Neural network based adaptive tracking control for a class of pure feedback nonlinear systems with input saturation

In this paper, an adaptive neural network (NN) tracking controller is developed for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with input saturation. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions in the MIMO system. A novel auxiliary system is developed to compensate the effects induced by input saturation (in both magnitude and rate) during tracking control. Endowed with a switching structure that integrates two existing representative auxiliary system designs, this novel auxiliary system improves control performance by preserving their advantages. It provides a comprehensive design structure in which parameters can be adjusted to meet the required control performance. The auxiliary system signal is utilized in both the control law and the neural network weight-update laws. The performance of the resultant closed-loop system is analyzed, and the bound of the transient error is established. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive neural network control.

In this work, considering the influence of input saturation and time-varying output constraints, an adaptive neural networks force/position control method is proposed for a class of uncertain robotic manipulators in contact with the external environment. Radial basis function neural networks are introduced to approximate the system uncertainty and only one parameter needs to be updated online. The output constraints are satisfied by converting the constrained system to an unconstrained one. Moreover, an auxiliary dynamic system is applied in the transformed unconstrained system to handle the input saturation nonlinearity and the Moore–Penrose pseudo-inverse term is introduced for controller design. All signals in the closed-loop system are proved to be bounded by using the Lyapunov method. To show the good performance of the given scheme, comparative simulation is conducted on a two-joint manipulator, which is controlled by the proposed adaptive neural networks force/position tracking controller and a conventional force/position controller without considering input saturation and output constraints. Simulation results show that the adaptive neural network force/position controller has better control performance than the traditional method.

In this work, an adaptive neural network (NN) optimized output-feedback control problem is studied for a class of stochastic nonlinear systems with unknown nonlinear dynamics, input saturation, and state constraints. A nonlinear state observer is designed to estimate the unmeasured states, and the NNs are used to approximate the unknown nonlinear functions. Under the framework of the backstepping technique, the virtual and actual optimal controllers are developed by employing the actor-critic architecture. Meanwhile, the tan-type Barrier optimal performance index functions are developed to prevent the nonlinear systems from the state constraints, and all the states are confined within the preselected compact sets all the time. It is worth mentioning that the proposed optimized control is clearly simple since the reinforcement learning (RL) algorithm is derived based on the negative gradient of a simple positive function. Furthermore, the proposed optimal control strategy ensures that all the signals in the closed-loop system are bounded. Finally, a practical simulation example is carried out to further illustrate the effectiveness of the proposed optimal control method.

This paper focuses on the problem of adaptive neural network (NN) tracking control for a class of pure-feedback stochastic nonlinear systems. Via the dynamic surface control (DSC) technique and neural networks' approximation capability, a novel adaptive NN control scheme is proposed. Without using the mean value theorem, an affine variable at each step is constructed. By introducing the additional first-order low-pass filter for the actual control input, the algebraic loop problem in pure-feedback stochastic nonlinear systems is solved. It is proved that the proposed controller ensures that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) in probability while the tracking error converges to a small neighborhood of the origin. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.

This article studies the tracking control of a class of nonlinear systems with input saturation, subject to nonaffine faults and unknown control direction. A fault-tolerant command filtered control (CFC) method based on adaptive neural networks (NNs) is proposed for this kind of nonlinear system. First, the combination of CFC and error compensation overcomes the "explosion of complexity" issue and alleviates the impact of filter errors. Then, a set of radial basis function NNs is constructed to approximate the unknown nonlinear items containing the nonaffine fault function. Additionally, the issue of unknown control direction in the system is effectively resolved by using Nussbaum gain technology. It is proven that the designed controller can ensure that all signals in the closed-loop system are bounded and convergent, and the upper bound of the absolute value of system tracking error is given. Finally, three comparative simulation results are illustrated to show the effectiveness of the proposed method.

International audience

An adaptive neural network (NN) event-triggered control scheme is proposed for nonlinear nonstrict-feedback multiagent systems (MASs) against input saturation, unknown disturbance, and sensor faults. Mean-value theorem and Nussbaum-type function are invoked to transform the structure of the input saturation and overcome the difficulty of unknown control directions, respectively. On the basis of the universal approximation property of NNs, a nonlinear disturbance observer is designed to estimate the unknown compounded disturbance composed of external disturbance and the residual term of input saturation. According to the measurement error defined by control signal, an event-triggered mechanism is developed to save network transmission resource and reduce the number of controller update. Then, an adaptive NN compensation control approach is proposed to tackle the problem of sensor faults via the dynamic surface control (DSC) technique. It is proved that all signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, simulation results demonstrate the effectiveness of the presented control strategy.

Data-based adaptive neural network optimal output feedback control for nonlinear systems with actuator saturation

In this paper, an adaptive neural network (NN) output feedback control is investigated for incommensurate fractional-order permanent magnet synchronous motors under the condition of input saturation. First, a NN state observer is presented to obtain the ‘virtual estimate’ of angle speed, where the unknown function is approximated by the NN. Then, in order to solve the input saturation problem, an auxiliary system is developed under fractional-order framework. Next, the command filtered technology with an error compensation mechanism is used to handle the ‘explosion of complexity’ in backstepping and remove the filtering errors. In addition, the frequency distributed model is utilized such that the Lyapunov theory is available in the backstepping design and the system stability is demonstrated. Finally, numerical simulations confirm the availability of the proposed design.

Alterations in thermal hydraulic parameters directly affect the safety of reactors. Accurately predicting the trends of key thermal hydraulic parameters under various working conditions can greatly improve reactor safety, thereby effectively preventing the occurrence of nuclear power plant accidents. The thermal hydraulic characteristic parameters in the reactor are affected by many factors, in order to preliminarily study whose forecasting methods and determine the feasibility of neural network forecasting, the China Experimental Fast Reactor (CEFR) is selected as the research target in this study, and the maximum surface temperature of fuel rod sheath and mass flow rate are used as predictive variables. After data samples are generated through the reactor sub channel analysis code (named SUBCHANFLOW), two widely used adaptive neural networks are used to perform the thermal hydraulic parameter forecast analysis of CEFR fuel assembly under steady-state conditions. The 1/2 core model of CEFR is used to perform a single-step predictive analysis of thermal hydraulic parameters under transient conditions. The results show that the adaptive radial basis function (RBF) neural network exhibits a better fitting ability and higher forecasting accuracy than that of the adaptive back propagation neural network, and the maximum error under steady-state conditions is 0.5%. Under transient conditions, poor forecasting accuracy is observed for some local points; however, the adaptive RBF neural network is generally excellent at predicting temperature and mass flow. The mean relative error of temperature does not exceed 1%, and the mean relative error of flow does not exceed 6.5%. The proposed RBF neural network model can provide real-time forecasting in a short time under unstable flow conditions, and its forecasting results have a certain reference value.

The Sixth International Symposium on Neural Networks (ISNN 2009)

The H∞ tracking control problem is investigated for a class of incommensurate fractional order strict feedback nonlinear systems with unknown nonlinear functions and external disturbances in this paper. The adaptive neural network H∞ tracking controller of the system is designed by combining backstepping technique, adaptive neural network technique with H∞ control theory and utilizing the frequency distributed model to construct Lyapunov functions. The H∞ tracking controller proposed in this paper can guarantee that the tracking error and all the signals in the closed-loop system are bounded, and the system has an H∞ performance for external disturbances. Finally, the simulation results verify the feasibility and effectiveness of the proposed control method.

An adaptive output feedback formation control strategy based on high gain observer has been developed to solve the problem of underactuated surface vessels formation control with uncertain dynamics, ocean environment disturbance and input saturation. In this strategy, a high gain observer that only depends on position information is used to estimate the unmeasurable velocity, and in order to solve the ‘complex explosion problem’ in the conventional backstepping control algorithm, a first-order low-pass filter is adopted to obtain the derivative of the virtual control signal. In addition, adaptive neural networks (NNs) and minimum learning parameters (MLPs) algorithm are used to approximate environmental disturbances and uncertain dynamics, while reducing online update parameters. Stability analysis proved that all signals in closed-loop are uniformly ultimately bounded and the formation tracking errors are arbitrarily small. Simulation results demonstrate the effectiveness of the controller.

Observer-based adaptive prescribed performance tracking control for nonlinear systems with unknown control direction and input saturation

The stability of a hybrid AC-DC microgrid depends mainly upon the bidirectional interlinking converter (BIC), which is responsible for power transfer, power balance, voltage solidity, frequency and transients sanity. The varying generation from renewable resources, fluctuating loads, and bidirectional power flow from the utility grid, charging station, super-capacitor, and batteries produce various stability issues on hybrid microgrids, like net active-reactive power flow on the AC-bus, frequency oscillations, total harmonic distortion (THD), and voltage variations. Therefore, the control of BIC between AC and DC buses in grid-connected hybrid microgrid power systems is of great importance for the quality/smooth operation of power flow, power sharing and stability of the whole power system. In literature, various control schemes are suggested, like conventional droop control, communication-based control, model predictive control, etc., each addressing different stability issues of hybrid AC-DC microgrids. However, model dependence, single-point-failure (SPF), communication vulnerability, complex computations, and complicated multilayer structures motivated the authors to develop online adaptive neural network (NN) Q-learning-based full recurrent adaptive neurofuzzy nonlinear control paradigms for BIC in a grid-connected hybrid AC-DC microgrid. The proposed strategies successfully ensure the following: (i) frequency stabilization, (ii) THD reduction, (iii) voltage normalization and (iv) negligible net active-reactive power flow on the AC-bus. Three novel adaptive NN Q-learning-based full recurrent adaptive neurofuzzy nonlinear control paradigms are proposed for PQ-control of BIC in a grid-connected hybrid AC-DC microgrid. The control schemes are based on NN Q-learning and full recurrent adaptive neurofuzzy identifiers. Hybrid adaptive full recurrent Legendre wavelet-based Neural Network Q-learning-based full recurrent adaptive NeuroFuzzy control, Hybrid adaptive full recurrent Mexican hat wavelet-based Neural Network Q-learning-based full recurrent adaptive NeuroFuzzy control, and Hybrid adaptive full recurrent Morlet wavelet-based Neural Network Q-learning-based full recurrent adaptive NeuroFuzzy control are modeled and tested for the control of BIC. The controllers differ from each other, based on variants used in the antecedent part (Gaussian membership function and B-Spline membership function), and consequent part (Legendre wavelet, Mexican hat wavelet, and Morlet wavelet) of the full recurrent adaptive neurofuzzy identifiers. The performance of the proposed control schemes was validated for various quality and stability parameters, using a simulation testbench in MATLAB/Simulink. The simulation results were bench-marked against an aPID controller, and each proposed control scheme, for a simulation time of a complete solar day.