Composite adaptive fuzzy H∞ tracking control of uncertain nonlinear systems

Adaptive Learning Control of Switched Strict-Feedback Nonlinear Systems With Dead Zone Using NN and DOB

This article investigates the adaptive learning control for a class of switched strict-feedback nonlinear systems with external disturbances and input dead zone. To handle unknown nonlinearity and compound disturbances, a collaborative estimation learning strategy based on neural approximation and disturbance observation is proposed, and the adaptive neural switched control scheme is studied in a dynamic surface control framework. In the adaptive learning control design, to obtain the evaluation information of uncertain learning, the prediction error is constructed based on the composite learning scheme. Then, the prediction error and the compensated tracking error are applied to construct the adaptive laws of switched neural weights and switched disturbance observers. The system stability analysis is carried out through the Lyapunov approach, where the switching signal with average dwell time is considered. Through the simulation test, the effectiveness of the proposed adaptive learning controller is verified.

Robust Intelligent Control of SISO Nonlinear Systems Using Switching Mechanism

In this article, a robust adaptive learning control strategy for uncertain single-input-single-output systems in strict-feedback form and controllability canonical form (CCF) is studied. For the strict-feedback system, the dynamic surface control is introduced while for the controllability canonical system, sliding-mode control is further constructed. The finite-time design is introduced for fast convergence. Under the switching mechanism, the intelligent design and the robust technique work together to obtain robust tracking performance. Once the states run out of the domain of intelligent control, the robust item will pull the states back while inside the neural working domain, the composite learning is developed to achieve higher approximation precision by building the prediction error for the weight update. The closed-loop system stability is analyzed via the Lyapunov approach. Especially for the CCF, the finite-time convergence is achieved while the system signals are globally uniformly ultimately bounded. Simulation studies on the general nonlinear systems and the flight dynamics show that the new design scheme obtains better tracking performance with higher precision and stronger robustness.

Composite Learning Adaptive Dynamic Surface Control of Fractional-Order Nonlinear Systems

Adaptive dynamic surface control (ADSC) is effective for solving the complexity problem in adaptive backstepping control of integer-order nonlinear systems. This article focuses on the ADSC design for parametric uncertain fractional-order nonlinear systems (FONSs). In each backstepping step, the virtual controller is driven to pass through a fractional dynamic surface whose fractional-order derivative can be calculated easily. An ADSC law that ensure tracking error convergence is designed. The proposed ADSC requires a stringent condition called persistent excitation (PE) to achieve parameter convergence. To relax this limitation, a prediction error is defined by using online recorded data and instantaneous data, and a composite learning law is proposed to utilize both the prediction error and the tracking error. Then, a composite learning ADSC (CLADSC) method is developed to guarantee tracking error convergence and accurate parameter estimation under an interval excitation condition that is weaker than the PE one. Finally, an illustrative example is presented to show the performance of our methods.

Barrier Lyapunov Function Based Learning Control of Hypersonic Flight Vehicle With AOA Constraint and Actuator Faults

This paper investigates a fault-tolerant control of the hypersonic flight vehicle using back-stepping and composite learning. With consideration of angle of attack (AOA) constraint caused by scramjet, the control laws are designed based on barrier Lyapunov function. To deal with the unknown actuator faults, a robust adaptive allocation law is proposed to provide the compensation. Meanwhile, to obtain good system uncertainty approximation, the composite learning is proposed for the update of neural weights by constructing the serial-parallel estimation model to obtain the prediction error which can dynamically indicate how the intelligent approximation is working. Simulation results show that the controller obtains good system tracking performance in the presence of AOA constraint and actuator faults.

Composite Intelligent Learning Control of Strict-Feedback Systems With Disturbance

This paper addresses the dynamic surface control of uncertain nonlinear systems on the basis of composite intelligent learning and disturbance observer in presence of unknown system nonlinearity and time-varying disturbance. The serial-parallel estimation model with intelligent approximation and disturbance estimation is built to obtain the prediction error and in this way the composite law for weights updating is constructed. The nonlinear disturbance observer is developed using intelligent approximation information while the disturbance estimation is guaranteed to converge to a bounded compact set. The highlight is that different from previous work directly toward asymptotic stability, the transparency of the intelligent approximation and disturbance estimation is included in the control scheme. The uniformly ultimate boundedness stability is analyzed via Lyapunov method. Through simulation verification, the composite intelligent learning with disturbance observer can efficiently estimate the effect caused by system nonlinearity and disturbance while the proposed approach obtains better performance with higher accuracy.

Composite learning from adaptive backstepping neural network control

In existing neural network (NN) learning control methods, the trajectory of NN inputs must be recurrent to satisfy a stringent condition termed persistent excitation (PE) so that NN parameter convergence is obtainable. This paper focuses on command-filtered backstepping adaptive control for a class of strict-feedback nonlinear systems with functional uncertainties, where an NN composite learning technique is proposed to guarantee convergence of NN weights to their ideal values without the PE condition. In the NN composite learning, spatially localized NN approximation is employed to handle functional uncertainties, online historical data together with instantaneous data are exploited to generate prediction errors, and both tracking errors and prediction errors are employed to update NN weights. The influence of NN approximation errors on the control performance is also clearly shown. The distinctive feature of the proposed NN composite learning is that NN parameter convergence is guaranteed without the requirement of the trajectory of NN inputs being recurrent. Illustrative results have verified effectiveness and superiority of the proposed method compared with existing NN learning control methods.

Biomimetic Hybrid Feedback Feedforward Neural-Network Learning Control

This brief presents a biomimetic hybrid feedback feedforward neural-network learning control (NNLC) strategy inspired by the human motor learning control mechanism for a class of uncertain nonlinear systems. The control structure includes a proportional-derivative controller acting as a feedback servo machine and a radial-basis-function (RBF) NN acting as a feedforward predictive machine. Under the sufficient constraints on control parameters, the closed-loop system achieves semiglobal practical exponential stability, such that an accurate NN approximation is guaranteed in a local region along recurrent reference trajectories. Compared with the existing NNLC methods, the novelties of the proposed method include: 1) the implementation of an adaptive NN control to guarantee plant states being recurrent is not needed, since recurrent reference signals rather than plant states are utilized as NN inputs, which greatly simplifies the analysis and synthesis of the NNLC and 2) the domain of NN approximation can be determined a priori by the given reference signals, which leads to an easy construction of the RBF-NNs. Simulation results have verified the effectiveness of this approach.

Wavelet neural network-based H∞trajectory tracking for robot manipulators using fast terminal sliding mode control

This paper focuses on fast terminal sliding mode control (FTSMC) of robot manipulators using wavelet neural networks (WNN) with guaranteed H∞tracking performance. The FTSMC for trajectory tracking is employed to drive the tracking error of the system to converge to an equilibrium point in finite time. The tracking error arrives at the sliding surface in finite time and then converges to zero in finite time along the sliding surface. To deal with the case of uncertain and unknown robot dynamics, a WNN is proposed to fully compensate the robot dynamics. The online tuning algorithms for the WNN parameters are derived using Lyapunov approach. To attenuate the effect of approximation errors to a prescribed level, H∞tracking performance is proposed. It is shown that the proposed WNN is able to learn the system dynamics with guaranteed H∞tracking performance and finite time convergence for trajectory tracking. Finally, the simulation results are performed on a 3D-Microbot manipulator to show the effectiveness of the controller.

Peaking-Free Output-Feedback Adaptive Neural Control Under a Nonseparation Principle

High-gain observers have been extensively applied to construct output-feedback adaptive neural control (ANC) for a class of feedback linearizable uncertain nonlinear systems under a nonlinear separation principle. Yet due to static-gain and linear properties, high-gain observers are usually subject to peaking responses and noise sensitivity. Existing adaptive neural network (NN) observers cannot effectively relax the limitations of high-gain observers. This paper presents an output-feedback indirect ANC strategy under a nonseparation principle, where a hybrid estimation scheme that integrates an adaptive NN observer with state variable filters is proposed to estimate plant states. By applying a single Lyapunov function candidate to the entire system, it is proved that the closed-loop system achieves practical asymptotic stability under a relatively low observer gain dominated by controller parameters. Our approach can completely avoid peaking responses without control saturation while keeping favourable noise rejection ability. Simulation results have shown effectiveness and superiority of this approach.

Composite Adaptive Fuzzy Output Feedback Control Design for Uncertain Nonlinear Strict-Feedback Systems With Input Saturation

In this paper, a composite adaptive fuzzy output-feedback control approach is proposed for a class of single-input and single-output strict-feedback nonlinear systems with unmeasured states and input saturation. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. By utilizing the designed fuzzy state observer, a serial-parallel estimation model is established. Based on adaptive backstepping dynamic surface control technique and utilizing the prediction error between the system states observer model and the serial-parallel estimation model, a new fuzzy controller with the composite parameters adaptive laws are developed. It is proved that all the signals of the closed-loop system are bounded and the system output can follow the given bounded reference signal. A numerical example and simulation comparisons with previous control methods are provided to show the effectiveness of the proposed approach.

Global neural dynamic surface tracking control of strict-feedback systems with application to hypersonic flight vehicle

This paper studies both indirect and direct global neural control of strict-feedback systems in the presence of unknown dynamics, using the dynamic surface control (DSC) technique in a novel manner. A new switching mechanism is designed to combine an adaptive neural controller in the neural approximation domain, together with the robust controller that pulls the transient states back into the neural approximation domain from the outside. In comparison with the conventional control techniques, which could only achieve semiglobally uniformly ultimately bounded stability, the proposed control scheme guarantees all the signals in the closed-loop system are globally uniformly ultimately bounded, such that the conventional constraints on initial conditions of the neural control system can be relaxed. The simulation studies of hypersonic flight vehicle (HFV) are performed to demonstrate the effectiveness of the proposed global neural DSC design.

Global asymptotic stabilization using adaptive fuzzy PD control

It is well-known that standard adaptive fuzzy control (AFC) can only guarantee uniformly ultimately bounded stability due to inherent fuzzy approximation errors (FAEs). This paper proves that standard AFC with proportional-derivative (PD) control can guarantee global asymptotic stabilization even in the presence of FAEs for a class of uncertain affine nonlinear systems. Variable-gain PD control is designed to globally stabilize the plant. An optimal FAE is shown to be bounded by the norm of the plant state vector multiplied by a globally invertible and nondecreasing function, which provides a pivotal property for stability analysis. Without discontinuous control compensation, the closed-loop system achieves global and partially asymptotic stability in the sense that all plant states converge to zero. Compared with previous adaptive approximation-based global/asymptotic stabilization approaches, the major advantage of our approach is that global stability and asymptotic stabilization are achieved concurrently by a much simpler control law. Illustrative examples have further verified the theoretical results.

Output feedback adaptive fuzzy control of uncertain MIMO nonlinear systems with unknown input nonlinearities

An adaptive fuzzy output feedback controller is proposed for a class of uncertain MIMO nonlinear systems with unknown input nonlinearities. The input nonlinearities can be backlash-like hysteresis or dead-zone. Besides, the gains of unknown input nonlinearities are unknown nonlinear functions. Based on universal approximation theorem, the unknown nonlinear functions are approximated by fuzzy systems. The proposed method does not need the availability of the states and an observer based on strictly positive real (SPR) theory is designed to estimate the states. An adaptive robust structure is used to cope with fuzzy approximation error and external disturbances. The semi-global asymptotic stability of the closed-loop system is guaranteed via Lyapunov approach. The applicability of the proposed method is also shown via simulations.

Composite neural dynamic surface control of a class of uncertain nonlinear systems in strict-feedback form

This paper studies the composite adaptive tracking control for a class of uncertain nonlinear systems in strict-feedback form. Dynamic surface control technique is incorporated into radial-basis-function neural networks (NNs)-based control framework to eliminate the problem of explosion of complexity. To avoid the analytic computation, the command filter is employed to produce the command signals and their derivatives. Different from directly toward the asymptotic tracking, the accuracy of the identified neural models is taken into consideration. The prediction error between system state and serial-parallel estimation model is combined with compensated tracking error to construct the composite laws for NN weights updating. The uniformly ultimate boundedness stability is established using Lyapunov method. Simulation results are presented to demonstrate that the proposed method achieves smoother parameter adaption, better accuracy, and improved performance.

Adaptive neural PD control with semiglobal asymptotic stabilization guarantee

This paper proves that adaptive neural plus proportional-derivative (PD) control can lead to semiglobal asymptotic stabilization rather than uniform ultimate boundedness for a class of uncertain affine nonlinear systems. An integral Lyapunov function-based ideal control law is introduced to avoid the control singularity problem. A variable-gain PD control term without the knowledge of plant bounds is presented to semiglobally stabilize the closed-loop system. Based on a linearly parameterized raised-cosine radial basis function neural network, a key property of optimal approximation is exploited to facilitate stability analysis. It is proved that the closed-loop system achieves semiglobal asymptotic stability by the appropriate choice of control parameters. Compared with previous adaptive approximation-based semiglobal or asymptotic stabilization approaches, our approach not only significantly simplifies control design, but also relaxes constraint conditions on the plant. Two illustrative examples have been provided to verify the theoretical results.

H∞ output tracking control of discrete-time nonlinear systems via standard neural network models

This brief proposes an output tracking control for a class of discrete-time nonlinear systems with disturbances. A standard neural network model is used to represent discrete-time nonlinear systems whose nonlinearity satisfies the sector conditions. H∞ control performance for the closed-loop system including the standard neural network model, the reference model, and state feedback controller is analyzed using Lyapunov-Krasovskii stability theorem and linear matrix inequality (LMI) approach. The H∞ controller, of which the parameters are obtained by solving LMIs, guarantees that the output of the closed-loop system closely tracks the output of a given reference model well, and reduces the influence of disturbances on the tracking error. Three numerical examples are provided to show the effectiveness of the proposed H∞ output tracking design approach.