Distributed Adaptive Output Feedback Leader-Following Consensus Control for Nonlinear Multiagent Systems

This paper investigates the problem of the distributed adaptive output feedback leader-following consensus control for a class of high-order nonlinear multiagent systems with unknown parameters and nonlinear terms. First, the reduced order dynamic gain k-filters are built to estimate the unmeasured state variables. The bounds of the unknown parameters are estimated in order to avoid the over-estimation problem. Then, the dynamic surface control technique is used to design the distributed controller, and the computation load of the system is greatly reduced. Finally, a numerical example is shown to verify the effectiveness of the designed controller.

An adaptive fault-tolerant control scheme for a class of fractional-order systems with unknown input dead-zones

An adaptive backstepping fault-tolerant control scheme is presented for a class of fractional-order systems in the presence of unknown input dead-zones. The proposed fault-tolerant control scheme ensures all the closed-loop signals are bounded ultimately. Especially, the tracking error can be made as small as possible by choosing appropriate design parameters. Furthermore, this scheme not only works for fractional-order systems with unknown linear terms but also works for these with unknown nonlinear terms. Finally, several practical examples are simulated to verify the effectiveness of the proposed fault-tolerant control scheme.

Neural Adaptive Dynamic Surface Asymptotic Tracking Control for a Class of Uncertain Nonlinear System

In this paper, by incorporating the neural network into an adaptive dynamic surface control (DSC) framework, a neural adaptive DSC algorithm is developed for a class of uncertain nonlinear system to ensure the asymptotic output tracking. Neural network is used to approximate the unknown nonlinear term in the system such that the requirements for known nonlinear term in control laws design procedure are released. In order to eliminate the boundary layer effects, which are caused by the linear filters at each step in the DSC procedure, the nonlinear filters with the compensation term are designed skillfully. The proposed neural adaptive DSC algorithm not only avoids the inherent problem of “explosion of complexity” in the backstepping procedure, but also has its own advantages: (1) releasing the requirements for known nonlinear term in control laws design procedure; (2) holding the asymptotic output tracking performance. Some simulations are shown to demonstrate the effectiveness and advantages of the proposed controller.

Distributed Adaptive Fixed-Time Tracking Consensus Control for Multiple Uncertain Nonlinear Strict-Feedback Systems under a Directed Graph

In this brief, we study the distributed adaptive fixed-time tracking consensus control problem for multiple strict-feedback systems with uncertain nonlinearities under a directed graph topology. It is assumed that the leader’s output is time varying and has been accessed by only a small fraction of followers in a group. The distributed fixed-time tracking consensus control is proposed to design local consensus controllers in order to guarantee the consensus tracking between the followers and the leader and ensure the error convergence time is independent of the systems’ initial state. The function approximation technique using radial basis function neural networks (RBFNNs) is employed to compensate for unknown nonlinear terms induced from the controller design procedure. From the Lyapunov stability theorem and graph theory, it is shown that, by using the proposed fixed-time control strategy, all signals in the closed-loop system and the consensus tracking errors are cooperatively semiglobally uniformly bounded and the errors converge to a neighborhood of the origin within a fixed time. Finally, the effectiveness of the proposed control strategy has been proved by rigorous stability analysis and two simulation examples.

Output-feedback formation tracking control of networked nonholonomic multi-robots with connectivity preservation and collision avoidance

This paper studies the problem of adaptive output-feedback formation tracking control for networked uncertain nonholonomic mobile robots (NMRs) with different limited communication distances, while achieving connectivity preservation and collision avoidance. In robot control, equipping all the speed sensors not only increases the cost of the system but also risks losing accuracy and reliability. In this paper, it is assumed that the velocities of the nonholonomic mobile robots in this paper are unknown, they are estimated according to the output of the systems by an adaptive observer via a neural network. The designed dynamic surface based on nonlinear transformation errors can achieve the above three control objectives at the same time, avoiding the situation of using multiple potential functions to solve such problems, which will lead to conflicts in the selection of the design parameters. Compared with the existing references about formation tracking to maintain connectivity and avoid collisions, the main contribution of this paper is to design an observer of robot speed estimation and use only a neural network to estimate the unknown nonlinear term of the system itself. The unknown nonlinearity produced in the process of controller design does not need an additional neural network. Furthermore, the effectiveness of the proposed strategy is verified by simulation examples.

Event-triggered adaptive fuzzy tracking control for stochastic nonlinear systems

In this paper, the problem of event-triggered mechanism based adaptive fuzzy tracking control is studied for strict-feedback stochastic nonlinear systems. The fuzzy logic systems are introduced to approximate the unknown nonlinear terms. A novel event-triggered tracking controller is designed by incorporating the backstepping design approach with the method of fuzzy control. The newly designed controller not only ensures that the output signal tracks the given reference signal within a sufficiently small neighborhood of the origin, but also ensures that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded in the sense of the four-moment. Meanwhile, an event-triggered control mechanism is introduced to reduce the communication burden from the controller to the actuator. Finally, simulation results demonstrate the effectiveness of the designed controller.

Fuzzy Adaptive Containment Control for Nonlinear Nonaffine Pure-Feedback Multiagent Systems

This article addresses the containment control problem of multiagent systems under directed topologies, where the model of each agent is an unknown nonlinear nonaffine pure-feedback dynamic, and at the same time, the outputs and their derivatives of the leaders are unknown. To avoid the complex design process with the recursive methods (i.e., backstepping and dynamic surface), each unknown higher order nonlinear dynamic is transformed into a simple high-order integral model with unknown affine nonlinear terms in the last-order dynamic at first. Then, the fuzzy logic systems and the fuzzy state observers are constructed to approximate the unknown affine nonlinear terms and the unknown transformed states. Finally, a novel fully distributed fuzzy adaptive containment control law is generated according to the state observers and the supervised control. The stability of the closed-loop system is analyzed in the Lyapunov sense and the containment errors converge to a small neighborhood of the origin. Simulation results show the feasibility and effectiveness of the proposed scheme.